%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HAL004+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:36:53 PM UTC 2026
% Result : Theorem 72.45s 12.29s
% Output : CNFRefutation 73.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 32
% Syntax : Number of formulae : 1676 ( 162 unt; 1 def)
% Number of atoms : 6482 (2220 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 7484 (2823 ~;4541 |; 91 &)
% ( 4 <=>; 23 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-4 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-5 aty)
% Number of variables : 3973 ( 0 sgn3939 !; 34 ?;3550 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',injection_properties) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',surjection_properties) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] :
( ( morphism(X1,X3,X4)
& morphism(X0,X2,X3)
& exact(X0,X1) )
=> ! [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',exact_properties) ).
fof(f7,axiom,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& morphism(X1,X3,X4)
& morphism(X0,X2,X3) )
=> exact(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_exact) ).
fof(f8,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5)
& commute(X0,X1,X2,X3) )
=> ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',commute_properties) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) )
& morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5) )
=> commute(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_commute) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(f11,axiom,
! [X0,X1] :
( element(X1,X0)
=> subtract(X0,X1,X1) = zero(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(f14,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_morphism) ).
fof(f15,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_morphism) ).
fof(f16,axiom,
morphism(gamma,d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gamma_morphism) ).
fof(f17,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(f18,axiom,
morphism(f,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_morphism) ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(f20,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_morphism) ).
fof(f21,axiom,
injection(alpha),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_injection) ).
fof(f22,axiom,
injection(gamma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gamma_injection) ).
fof(f23,axiom,
surjection(beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_surjection) ).
fof(f24,axiom,
surjection(delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_surjection) ).
fof(f25,axiom,
exact(alpha,beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_beta_exact) ).
fof(f26,axiom,
exact(gammma,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gamma_delta_exact) ).
fof(f27,axiom,
commute(alpha,g,f,gamma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
fof(f28,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(f29,axiom,
surjection(f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_surjection) ).
fof(f30,axiom,
surjection(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_surjection) ).
fof(f31,conjecture,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(delta,apply(g,X2)) = X1
& apply(h,apply(beta,X2)) = X1
& element(X2,b)
& apply(delta,X0) = X1
& element(X1,r) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(delta,apply(g,X2)) = X1
& apply(h,apply(beta,X2)) = X1
& element(X2,b)
& apply(delta,X0) = X1
& element(X1,r) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( ~ element(X3,X1)
| element(apply(X0,X3),X2) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ injection(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| X3 = X4 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ injection(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| X3 = X4 ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1)
& X3 != X4 )
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1)
& X3 != X4 )
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X3] :
( element(X3,X2)
& ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X3] :
( element(X3,X2)
& ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3)
| ! [X8] :
( ~ element(X8,X4)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3)
| ! [X8] :
( ~ element(X8,X4)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X8] :
( element(X8,X4)
& apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8)) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| commute(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X8] :
( element(X8,X4)
& apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8)) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| commute(X0,X1,X2,X3) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(ennf_transformation,[],[f12]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ! [X3,X4] :
( ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ! [X3,X4] :
( ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
? [X0] :
( element(X0,e)
& ! [X1,X2] :
( apply(delta,apply(g,X2)) != X1
| apply(h,apply(beta,X2)) != X1
| ~ element(X2,b)
| apply(delta,X0) != X1
| ~ element(X1,r) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
& element(sK1(X0,X1),X1)
& element(sK0(X0,X1),X1)
& sK0(X0,X1) != sK1(X0,X1) )
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1)),skolemize(X4,sK1(X0,X1))],[f37]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ( apply(X0,sK2(X0,X1,X3)) = X3
& element(sK2(X0,X1,X3),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X0,X1,X3))],[f39]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( element(sK3(X0,X1,X2),X2)
& ! [X4] :
( apply(X0,X4) != sK3(X0,X1,X2)
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f41]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| ( apply(X1,X5) = zero(X4)
& element(X5,X3) ) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| ( apply(X1,X5) = zero(X4)
& element(X5,X3) ) ) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| ( apply(X1,X5) = zero(X4)
& element(X5,X3) ) ) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ! [X5] :
( ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ( apply(X0,sK4(X0,X2,X5)) = X5
& element(sK4(X0,X2,X5),X2) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| ( apply(X1,X5) = zero(X4)
& element(X5,X3) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X7,sK4(X0,X2,X5))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
| ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(nnf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
| ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( ( apply(X1,X5) = zero(X4)
& element(X5,X3) )
| ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) ) )
& ( apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ( ( ( zero(X4) = apply(X1,sK5(X0,X1,X2,X3,X4))
& element(sK5(X0,X1,X2,X3,X4),X3) )
| ( sK5(X0,X1,X2,X3,X4) = apply(X0,sK6(X0,X1,X2,X3,X4))
& element(sK6(X0,X1,X2,X3,X4),X2) ) )
& ( zero(X4) != apply(X1,sK5(X0,X1,X2,X3,X4))
| ~ element(sK5(X0,X1,X2,X3,X4),X3)
| ! [X6] :
( apply(X0,X6) != sK5(X0,X1,X2,X3,X4)
| ~ element(X6,X2) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X5,sK5(X0,X1,X2,X3,X4)),skolemize(X7,sK6(X0,X1,X2,X3,X4))],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( element(sK7(X0,X1,X2,X3,X4),X4)
& apply(X1,apply(X0,sK7(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK7(X0,X1,X2,X3,X4))) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| commute(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X8,sK7(X0,X1,X2,X3,X4))],[f49]) ).
fof(f70,plain,
( element(sK8,e)
& ! [X1,X2] :
( apply(delta,apply(g,X2)) != X1
| apply(h,apply(beta,X2)) != X1
| ~ element(X2,b)
| apply(delta,sK8) != X1
| ~ element(X1,r) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f57]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ injection(X0)
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| X3 = X4 ),
inference(cnf_transformation,[],[f35]) ).
fof(f74,plain,
! [X2,X0,X1] :
( apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f75,plain,
! [X2,X0,X1] :
( element(sK1(X0,X1),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f76,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f77,plain,
! [X2,X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ~ element(X3,X2)
| apply(X0,sK2(X0,X1,X3)) = X3 ),
inference(cnf_transformation,[],[f59]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ~ element(X3,X2)
| element(sK2(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f80,plain,
! [X2,X0,X1] :
( element(sK3(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4) != sK3(X0,X1,X2)
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| apply(X0,sK4(X0,X2,X5)) = X5 ),
inference(cnf_transformation,[],[f64]) ).
fof(f83,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| apply(X1,X5) != zero(X4)
| ~ element(X5,X3)
| element(sK4(X0,X2,X5),X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| apply(X0,X6) != X5
| ~ element(X6,X2)
| apply(X1,X5) = zero(X4) ),
inference(cnf_transformation,[],[f64]) ).
fof(f86,plain,
! [X2,X3,X0,X1,X4] :
( zero(X4) = apply(X1,sK5(X0,X1,X2,X3,X4))
| sK5(X0,X1,X2,X3,X4) = apply(X0,sK6(X0,X1,X2,X3,X4))
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4] :
( element(sK5(X0,X1,X2,X3,X4),X3)
| sK5(X0,X1,X2,X3,X4) = apply(X0,sK6(X0,X1,X2,X3,X4))
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( zero(X4) = apply(X1,sK5(X0,X1,X2,X3,X4))
| element(sK6(X0,X1,X2,X3,X4),X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X4] :
( element(sK5(X0,X1,X2,X3,X4),X3)
| element(sK6(X0,X1,X2,X3,X4),X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4] :
( zero(X4) != apply(X1,sK5(X0,X1,X2,X3,X4))
| ~ element(sK5(X0,X1,X2,X3,X4),X3)
| apply(X0,X6) != sK5(X0,X1,X2,X3,X4)
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| exact(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3)
| ~ element(X8,X4)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( element(sK7(X0,X1,X2,X3,X4),X4)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| commute(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(X1,apply(X0,sK7(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK7(X0,X1,X2,X3,X4)))
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| commute(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f95,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f54]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[],[f14]) ).
fof(f99,plain,
morphism(beta,b,c),
inference(cnf_transformation,[],[f15]) ).
fof(f100,plain,
morphism(gamma,d,e),
inference(cnf_transformation,[],[f16]) ).
fof(f101,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f17]) ).
fof(f102,plain,
morphism(f,a,d),
inference(cnf_transformation,[],[f18]) ).
fof(f103,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f104,plain,
morphism(h,c,r),
inference(cnf_transformation,[],[f20]) ).
fof(f105,plain,
injection(alpha),
inference(cnf_transformation,[],[f21]) ).
fof(f106,plain,
injection(gamma),
inference(cnf_transformation,[],[f22]) ).
fof(f107,plain,
surjection(beta),
inference(cnf_transformation,[],[f23]) ).
fof(f108,plain,
surjection(delta),
inference(cnf_transformation,[],[f24]) ).
fof(f109,plain,
exact(alpha,beta),
inference(cnf_transformation,[],[f25]) ).
fof(f110,plain,
exact(gammma,delta),
inference(cnf_transformation,[],[f26]) ).
fof(f111,plain,
commute(alpha,g,f,gamma),
inference(cnf_transformation,[],[f27]) ).
fof(f112,plain,
commute(beta,h,g,delta),
inference(cnf_transformation,[],[f28]) ).
fof(f113,plain,
surjection(f),
inference(cnf_transformation,[],[f29]) ).
fof(f114,plain,
surjection(h),
inference(cnf_transformation,[],[f30]) ).
fof(f115,plain,
element(sK8,e),
inference(cnf_transformation,[],[f70]) ).
fof(f116,plain,
! [X2,X1] :
( apply(delta,apply(g,X2)) != X1
| apply(h,apply(beta,X2)) != X1
| ~ element(X2,b)
| apply(delta,sK8) != X1
| ~ element(X1,r) ),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X6,X4] :
( ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1)
| ~ element(X6,X2)
| zero(X4) = apply(X1,apply(X0,X6)) ),
inference(equality_resolution,[],[f84]) ).
fof(f119,plain,
! [X2] :
( apply(delta,apply(g,X2)) != apply(delta,sK8)
| apply(h,apply(beta,X2)) != apply(delta,sK8)
| ~ element(X2,b)
| ~ element(apply(delta,sK8),r) ),
inference(equality_resolution,[],[f116]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,zero(X1)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ~ injection(X0)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ morphism(X0,X3,X4)
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK1(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| ( apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) )
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,X3),X1)
| ~ surjection(X0)
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X0,sK2(X0,X1,X3)) = X3 )
| ~ surjection(X0)
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjection(X0)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ( sK3(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| element(sK3(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X3,apply(X0,X5)) = zero(X4) )
| ~ exact(X0,X3)
| ~ element(X5,X1)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK4(X3,X4,X1),X4)
| ~ exact(X3,X0)
| ~ element(X1,X5)
| ~ morphism(X3,X4,X5)
| ~ morphism(X0,X5,X2)
| ( apply(X0,X1) != zero(X2) ) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X3,sK4(X3,X4,X1)) = X1 )
| ~ exact(X3,X0)
| ~ element(X1,X5)
| ~ morphism(X3,X4,X5)
| ~ morphism(X0,X5,X2)
| ( apply(X0,X1) != zero(X2) ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X1)
| ~ element(X5,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(sK5(X0,X1,X2,X3,X4),X3)
| ( sK5(X0,X1,X2,X3,X4) != apply(X0,X5) )
| ( apply(X1,sK5(X0,X1,X2,X3,X4)) != zero(X4) ) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| element(sK6(X0,X3,X1,X2,X4),X1)
| element(sK5(X0,X3,X1,X2,X4),X2)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| element(sK6(X0,X3,X1,X2,X4),X1)
| ( apply(X3,sK5(X0,X3,X1,X2,X4)) = zero(X4) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| element(sK5(X0,X3,X1,X2,X4),X2)
| ( apply(X0,sK6(X0,X3,X1,X2,X4)) = sK5(X0,X3,X1,X2,X4) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| ( apply(X3,sK5(X0,X3,X1,X2,X4)) = zero(X4) )
| ( apply(X0,sK6(X0,X3,X1,X2,X4)) = sK5(X0,X3,X1,X2,X4) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) )
| ~ element(X8,X4)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( commute(X1,X0,X2,X3)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X4,X5)
| ~ morphism(X0,X5,X7)
| ( apply(X0,apply(X1,sK7(X1,X0,X2,X3,X4))) != apply(X3,apply(X2,sK7(X1,X0,X2,X3,X4))) ) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( commute(X0,X7,X6,X3)
| element(sK7(X0,X7,X6,X3,X1),X1)
| ~ morphism(X7,X2,X5)
| ~ morphism(X6,X1,X4)
| ~ morphism(X3,X4,X5)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subtract(X1,X2,X0),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ( subtract(X1,X0,X0) = zero(X1) )
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(X1,X2,subtract(X1,X2,X0)) = X0 )
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( subtract(X2,apply(X0,X3),apply(X0,X4)) = apply(X0,subtract(X1,X3,X4)) )
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_76,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[],[f98]) ).
tcf(c_77,plain,
morphism(beta,b,c),
inference(cnf_transformation,[],[f99]) ).
tcf(c_78,plain,
morphism(gamma,d,e),
inference(cnf_transformation,[],[f100]) ).
tcf(c_79,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f101]) ).
tcf(c_80,plain,
morphism(f,a,d),
inference(cnf_transformation,[],[f102]) ).
tcf(c_81,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f103]) ).
tcf(c_82,plain,
morphism(h,c,r),
inference(cnf_transformation,[],[f104]) ).
tcf(c_83,plain,
injection(alpha),
inference(cnf_transformation,[],[f105]) ).
tcf(c_84,plain,
injection(gamma),
inference(cnf_transformation,[],[f106]) ).
tcf(c_85,plain,
surjection(beta),
inference(cnf_transformation,[],[f107]) ).
tcf(c_86,plain,
surjection(delta),
inference(cnf_transformation,[],[f108]) ).
tcf(c_87,plain,
exact(alpha,beta),
inference(cnf_transformation,[],[f109]) ).
tcf(c_88,plain,
exact(gammma,delta),
inference(cnf_transformation,[],[f110]) ).
tcf(c_89,plain,
commute(alpha,g,f,gamma),
inference(cnf_transformation,[],[f111]) ).
tcf(c_90,plain,
commute(beta,h,g,delta),
inference(cnf_transformation,[],[f112]) ).
tcf(c_91,plain,
surjection(f),
inference(cnf_transformation,[],[f113]) ).
tcf(c_92,plain,
surjection(h),
inference(cnf_transformation,[],[f114]) ).
tcf(c_93,negated_conjecture,
! [X0: $i] :
( ~ element(X0,b)
| ~ element(apply(delta,sK8),r)
| ( apply(h,apply(beta,X0)) != apply(delta,sK8) )
| ( apply(delta,apply(g,X0)) != apply(delta,sK8) ) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_94,negated_conjecture,
element(sK8,e),
inference(cnf_transformation,[],[f115]) ).
tcf(c_3529,definition,
iPr_def_10 = apply(delta,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3530,negated_conjecture,
element(sK8,e),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_3531,negated_conjecture,
! [X0: $i] :
( ~ element(iPr_def_10,r)
| ~ element(X0,b)
| ( apply(h,apply(beta,X0)) != iPr_def_10 )
| ( apply(delta,apply(g,X0)) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_93,c_3529]) ).
tcf(c_4286,plain,
! [X0: $i] :
( element(apply(delta,X0),r)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_79,c_49]) ).
tcf(c_4356,plain,
apply(beta,zero(b)) = zero(c),
inference(superposition,[status(thm)],[c_77,c_50]) ).
tcf(c_4358,plain,
apply(delta,zero(e)) = zero(r),
inference(superposition,[status(thm)],[c_79,c_50]) ).
tcf(c_4360,plain,
apply(g,zero(b)) = zero(e),
inference(superposition,[status(thm)],[c_81,c_50]) ).
tcf(c_4361,plain,
apply(h,zero(c)) = zero(r),
inference(superposition,[status(thm)],[c_82,c_50]) ).
tcf(c_4414,plain,
( ~ element(iPr_def_10,r)
| ~ element(zero(b),b)
| ( apply(delta,zero(e)) != iPr_def_10 )
| ( apply(h,apply(beta,zero(b))) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4360,c_3531]) ).
tcf(c_4415,plain,
( ~ element(iPr_def_10,r)
| ~ element(zero(b),b)
| ( zero(r) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_4414,c_4356,c_4358,c_4361]) ).
tcf(c_4447,plain,
! [X0: $i] :
( element(sK2(beta,b,X0),b)
| ~ surjection(beta)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_77,c_56]) ).
tcf(c_4452,plain,
! [X0: $i] :
( element(sK2(h,c,X0),c)
| ~ surjection(h)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_82,c_56]) ).
tcf(c_4453,plain,
! [X0: $i] :
( element(sK2(h,c,X0),c)
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4452,c_92]) ).
tcf(c_4468,plain,
! [X0: $i] :
( element(sK2(beta,b,X0),b)
| ~ element(X0,c) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4447,c_85]) ).
tcf(c_4873,plain,
( element(iPr_def_10,r)
| ~ element(sK8,e) ),
inference(superposition,[status(thm)],[c_3529,c_4286]) ).
tcf(c_4877,plain,
element(iPr_def_10,r),
inference(forward_subsumption_resolution,[status(thm)],[c_4873,c_3530]) ).
tcf(c_4884,plain,
( ~ element(zero(b),b)
| ( zero(r) != iPr_def_10 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4415,c_4877]) ).
tcf(c_5820,plain,
subtract(e,sK8,sK8) = zero(e),
inference(superposition,[status(thm)],[c_3530,c_73]) ).
tcf(c_6370,plain,
! [X0: $i] :
( ( subtract(c,sK2(h,c,X0),sK2(h,c,X0)) = zero(c) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_4453,c_73]) ).
tcf(c_7234,plain,
! [X0: $i] :
( ( subtract(b,sK2(beta,b,X0),sK2(beta,b,X0)) = zero(b) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_4468,c_73]) ).
tcf(c_11532,plain,
subtract(c,sK2(h,c,iPr_def_10),sK2(h,c,iPr_def_10)) = zero(c),
inference(superposition,[status(thm)],[c_4877,c_6370]) ).
tcf(c_11677,plain,
( element(zero(c),c)
| ~ element(sK2(h,c,iPr_def_10),c) ),
inference(superposition,[status(thm)],[c_11532,c_72]) ).
tcf(c_11684,plain,
( element(zero(c),c)
| ~ element(iPr_def_10,r) ),
inference(superposition,[status(thm)],[c_4453,c_11677]) ).
tcf(c_11685,plain,
element(zero(c),c),
inference(forward_subsumption_resolution,[status(thm)],[c_11684,c_4877]) ).
tcf(c_12211,plain,
subtract(b,sK2(beta,b,zero(c)),sK2(beta,b,zero(c))) = zero(b),
inference(superposition,[status(thm)],[c_11685,c_7234]) ).
tcf(c_14577,plain,
( element(zero(b),b)
| ~ element(sK2(beta,b,zero(c)),b) ),
inference(superposition,[status(thm)],[c_12211,c_72]) ).
tcf(c_14584,plain,
( element(zero(b),b)
| ~ element(zero(c),c) ),
inference(superposition,[status(thm)],[c_4468,c_14577]) ).
tcf(c_14585,plain,
element(zero(b),b),
inference(forward_subsumption_resolution,[status(thm)],[c_14584,c_11685]) ).
tcf(c_121711,plain,
! [X0: $i] :
( ( apply(delta,apply(g,X0)) != iPr_def_10 )
| ( apply(h,apply(beta,X0)) != iPr_def_10 )
| ~ element(X0,b) ),
inference(global_subsumption_just,[status(thm)],[c_3531,c_3531,c_4877]) ).
tcf(c_121712,negated_conjecture,
! [X0: $i] :
( ~ element(X0,b)
| ( apply(h,apply(beta,X0)) != iPr_def_10 )
| ( apply(delta,apply(g,X0)) != iPr_def_10 ) ),
inference(renaming,[status(thm)],[c_121711]) ).
tcf(c_121723,plain,
( injection(beta)
| element(sK0(beta,b),b) ),
inference(superposition,[status(thm)],[c_77,c_53]) ).
tcf(c_121725,plain,
( injection(delta)
| element(sK0(delta,e),e) ),
inference(superposition,[status(thm)],[c_79,c_53]) ).
tcf(c_121726,plain,
( injection(f)
| element(sK0(f,a),a) ),
inference(superposition,[status(thm)],[c_80,c_53]) ).
tcf(c_121727,plain,
( injection(g)
| element(sK0(g,b),b) ),
inference(superposition,[status(thm)],[c_81,c_53]) ).
tcf(c_121728,plain,
( injection(h)
| element(sK0(h,c),c) ),
inference(superposition,[status(thm)],[c_82,c_53]) ).
tcf(c_121757,plain,
! [X0: $i] :
( element(apply(alpha,X0),b)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_76,c_49]) ).
tcf(c_121758,plain,
! [X0: $i] :
( element(apply(beta,X0),c)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_77,c_49]) ).
tcf(c_121759,plain,
! [X0: $i] :
( element(apply(gamma,X0),e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_78,c_49]) ).
tcf(c_121760,plain,
! [X0: $i] :
( element(apply(delta,X0),r)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_79,c_49]) ).
tcf(c_121761,plain,
! [X0: $i] :
( element(apply(f,X0),d)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_80,c_49]) ).
tcf(c_121762,plain,
! [X0: $i] :
( element(apply(g,X0),e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_81,c_49]) ).
tcf(c_121763,plain,
! [X0: $i] :
( element(apply(h,X0),r)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_82,c_49]) ).
tcf(c_121785,plain,
( injection(beta)
| element(sK1(beta,b),b) ),
inference(superposition,[status(thm)],[c_77,c_54]) ).
tcf(c_121787,plain,
( injection(delta)
| element(sK1(delta,e),e) ),
inference(superposition,[status(thm)],[c_79,c_54]) ).
tcf(c_121788,plain,
( injection(f)
| element(sK1(f,a),a) ),
inference(superposition,[status(thm)],[c_80,c_54]) ).
tcf(c_121789,plain,
( injection(g)
| element(sK1(g,b),b) ),
inference(superposition,[status(thm)],[c_81,c_54]) ).
tcf(c_121790,plain,
( injection(h)
| element(sK1(h,c),c) ),
inference(superposition,[status(thm)],[c_82,c_54]) ).
tcf(c_121806,plain,
( injection(beta)
| ( subtract(b,sK0(beta,b),sK0(beta,b)) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121723,c_73]) ).
tcf(c_121807,plain,
( injection(delta)
| ( subtract(e,sK0(delta,e),sK0(delta,e)) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121725,c_73]) ).
tcf(c_121808,plain,
( injection(f)
| ( subtract(a,sK0(f,a),sK0(f,a)) = zero(a) ) ),
inference(superposition,[status(thm)],[c_121726,c_73]) ).
tcf(c_121819,plain,
apply(alpha,zero(a)) = zero(b),
inference(superposition,[status(thm)],[c_76,c_50]) ).
tcf(c_121820,plain,
apply(beta,zero(b)) = zero(c),
inference(superposition,[status(thm)],[c_77,c_50]) ).
tcf(c_121821,plain,
apply(gamma,zero(d)) = zero(e),
inference(superposition,[status(thm)],[c_78,c_50]) ).
tcf(c_121822,plain,
apply(delta,zero(e)) = zero(r),
inference(superposition,[status(thm)],[c_79,c_50]) ).
tcf(c_121823,plain,
apply(f,zero(a)) = zero(d),
inference(superposition,[status(thm)],[c_80,c_50]) ).
tcf(c_121824,plain,
apply(g,zero(b)) = zero(e),
inference(superposition,[status(thm)],[c_81,c_50]) ).
tcf(c_121825,plain,
apply(h,zero(c)) = zero(r),
inference(superposition,[status(thm)],[c_82,c_50]) ).
tcf(c_121832,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(X2,sK3(X0,X1,X2),sK3(X0,X1,X2)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_59,c_73]) ).
tcf(c_121840,plain,
( injection(g)
| ( subtract(b,sK0(g,b),sK0(g,b)) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121727,c_73]) ).
tcf(c_121847,plain,
( injection(h)
| ( subtract(c,sK0(h,c),sK0(h,c)) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121728,c_73]) ).
tcf(c_121854,plain,
( injection(beta)
| ( subtract(b,sK1(beta,b),sK1(beta,b)) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121785,c_73]) ).
tcf(c_121861,plain,
( injection(delta)
| ( subtract(e,sK1(delta,e),sK1(delta,e)) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121787,c_73]) ).
tcf(c_121868,plain,
( injection(f)
| ( subtract(a,sK1(f,a),sK1(f,a)) = zero(a) ) ),
inference(superposition,[status(thm)],[c_121788,c_73]) ).
tcf(c_121875,plain,
( injection(g)
| ( subtract(b,sK1(g,b),sK1(g,b)) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121789,c_73]) ).
tcf(c_121882,plain,
( injection(h)
| ( subtract(c,sK1(h,c),sK1(h,c)) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121790,c_73]) ).
tcf(c_121885,plain,
( ~ element(zero(b),b)
| ( apply(delta,zero(e)) != iPr_def_10 )
| ( apply(h,apply(beta,zero(b))) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_121824,c_121712]) ).
tcf(c_121886,plain,
( ~ element(zero(b),b)
| ( zero(r) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_121885,c_121820,c_121822,c_121825]) ).
tcf(c_121895,plain,
( element(zero(e),e)
| ~ element(sK8,e) ),
inference(superposition,[status(thm)],[c_5820,c_72]) ).
tcf(c_121896,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(X1,subtract(X1,X2,X0),subtract(X1,X2,X0)) = zero(X1) )
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_72,c_73]) ).
tcf(c_121897,plain,
element(zero(e),e),
inference(forward_subsumption_resolution,[status(thm)],[c_121895,c_3530]) ).
tcf(c_121915,plain,
! [X0: $i] :
( element(sK2(alpha,a,X0),a)
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_76,c_56]) ).
tcf(c_121916,plain,
! [X0: $i] :
( element(sK2(beta,b,X0),b)
| ~ surjection(beta)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_77,c_56]) ).
tcf(c_121917,plain,
! [X0: $i] :
( element(sK2(gamma,d,X0),d)
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_78,c_56]) ).
tcf(c_121918,plain,
! [X0: $i] :
( element(sK2(delta,e,X0),e)
| ~ surjection(delta)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_79,c_56]) ).
tcf(c_121919,plain,
! [X0: $i] :
( element(sK2(f,a,X0),a)
| ~ surjection(f)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_80,c_56]) ).
tcf(c_121920,plain,
! [X0: $i] :
( element(sK2(g,b,X0),b)
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_81,c_56]) ).
tcf(c_121921,plain,
! [X0: $i] :
( element(sK2(h,c,X0),c)
| ~ surjection(h)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_82,c_56]) ).
tcf(c_121922,plain,
! [X0: $i] :
( element(sK2(h,c,X0),c)
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121921,c_92]) ).
tcf(c_121928,plain,
! [X0: $i] :
( element(sK2(f,a,X0),a)
| ~ element(X0,d) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121919,c_91]) ).
tcf(c_121931,plain,
! [X0: $i] :
( element(sK2(delta,e,X0),e)
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121918,c_86]) ).
tcf(c_121937,plain,
! [X0: $i] :
( element(sK2(beta,b,X0),b)
| ~ element(X0,c) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121916,c_85]) ).
tcf(c_121949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjection(X0)
| ( subtract(X2,X3,subtract(X2,X3,sK3(X0,X1,X2))) = sK3(X0,X1,X2) )
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_121950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(X1,X3,subtract(X1,X3,subtract(X1,X2,X0))) = subtract(X1,X2,X0) )
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_72,c_74]) ).
tcf(c_121951,plain,
! [X0: $i] :
( ( subtract(e,X0,subtract(e,X0,sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_74]) ).
tcf(c_121952,plain,
! [X0: $i] :
( injection(beta)
| ( subtract(b,X0,subtract(b,X0,sK0(beta,b))) = sK0(beta,b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121723,c_74]) ).
tcf(c_121953,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,X0,subtract(e,X0,sK0(delta,e))) = sK0(delta,e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_74]) ).
tcf(c_121954,plain,
! [X0: $i] :
( injection(f)
| ( subtract(a,X0,subtract(a,X0,sK0(f,a))) = sK0(f,a) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121726,c_74]) ).
tcf(c_121955,plain,
! [X0: $i] :
( injection(g)
| ( subtract(b,X0,subtract(b,X0,sK0(g,b))) = sK0(g,b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121727,c_74]) ).
tcf(c_121956,plain,
! [X0: $i] :
( injection(h)
| ( subtract(c,X0,subtract(c,X0,sK0(h,c))) = sK0(h,c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121728,c_74]) ).
tcf(c_121957,plain,
! [X0: $i] :
( injection(beta)
| ( subtract(b,X0,subtract(b,X0,sK1(beta,b))) = sK1(beta,b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121785,c_74]) ).
tcf(c_121958,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,X0,subtract(e,X0,sK1(delta,e))) = sK1(delta,e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_74]) ).
tcf(c_121959,plain,
! [X0: $i] :
( injection(f)
| ( subtract(a,X0,subtract(a,X0,sK1(f,a))) = sK1(f,a) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121788,c_74]) ).
tcf(c_121960,plain,
! [X0: $i] :
( injection(g)
| ( subtract(b,X0,subtract(b,X0,sK1(g,b))) = sK1(g,b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121789,c_74]) ).
tcf(c_121961,plain,
! [X0: $i] :
( injection(h)
| ( subtract(c,X0,subtract(c,X0,sK1(h,c))) = sK1(h,c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121790,c_74]) ).
tcf(c_122002,plain,
! [X0: $i] :
( ( subtract(e,X0,subtract(e,X0,zero(e))) = zero(e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_74]) ).
tcf(c_122003,plain,
subtract(e,zero(e),zero(e)) = zero(e),
inference(superposition,[status(thm)],[c_121897,c_73]) ).
tcf(c_122010,plain,
( element(zero(b),b)
| ~ element(zero(a),a) ),
inference(superposition,[status(thm)],[c_121819,c_121757]) ).
tcf(c_122011,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,X1,subtract(b,X1,apply(alpha,X0))) = apply(alpha,X0) )
| ~ element(X1,b)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_74]) ).
tcf(c_122012,plain,
! [X0: $i] :
( ( subtract(b,apply(alpha,X0),apply(alpha,X0)) = zero(b) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_73]) ).
tcf(c_122030,plain,
( element(zero(c),c)
| ~ element(zero(b),b) ),
inference(superposition,[status(thm)],[c_121820,c_121758]) ).
tcf(c_122031,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,X1,subtract(c,X1,apply(beta,X0))) = apply(beta,X0) )
| ~ element(X1,c)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_74]) ).
tcf(c_122032,plain,
! [X0: $i] :
( ( subtract(c,apply(beta,X0),apply(beta,X0)) = zero(c) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_73]) ).
tcf(c_122044,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,sK3(X0,X1,e),subtract(e,sK3(X0,X1,e),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_121951]) ).
tcf(c_122045,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,X0),subtract(e,subtract(e,X1,X0),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_121951]) ).
tcf(c_122046,plain,
subtract(e,sK8,subtract(e,sK8,sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_121951]) ).
tcf(c_122047,plain,
( injection(delta)
| ( subtract(e,sK0(delta,e),subtract(e,sK0(delta,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_121951]) ).
tcf(c_122048,plain,
( injection(delta)
| ( subtract(e,sK1(delta,e),subtract(e,sK1(delta,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_121951]) ).
tcf(c_122049,plain,
subtract(e,zero(e),subtract(e,zero(e),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_121951]) ).
tcf(c_122050,plain,
subtract(e,sK8,zero(e)) = sK8,
inference(light_normalisation,[status(thm)],[c_122046,c_5820]) ).
tcf(c_122069,plain,
zero(r) != iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_121886,c_4884,c_14585]) ).
tcf(c_122076,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,sK3(X0,X1,e),subtract(e,sK3(X0,X1,e),zero(e))) = zero(e) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122002]) ).
tcf(c_122077,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,X0),subtract(e,subtract(e,X1,X0),zero(e))) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122002]) ).
tcf(c_122078,plain,
subtract(e,sK8,subtract(e,sK8,zero(e))) = zero(e),
inference(superposition,[status(thm)],[c_3530,c_122002]) ).
tcf(c_122079,plain,
( injection(delta)
| ( subtract(e,sK0(delta,e),subtract(e,sK0(delta,e),zero(e))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121725,c_122002]) ).
tcf(c_122080,plain,
( injection(delta)
| ( subtract(e,sK1(delta,e),subtract(e,sK1(delta,e),zero(e))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121787,c_122002]) ).
tcf(c_122081,plain,
subtract(e,zero(e),subtract(e,zero(e),zero(e))) = zero(e),
inference(superposition,[status(thm)],[c_121897,c_122002]) ).
tcf(c_122107,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,X1,subtract(e,X1,apply(gamma,X0))) = apply(gamma,X0) )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_74]) ).
tcf(c_122108,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,X0),apply(gamma,X0)) = zero(e) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_73]) ).
tcf(c_122109,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,X0),subtract(e,apply(gamma,X0),zero(e))) = zero(e) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122002]) ).
tcf(c_122110,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,X0),subtract(e,apply(gamma,X0),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_121951]) ).
tcf(c_122130,plain,
( injection(beta)
| ( apply(beta,sK0(beta,b)) = apply(beta,sK1(beta,b)) ) ),
inference(superposition,[status(thm)],[c_77,c_55]) ).
tcf(c_122132,plain,
( injection(delta)
| ( apply(delta,sK0(delta,e)) = apply(delta,sK1(delta,e)) ) ),
inference(superposition,[status(thm)],[c_79,c_55]) ).
tcf(c_122133,plain,
( injection(f)
| ( apply(f,sK0(f,a)) = apply(f,sK1(f,a)) ) ),
inference(superposition,[status(thm)],[c_80,c_55]) ).
tcf(c_122134,plain,
( injection(g)
| ( apply(g,sK0(g,b)) = apply(g,sK1(g,b)) ) ),
inference(superposition,[status(thm)],[c_81,c_55]) ).
tcf(c_122135,plain,
( injection(h)
| ( apply(h,sK0(h,c)) = apply(h,sK1(h,c)) ) ),
inference(superposition,[status(thm)],[c_82,c_55]) ).
tcf(c_122157,plain,
! [X0: $i] :
( ( apply(alpha,sK2(alpha,a,X0)) = X0 )
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_76,c_57]) ).
tcf(c_122158,plain,
! [X0: $i] :
( ( apply(beta,sK2(beta,b,X0)) = X0 )
| ~ surjection(beta)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_77,c_57]) ).
tcf(c_122159,plain,
! [X0: $i] :
( ( apply(gamma,sK2(gamma,d,X0)) = X0 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_78,c_57]) ).
tcf(c_122160,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,X0)) = X0 )
| ~ surjection(delta)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_79,c_57]) ).
tcf(c_122161,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,X0)) = X0 )
| ~ surjection(f)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_80,c_57]) ).
tcf(c_122162,plain,
! [X0: $i] :
( ( apply(g,sK2(g,b,X0)) = X0 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_81,c_57]) ).
tcf(c_122163,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,X0)) = X0 )
| ~ surjection(h)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_82,c_57]) ).
tcf(c_122164,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,X0)) = X0 )
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122163,c_92]) ).
tcf(c_122170,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,X0)) = X0 )
| ~ element(X0,d) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122161,c_91]) ).
tcf(c_122173,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,X0)) = X0 )
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122160,c_86]) ).
tcf(c_122179,plain,
! [X0: $i] :
( ( apply(beta,sK2(beta,b,X0)) = X0 )
| ~ element(X0,c) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122158,c_85]) ).
tcf(c_122209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(alpha,X2)) = zero(X1) )
| ~ exact(alpha,X0)
| ~ element(X2,a)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_76,c_61]) ).
tcf(c_122210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(beta,X2)) = zero(X1) )
| ~ exact(beta,X0)
| ~ element(X2,b)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_77,c_61]) ).
tcf(c_122211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(gamma,X2)) = zero(X1) )
| ~ exact(gamma,X0)
| ~ element(X2,d)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_78,c_61]) ).
tcf(c_122212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(delta,X2)) = zero(X1) )
| ~ exact(delta,X0)
| ~ element(X2,e)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_79,c_61]) ).
tcf(c_122213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(f,X2)) = zero(X1) )
| ~ exact(f,X0)
| ~ element(X2,a)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_80,c_61]) ).
tcf(c_122214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(g,X2)) = zero(X1) )
| ~ exact(g,X0)
| ~ element(X2,b)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_81,c_61]) ).
tcf(c_122215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,apply(h,X2)) = zero(X1) )
| ~ exact(h,X0)
| ~ element(X2,c)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_82,c_61]) ).
tcf(c_122254,plain,
( element(iPr_def_10,r)
| ~ element(sK8,e) ),
inference(superposition,[status(thm)],[c_3529,c_121760]) ).
tcf(c_122255,plain,
( element(zero(r),r)
| ~ element(zero(e),e) ),
inference(superposition,[status(thm)],[c_121822,c_121760]) ).
tcf(c_122256,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,X1,subtract(r,X1,apply(delta,X0))) = apply(delta,X0) )
| ~ element(X1,r)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_74]) ).
tcf(c_122257,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,X0),apply(delta,X0)) = zero(r) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_73]) ).
tcf(c_122258,plain,
element(iPr_def_10,r),
inference(forward_subsumption_resolution,[status(thm)],[c_122254,c_3530]) ).
tcf(c_122259,plain,
element(zero(r),r),
inference(forward_subsumption_resolution,[status(thm)],[c_122255,c_121897]) ).
tcf(c_122265,plain,
! [X0: $i] :
( ( subtract(r,X0,subtract(r,X0,iPr_def_10)) = iPr_def_10 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_122258,c_74]) ).
tcf(c_122266,plain,
subtract(r,iPr_def_10,iPr_def_10) = zero(r),
inference(superposition,[status(thm)],[c_122258,c_73]) ).
tcf(c_122275,plain,
! [X0: $i] :
( ( subtract(r,X0,subtract(r,X0,zero(r))) = zero(r) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_122259,c_74]) ).
tcf(c_122276,plain,
subtract(r,zero(r),zero(r)) = zero(r),
inference(superposition,[status(thm)],[c_122259,c_73]) ).
tcf(c_122284,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(r,sK3(X0,X1,r),subtract(r,sK3(X0,X1,r),iPr_def_10)) = iPr_def_10 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_122265]) ).
tcf(c_122285,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,subtract(r,X1,X0),subtract(r,subtract(r,X1,X0),iPr_def_10)) = iPr_def_10 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_122265]) ).
tcf(c_122286,plain,
subtract(r,iPr_def_10,subtract(r,iPr_def_10,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_122258,c_122265]) ).
tcf(c_122287,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,X0),subtract(r,apply(delta,X0),iPr_def_10)) = iPr_def_10 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_122265]) ).
tcf(c_122288,plain,
subtract(r,zero(r),subtract(r,zero(r),iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_122259,c_122265]) ).
tcf(c_122289,plain,
subtract(r,iPr_def_10,zero(r)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_122286,c_122266]) ).
tcf(c_122302,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,apply(gamma,sK3(X0,X1,d)),subtract(e,apply(gamma,sK3(X0,X1,d)),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_122110]) ).
tcf(c_122303,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(gamma,subtract(d,X1,X0)),subtract(e,apply(gamma,subtract(d,X1,X0)),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_122110]) ).
tcf(c_122318,plain,
( surjection(gamma)
| ( subtract(e,sK3(gamma,d,e),subtract(e,sK3(gamma,d,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_122044]) ).
tcf(c_122319,plain,
( surjection(g)
| ( subtract(e,sK3(g,b,e),subtract(e,sK3(g,b,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_122044]) ).
tcf(c_122336,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,X2,sK3(X0,X1,e)),subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122045]) ).
tcf(c_122337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,X2,subtract(e,X1,X0)),subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122045]) ).
tcf(c_122338,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,X0,sK8),subtract(e,subtract(e,X0,sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_122045]) ).
tcf(c_122339,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,X0,sK0(delta,e)),subtract(e,subtract(e,X0,sK0(delta,e)),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_122045]) ).
tcf(c_122340,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,apply(gamma,X0)),subtract(e,subtract(e,X1,apply(gamma,X0)),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122045]) ).
tcf(c_122341,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,X0,sK1(delta,e)),subtract(e,subtract(e,X0,sK1(delta,e)),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_122045]) ).
tcf(c_122342,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,X0,zero(e)),subtract(e,subtract(e,X0,zero(e)),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_122045]) ).
tcf(c_122368,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,sK3(X0,X1,e),sK8),subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122338]) ).
tcf(c_122369,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,X0),sK8),subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122338]) ).
tcf(c_122370,plain,
subtract(e,subtract(e,sK8,sK8),subtract(e,subtract(e,sK8,sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_122338]) ).
tcf(c_122371,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK0(delta,e),sK8),subtract(e,subtract(e,sK0(delta,e),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_122338]) ).
tcf(c_122372,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,X0),sK8),subtract(e,subtract(e,apply(gamma,X0),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122338]) ).
tcf(c_122373,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK1(delta,e),sK8),subtract(e,subtract(e,sK1(delta,e),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_122338]) ).
tcf(c_122374,plain,
subtract(e,subtract(e,zero(e),sK8),subtract(e,subtract(e,zero(e),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_122338]) ).
tcf(c_122399,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122342]) ).
tcf(c_122400,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122342]) ).
tcf(c_122401,plain,
subtract(e,subtract(e,sK8,zero(e)),subtract(e,subtract(e,sK8,zero(e)),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_122342]) ).
tcf(c_122402,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK0(delta,e),zero(e)),subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_122342]) ).
tcf(c_122403,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,X0),zero(e)),subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122342]) ).
tcf(c_122404,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK1(delta,e),zero(e)),subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_122342]) ).
tcf(c_122405,plain,
subtract(e,subtract(e,zero(e),zero(e)),subtract(e,subtract(e,zero(e),zero(e)),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_122342]) ).
tcf(c_122457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK8 )
| ~ injection(delta)
| ~ element(sK8,X1)
| ~ element(X0,X1)
| ~ morphism(delta,X1,X2)
| ( apply(delta,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3529,c_51]) ).
tcf(c_122458,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(a) = X0 )
| ~ injection(alpha)
| ~ element(X0,X1)
| ~ element(zero(a),X1)
| ~ morphism(alpha,X1,X2)
| ( apply(alpha,X0) != zero(b) ) ),
inference(superposition,[status(thm)],[c_121819,c_51]) ).
tcf(c_122459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(b) = X0 )
| ~ injection(beta)
| ~ element(X0,X1)
| ~ element(zero(b),X1)
| ~ morphism(beta,X1,X2)
| ( apply(beta,X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_121820,c_51]) ).
tcf(c_122460,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(d) = X0 )
| ~ injection(gamma)
| ~ element(X0,X1)
| ~ element(zero(d),X1)
| ~ morphism(gamma,X1,X2)
| ( apply(gamma,X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121821,c_51]) ).
tcf(c_122461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(e) = X0 )
| ~ injection(delta)
| ~ element(X0,X1)
| ~ element(zero(e),X1)
| ~ morphism(delta,X1,X2)
| ( apply(delta,X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121822,c_51]) ).
tcf(c_122462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(a) = X0 )
| ~ injection(f)
| ~ element(X0,X1)
| ~ element(zero(a),X1)
| ~ morphism(f,X1,X2)
| ( apply(f,X0) != zero(d) ) ),
inference(superposition,[status(thm)],[c_121823,c_51]) ).
tcf(c_122463,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(b) = X0 )
| ~ injection(g)
| ~ element(X0,X1)
| ~ element(zero(b),X1)
| ~ morphism(g,X1,X2)
| ( apply(g,X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121824,c_51]) ).
tcf(c_122464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(c) = X0 )
| ~ injection(h)
| ~ element(X0,X1)
| ~ element(zero(c),X1)
| ~ morphism(h,X1,X2)
| ( apply(h,X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121825,c_51]) ).
tcf(c_122496,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(d) = X0 )
| ~ element(X0,X1)
| ~ element(zero(d),X1)
| ~ morphism(gamma,X1,X2)
| ( apply(gamma,X0) != zero(e) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122460,c_84]) ).
tcf(c_122508,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zero(a) = X0 )
| ~ element(X0,X1)
| ~ element(zero(a),X1)
| ~ morphism(alpha,X1,X2)
| ( apply(alpha,X0) != zero(b) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122458,c_83]) ).
tcf(c_122536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| element(sK5(X0,X3,X1,X2,X4),X2)
| ( subtract(X1,X5,subtract(X1,X5,sK6(X0,X3,X1,X2,X4))) = sK6(X0,X3,X1,X2,X4) )
| ~ element(X5,X1)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_74]) ).
tcf(c_122537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| element(sK5(X0,X3,X1,X2,X4),X2)
| ( subtract(X1,sK6(X0,X3,X1,X2,X4),sK6(X0,X3,X1,X2,X4)) = zero(X1) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_73]) ).
tcf(c_122538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122110]) ).
tcf(c_122539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122342]) ).
tcf(c_122540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122338]) ).
tcf(c_122541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122045]) ).
tcf(c_122542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),zero(e))) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122002]) ).
tcf(c_122543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_121951]) ).
tcf(c_122544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(r,sK6(X3,X0,r,X1,X2),subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10)) = iPr_def_10 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122265]) ).
tcf(c_122545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| element(sK6(X0,X3,X1,X2,X4),X1)
| ( subtract(X2,X5,subtract(X2,X5,sK5(X0,X3,X1,X2,X4))) = sK5(X0,X3,X1,X2,X4) )
| ~ element(X5,X2)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_74]) ).
tcf(c_122546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| element(sK6(X0,X3,X1,X2,X4),X1)
| ( subtract(X2,sK5(X0,X3,X1,X2,X4),sK5(X0,X3,X1,X2,X4)) = zero(X2) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_73]) ).
tcf(c_122547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_122110]) ).
tcf(c_122548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122342]) ).
tcf(c_122549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122338]) ).
tcf(c_122550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122045]) ).
tcf(c_122551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),zero(e))) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122002]) ).
tcf(c_122552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_121951]) ).
tcf(c_122553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(r,sK5(X0,X2,X1,r,X3),subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10)) = iPr_def_10 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_122265]) ).
tcf(c_122669,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,apply(alpha,X0),apply(alpha,X1)) = apply(alpha,subtract(a,X0,X1)) )
| ~ element(X1,a)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_76,c_75]) ).
tcf(c_122670,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,apply(beta,X0),apply(beta,X1)) = apply(beta,subtract(b,X0,X1)) )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_77,c_75]) ).
tcf(c_122671,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(gamma,X0),apply(gamma,X1)) = apply(gamma,subtract(d,X0,X1)) )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_78,c_75]) ).
tcf(c_122672,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,apply(delta,X0),apply(delta,X1)) = apply(delta,subtract(e,X0,X1)) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_79,c_75]) ).
tcf(c_122673,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,apply(f,X0),apply(f,X1)) = apply(f,subtract(a,X0,X1)) )
| ~ element(X1,a)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_80,c_75]) ).
tcf(c_122674,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(g,X0),apply(g,X1)) = apply(g,subtract(b,X0,X1)) )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_81,c_75]) ).
tcf(c_122675,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,apply(h,X0),apply(h,X1)) = apply(h,subtract(c,X0,X1)) )
| ~ element(X1,c)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_82,c_75]) ).
tcf(c_122721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,sK8),X2)
| ~ exact(X1,delta)
| ~ element(sK8,X3)
| ~ morphism(delta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3529,c_62]) ).
tcf(c_122722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(a)),X2)
| ~ exact(X1,alpha)
| ~ element(zero(a),X3)
| ~ morphism(alpha,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(b) ) ),
inference(superposition,[status(thm)],[c_121819,c_62]) ).
tcf(c_122723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(b)),X2)
| ~ exact(X1,beta)
| ~ element(zero(b),X3)
| ~ morphism(beta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_121820,c_62]) ).
tcf(c_122724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(d)),X2)
| ~ exact(X1,gamma)
| ~ element(zero(d),X3)
| ~ morphism(gamma,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121821,c_62]) ).
tcf(c_122725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(e)),X2)
| ~ exact(X1,delta)
| ~ element(zero(e),X3)
| ~ morphism(delta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121822,c_62]) ).
tcf(c_122726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(a)),X2)
| ~ exact(X1,f)
| ~ element(zero(a),X3)
| ~ morphism(f,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(d) ) ),
inference(superposition,[status(thm)],[c_121823,c_62]) ).
tcf(c_122727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(b)),X2)
| ~ exact(X1,g)
| ~ element(zero(b),X3)
| ~ morphism(g,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121824,c_62]) ).
tcf(c_122728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,X2,zero(c)),X2)
| ~ exact(X1,h)
| ~ element(zero(c),X3)
| ~ morphism(h,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121825,c_62]) ).
tcf(c_122796,plain,
( element(zero(d),d)
| ~ element(zero(a),a) ),
inference(superposition,[status(thm)],[c_121823,c_121761]) ).
tcf(c_122797,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,X1,subtract(d,X1,apply(f,X0))) = apply(f,X0) )
| ~ element(X1,d)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_74]) ).
tcf(c_122798,plain,
! [X0: $i] :
( ( subtract(d,apply(f,X0),apply(f,X0)) = zero(d) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_73]) ).
tcf(c_122799,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,apply(f,X0)),subtract(e,apply(gamma,apply(f,X0)),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_122110]) ).
tcf(c_122842,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,X1,subtract(e,X1,apply(g,X0))) = apply(g,X0) )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_74]) ).
tcf(c_122843,plain,
! [X0: $i] :
( ( subtract(e,apply(g,X0),apply(g,X0)) = zero(e) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_73]) ).
tcf(c_122844,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,X0),zero(e)),subtract(e,subtract(e,apply(g,X0),zero(e)),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122342]) ).
tcf(c_122845,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,X0),sK8),subtract(e,subtract(e,apply(g,X0),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122338]) ).
tcf(c_122846,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,apply(g,X0)),subtract(e,subtract(e,X1,apply(g,X0)),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122045]) ).
tcf(c_122847,plain,
! [X0: $i] :
( ( subtract(e,apply(g,X0),subtract(e,apply(g,X0),zero(e))) = zero(e) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122002]) ).
tcf(c_122848,plain,
! [X0: $i] :
( ( subtract(e,apply(g,X0),subtract(e,apply(g,X0),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_121951]) ).
tcf(c_122870,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,X1,subtract(r,X1,apply(h,X0))) = apply(h,X0) )
| ~ element(X1,r)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_74]) ).
tcf(c_122871,plain,
! [X0: $i] :
( ( subtract(r,apply(h,X0),apply(h,X0)) = zero(r) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_73]) ).
tcf(c_122872,plain,
! [X0: $i] :
( ( subtract(r,apply(h,X0),subtract(r,apply(h,X0),iPr_def_10)) = iPr_def_10 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_122265]) ).
tcf(c_122898,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,apply(g,sK3(X0,X1,b)),subtract(e,apply(g,sK3(X0,X1,b)),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_122848]) ).
tcf(c_122899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_122848]) ).
tcf(c_122900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122848]) ).
tcf(c_122901,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(g,subtract(b,X1,X0)),subtract(e,apply(g,subtract(b,X1,X0)),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_122848]) ).
tcf(c_122902,plain,
( injection(beta)
| ( subtract(e,apply(g,sK0(beta,b)),subtract(e,apply(g,sK0(beta,b)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_122848]) ).
tcf(c_122903,plain,
( injection(g)
| ( subtract(e,apply(g,sK0(g,b)),subtract(e,apply(g,sK0(g,b)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_122848]) ).
tcf(c_122904,plain,
! [X0: $i] :
( ( subtract(e,apply(g,apply(alpha,X0)),subtract(e,apply(g,apply(alpha,X0)),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_122848]) ).
tcf(c_122905,plain,
( injection(beta)
| ( subtract(e,apply(g,sK1(beta,b)),subtract(e,apply(g,sK1(beta,b)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_122848]) ).
tcf(c_122906,plain,
( injection(g)
| ( subtract(e,apply(g,sK1(g,b)),subtract(e,apply(g,sK1(g,b)),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_122848]) ).
tcf(c_122982,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_122372]) ).
tcf(c_122983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_122372]) ).
tcf(c_122984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122372]) ).
tcf(c_122985,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_122372]) ).
tcf(c_122986,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_122372]) ).
tcf(c_123022,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_122845]) ).
tcf(c_123023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_122845]) ).
tcf(c_123024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122845]) ).
tcf(c_123025,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_122845]) ).
tcf(c_123026,plain,
( injection(beta)
| ( subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_122845]) ).
tcf(c_123027,plain,
( injection(g)
| ( subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_122845]) ).
tcf(c_123028,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_122845]) ).
tcf(c_123029,plain,
( injection(beta)
| ( subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_122845]) ).
tcf(c_123030,plain,
( injection(g)
| ( subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_122845]) ).
tcf(c_123068,plain,
( surjection(gamma)
| ( subtract(e,subtract(e,sK3(gamma,d,e),sK8),subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_122368]) ).
tcf(c_123069,plain,
( surjection(g)
| ( subtract(e,subtract(e,sK3(g,b,e),sK8),subtract(e,subtract(e,sK3(g,b,e),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_122368]) ).
tcf(c_123107,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122369]) ).
tcf(c_123108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122369]) ).
tcf(c_123109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122369]) ).
tcf(c_123110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122369]) ).
tcf(c_123111,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,X0,sK8),sK8),subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_122369]) ).
tcf(c_123112,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_122369]) ).
tcf(c_123113,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122369]) ).
tcf(c_123114,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122369]) ).
tcf(c_123115,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_122369]) ).
tcf(c_123116,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_122369]) ).
tcf(c_123161,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_123111]) ).
tcf(c_123162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_123111]) ).
tcf(c_123163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123111]) ).
tcf(c_123164,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_123111]) ).
tcf(c_123165,plain,
subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_123111]) ).
tcf(c_123166,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_123111]) ).
tcf(c_123167,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_123111]) ).
tcf(c_123168,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_123111]) ).
tcf(c_123169,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_123111]) ).
tcf(c_123170,plain,
subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_123111]) ).
tcf(c_123235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| ( apply(X3,sK5(X0,X3,X1,X2,X4)) = zero(X4) )
| ( subtract(X1,X5,subtract(X1,X5,sK6(X0,X3,X1,X2,X4))) = sK6(X0,X3,X1,X2,X4) )
| ~ element(X5,X1)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_74]) ).
tcf(c_123236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| ( apply(X3,sK5(X0,X3,X1,X2,X4)) = zero(X4) )
| ( subtract(X1,sK6(X0,X3,X1,X2,X4),sK6(X0,X3,X1,X2,X4)) = zero(X1) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_73]) ).
tcf(c_123237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122845]) ).
tcf(c_123238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122848]) ).
tcf(c_123239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122372]) ).
tcf(c_123240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122110]) ).
tcf(c_123241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123111]) ).
tcf(c_123242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122369]) ).
tcf(c_123243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122342]) ).
tcf(c_123244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122338]) ).
tcf(c_123245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122045]) ).
tcf(c_123246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),zero(e))) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122002]) ).
tcf(c_123247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_121951]) ).
tcf(c_123248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(r,sK6(X3,X0,r,X1,X2),subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10)) = iPr_def_10 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122265]) ).
tcf(c_123366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(alpha,X4,X3,X0)
| element(sK7(alpha,X4,X3,X0,a),a)
| ~ morphism(X4,b,X2)
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_76,c_71]) ).
tcf(c_123367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(beta,X4,X3,X0)
| element(sK7(beta,X4,X3,X0,b),b)
| ~ morphism(X4,c,X2)
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_77,c_71]) ).
tcf(c_123368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(gamma,X4,X3,X0)
| element(sK7(gamma,X4,X3,X0,d),d)
| ~ morphism(X4,e,X2)
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_78,c_71]) ).
tcf(c_123369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(delta,X4,X3,X0)
| element(sK7(delta,X4,X3,X0,e),e)
| ~ morphism(X4,r,X2)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_79,c_71]) ).
tcf(c_123370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(f,X4,X3,X0)
| element(sK7(f,X4,X3,X0,a),a)
| ~ morphism(X4,d,X2)
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_80,c_71]) ).
tcf(c_123371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(g,X4,X3,X0)
| element(sK7(g,X4,X3,X0,b),b)
| ~ morphism(X4,e,X2)
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_81,c_71]) ).
tcf(c_123372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( commute(h,X4,X3,X0)
| element(sK7(h,X4,X3,X0,c),c)
| ~ morphism(X4,r,X2)
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_82,c_71]) ).
tcf(c_123432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,sK8)) = sK8 )
| ~ exact(X1,delta)
| ~ element(sK8,X3)
| ~ morphism(delta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3529,c_63]) ).
tcf(c_123433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(a))) = zero(a) )
| ~ exact(X1,alpha)
| ~ element(zero(a),X3)
| ~ morphism(alpha,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(b) ) ),
inference(superposition,[status(thm)],[c_121819,c_63]) ).
tcf(c_123434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(b))) = zero(b) )
| ~ exact(X1,beta)
| ~ element(zero(b),X3)
| ~ morphism(beta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_121820,c_63]) ).
tcf(c_123435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(d))) = zero(d) )
| ~ exact(X1,gamma)
| ~ element(zero(d),X3)
| ~ morphism(gamma,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121821,c_63]) ).
tcf(c_123436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(e))) = zero(e) )
| ~ exact(X1,delta)
| ~ element(zero(e),X3)
| ~ morphism(delta,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121822,c_63]) ).
tcf(c_123437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(a))) = zero(a) )
| ~ exact(X1,f)
| ~ element(zero(a),X3)
| ~ morphism(f,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(d) ) ),
inference(superposition,[status(thm)],[c_121823,c_63]) ).
tcf(c_123438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(b))) = zero(b) )
| ~ exact(X1,g)
| ~ element(zero(b),X3)
| ~ morphism(g,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(e) ) ),
inference(superposition,[status(thm)],[c_121824,c_63]) ).
tcf(c_123439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,zero(c))) = zero(c) )
| ~ exact(X1,h)
| ~ element(zero(c),X3)
| ~ morphism(h,X3,X0)
| ~ morphism(X1,X2,X3)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_121825,c_63]) ).
tcf(c_123506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| ( apply(X0,sK6(X0,X3,X1,X2,X4)) = sK5(X0,X3,X1,X2,X4) )
| ( subtract(X2,X5,subtract(X2,X5,sK5(X0,X3,X1,X2,X4))) = sK5(X0,X3,X1,X2,X4) )
| ~ element(X5,X2)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_67,c_74]) ).
tcf(c_123507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X3)
| ( apply(X0,sK6(X0,X3,X1,X2,X4)) = sK5(X0,X3,X1,X2,X4) )
| ( subtract(X2,sK5(X0,X3,X1,X2,X4),sK5(X0,X3,X1,X2,X4)) = zero(X2) )
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_67,c_73]) ).
tcf(c_123508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_122845]) ).
tcf(c_123509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_122848]) ).
tcf(c_123510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_122372]) ).
tcf(c_123511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_122110]) ).
tcf(c_123512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_123111]) ).
tcf(c_123513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122369]) ).
tcf(c_123514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122342]) ).
tcf(c_123515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122338]) ).
tcf(c_123516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122045]) ).
tcf(c_123517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),zero(e))) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122002]) ).
tcf(c_123518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_121951]) ).
tcf(c_123519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(r,sK5(X0,X2,X1,r,X3),subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10)) = iPr_def_10 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_122265]) ).
tcf(c_123652,plain,
element(zero(b),b),
inference(global_subsumption_just,[status(thm)],[c_122010,c_14585]) ).
tcf(c_123654,plain,
! [X0: $i] :
( ( subtract(b,X0,subtract(b,X0,zero(b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_123652,c_74]) ).
tcf(c_123655,plain,
subtract(b,zero(b),zero(b)) = zero(b),
inference(superposition,[status(thm)],[c_123652,c_73]) ).
tcf(c_123656,plain,
subtract(e,subtract(e,apply(g,zero(b)),sK8),subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_122845]) ).
tcf(c_123657,plain,
subtract(e,apply(g,zero(b)),subtract(e,apply(g,zero(b)),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_122848]) ).
tcf(c_123669,plain,
element(zero(c),c),
inference(global_subsumption_just,[status(thm)],[c_122030,c_11685]) ).
tcf(c_123671,plain,
! [X0: $i] :
( ( subtract(c,X0,subtract(c,X0,zero(c))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_123669,c_74]) ).
tcf(c_123672,plain,
subtract(c,zero(c),zero(c)) = zero(c),
inference(superposition,[status(thm)],[c_123669,c_73]) ).
tcf(c_123700,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,X1,subtract(c,X1,sK2(h,c,X0))) = sK2(h,c,X0) )
| ~ element(X1,c)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_74]) ).
tcf(c_123701,plain,
! [X0: $i] :
( ( subtract(c,sK2(h,c,X0),sK2(h,c,X0)) = zero(c) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_73]) ).
tcf(c_123711,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_123116]) ).
tcf(c_123712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_123116]) ).
tcf(c_123713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_123116]) ).
tcf(c_123714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123116]) ).
tcf(c_123715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123116]) ).
tcf(c_123716,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_123116]) ).
tcf(c_123717,plain,
subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_123116]) ).
tcf(c_123718,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_123116]) ).
tcf(c_123719,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_123116]) ).
tcf(c_123720,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_123116]) ).
tcf(c_123721,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_123116]) ).
tcf(c_123722,plain,
subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_123116]) ).
tcf(c_123796,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_123167]) ).
tcf(c_123797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_123167]) ).
tcf(c_123798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_123167]) ).
tcf(c_123799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123167]) ).
tcf(c_123800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123167]) ).
tcf(c_123801,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_123167]) ).
tcf(c_123802,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_123167]) ).
tcf(c_123858,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_123168]) ).
tcf(c_123859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_123168]) ).
tcf(c_123860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_123168]) ).
tcf(c_123861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123168]) ).
tcf(c_123862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123168]) ).
tcf(c_123863,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_123168]) ).
tcf(c_123864,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_123168]) ).
tcf(c_123865,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_123168]) ).
tcf(c_123866,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_123168]) ).
tcf(c_123867,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_123168]) ).
tcf(c_123868,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_123168]) ).
tcf(c_123869,plain,
subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_123168]) ).
tcf(c_123966,plain,
( surjection(gamma)
| ( subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_123161]) ).
tcf(c_123967,plain,
( surjection(g)
| ( subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_123161]) ).
tcf(c_123978,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_123164]) ).
tcf(c_123979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_123164]) ).
tcf(c_123980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_123164]) ).
tcf(c_123981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123164]) ).
tcf(c_123982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123164]) ).
tcf(c_123983,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_123164]) ).
tcf(c_123984,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_123164]) ).
tcf(c_123985,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_123164]) ).
tcf(c_123986,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_123164]) ).
tcf(c_123987,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_123164]) ).
tcf(c_123988,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_123164]) ).
tcf(c_123989,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_123164]) ).
tcf(c_124053,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_123984]) ).
tcf(c_124054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_123984]) ).
tcf(c_124055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_123984]) ).
tcf(c_124056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123984]) ).
tcf(c_124057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123984]) ).
tcf(c_124058,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_123984]) ).
tcf(c_124059,plain,
subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_123984]) ).
tcf(c_124060,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_123984]) ).
tcf(c_124061,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_123984]) ).
tcf(c_124062,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_123984]) ).
tcf(c_124063,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_123984]) ).
tcf(c_124064,plain,
subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_123984]) ).
tcf(c_124213,plain,
! [X0: $i,X1: $i] :
( exact(alpha,X0)
| ( apply(alpha,sK6(alpha,X0,a,b,X1)) = sK5(alpha,X0,a,b,X1) )
| ( apply(X0,sK5(alpha,X0,a,b,X1)) = zero(X1) )
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_76,c_68]) ).
tcf(c_124214,plain,
! [X0: $i,X1: $i] :
( exact(beta,X0)
| ( apply(beta,sK6(beta,X0,b,c,X1)) = sK5(beta,X0,b,c,X1) )
| ( apply(X0,sK5(beta,X0,b,c,X1)) = zero(X1) )
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_77,c_68]) ).
tcf(c_124215,plain,
! [X0: $i,X1: $i] :
( exact(gamma,X0)
| ( apply(gamma,sK6(gamma,X0,d,e,X1)) = sK5(gamma,X0,d,e,X1) )
| ( apply(X0,sK5(gamma,X0,d,e,X1)) = zero(X1) )
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_78,c_68]) ).
tcf(c_124216,plain,
! [X0: $i,X1: $i] :
( exact(delta,X0)
| ( apply(delta,sK6(delta,X0,e,r,X1)) = sK5(delta,X0,e,r,X1) )
| ( apply(X0,sK5(delta,X0,e,r,X1)) = zero(X1) )
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_79,c_68]) ).
tcf(c_124217,plain,
! [X0: $i,X1: $i] :
( exact(f,X0)
| ( apply(f,sK6(f,X0,a,d,X1)) = sK5(f,X0,a,d,X1) )
| ( apply(X0,sK5(f,X0,a,d,X1)) = zero(X1) )
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_80,c_68]) ).
tcf(c_124218,plain,
! [X0: $i,X1: $i] :
( exact(g,X0)
| ( apply(g,sK6(g,X0,b,e,X1)) = sK5(g,X0,b,e,X1) )
| ( apply(X0,sK5(g,X0,b,e,X1)) = zero(X1) )
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_81,c_68]) ).
tcf(c_124219,plain,
! [X0: $i,X1: $i] :
( exact(h,X0)
| ( apply(h,sK6(h,X0,c,r,X1)) = sK5(h,X0,c,r,X1) )
| ( apply(X0,sK5(h,X0,c,r,X1)) = zero(X1) )
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_82,c_68]) ).
tcf(c_124262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(gamma,apply(f,X4)) = apply(g,apply(alpha,X4)) )
| ~ element(X4,X0)
| ~ morphism(g,X1,X3)
| ~ morphism(f,X0,X2)
| ~ morphism(gamma,X2,X3)
| ~ morphism(alpha,X0,X1) ),
inference(superposition,[status(thm)],[c_89,c_69]) ).
tcf(c_124263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(delta,apply(g,X4)) = apply(h,apply(beta,X4)) )
| ~ element(X4,X0)
| ~ morphism(h,X1,X3)
| ~ morphism(g,X0,X2)
| ~ morphism(delta,X2,X3)
| ~ morphism(beta,X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_69]) ).
tcf(c_124288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( commute(X4,X0,X4,X0)
| ~ morphism(X4,X5,X3)
| ~ morphism(X4,X5,X1)
| ~ morphism(X0,X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_70]) ).
tcf(c_124314,plain,
! [X0: $i,X1: $i] :
( ( subtract(a,X1,subtract(a,X1,sK2(f,a,X0))) = sK2(f,a,X0) )
| ~ element(X1,a)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_74]) ).
tcf(c_124315,plain,
! [X0: $i] :
( ( subtract(a,sK2(f,a,X0),sK2(f,a,X0)) = zero(a) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_73]) ).
tcf(c_124331,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,X1,subtract(e,X1,sK2(delta,e,X0))) = sK2(delta,e,X0) )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_74]) ).
tcf(c_124332,plain,
! [X0: $i] :
( ( subtract(e,sK2(delta,e,X0),sK2(delta,e,X0)) = zero(e) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_73]) ).
tcf(c_124333,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_123984]) ).
tcf(c_124334,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_123164]) ).
tcf(c_124335,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_123116]) ).
tcf(c_124336,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_123111]) ).
tcf(c_124337,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122369]) ).
tcf(c_124338,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122342]) ).
tcf(c_124339,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,X0),sK8),subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122338]) ).
tcf(c_124340,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,sK2(delta,e,X0)),subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122045]) ).
tcf(c_124341,plain,
! [X0: $i] :
( ( subtract(e,sK2(delta,e,X0),subtract(e,sK2(delta,e,X0),zero(e))) = zero(e) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122002]) ).
tcf(c_124342,plain,
! [X0: $i] :
( ( subtract(e,sK2(delta,e,X0),subtract(e,sK2(delta,e,X0),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_121951]) ).
tcf(c_124386,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,X1,subtract(b,X1,sK2(beta,b,X0))) = sK2(beta,b,X0) )
| ~ element(X1,b)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_74]) ).
tcf(c_124387,plain,
! [X0: $i] :
( ( subtract(b,sK2(beta,b,X0),sK2(beta,b,X0)) = zero(b) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_73]) ).
tcf(c_124388,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_123168]) ).
tcf(c_124389,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_122845]) ).
tcf(c_124390,plain,
! [X0: $i] :
( ( subtract(e,apply(g,sK2(beta,b,X0)),subtract(e,apply(g,sK2(beta,b,X0)),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_122848]) ).
tcf(c_124418,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,sK2(delta,e,sK3(X0,X1,r)),subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_124342]) ).
tcf(c_124419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_124342]) ).
tcf(c_124420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_124342]) ).
tcf(c_124421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124342]) ).
tcf(c_124422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124342]) ).
tcf(c_124423,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,sK2(delta,e,subtract(r,X1,X0)),subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_124342]) ).
tcf(c_124424,plain,
subtract(e,sK2(delta,e,iPr_def_10),subtract(e,sK2(delta,e,iPr_def_10),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_124342]) ).
tcf(c_124425,plain,
! [X0: $i] :
( ( subtract(e,sK2(delta,e,apply(delta,X0)),subtract(e,sK2(delta,e,apply(delta,X0)),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_124342]) ).
tcf(c_124426,plain,
! [X0: $i] :
( ( subtract(e,sK2(delta,e,apply(h,X0)),subtract(e,sK2(delta,e,apply(h,X0)),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_124342]) ).
tcf(c_124427,plain,
subtract(e,sK2(delta,e,zero(r)),subtract(e,sK2(delta,e,zero(r)),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_124342]) ).
tcf(c_124468,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_124339]) ).
tcf(c_124469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_124339]) ).
tcf(c_124470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_124339]) ).
tcf(c_124471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124339]) ).
tcf(c_124472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124339]) ).
tcf(c_124473,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_124339]) ).
tcf(c_124474,plain,
subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_124339]) ).
tcf(c_124475,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_124339]) ).
tcf(c_124476,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_124339]) ).
tcf(c_124477,plain,
subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_124339]) ).
tcf(c_124535,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_124336]) ).
tcf(c_124536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_124336]) ).
tcf(c_124537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_124336]) ).
tcf(c_124538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124336]) ).
tcf(c_124539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124336]) ).
tcf(c_124540,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_124336]) ).
tcf(c_124541,plain,
subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_124336]) ).
tcf(c_124542,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_124336]) ).
tcf(c_124543,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_124336]) ).
tcf(c_124544,plain,
subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_124336]) ).
tcf(c_124603,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_123989]) ).
tcf(c_124604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_123989]) ).
tcf(c_124605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_123989]) ).
tcf(c_124606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123989]) ).
tcf(c_124607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123989]) ).
tcf(c_124608,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_123989]) ).
tcf(c_124609,plain,
subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_123989]) ).
tcf(c_124610,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_123989]) ).
tcf(c_124611,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_123989]) ).
tcf(c_124612,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_123989]) ).
tcf(c_124613,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_123989]) ).
tcf(c_124614,plain,
subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_123989]) ).
tcf(c_124615,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_123989]) ).
tcf(c_124690,plain,
! [X0: $i,X1: $i] :
( ( subtract(a,X1,subtract(a,X1,sK2(alpha,a,X0))) = sK2(alpha,a,X0) )
| ~ surjection(alpha)
| ~ element(X1,a)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_74]) ).
tcf(c_124691,plain,
! [X0: $i] :
( ( subtract(a,sK2(alpha,a,X0),sK2(alpha,a,X0)) = zero(a) )
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_73]) ).
tcf(c_124705,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,X1,subtract(d,X1,sK2(gamma,d,X0))) = sK2(gamma,d,X0) )
| ~ surjection(gamma)
| ~ element(X1,d)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_74]) ).
tcf(c_124706,plain,
! [X0: $i] :
( ( subtract(d,sK2(gamma,d,X0),sK2(gamma,d,X0)) = zero(d) )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_73]) ).
tcf(c_124707,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_123167]) ).
tcf(c_124708,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_122372]) ).
tcf(c_124709,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,sK2(gamma,d,X0)),subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_122110]) ).
tcf(c_124737,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,X1,subtract(b,X1,sK2(g,b,X0))) = sK2(g,b,X0) )
| ~ surjection(g)
| ~ element(X1,b)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_74]) ).
tcf(c_124738,plain,
! [X0: $i] :
( ( subtract(b,sK2(g,b,X0),sK2(g,b,X0)) = zero(b) )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_73]) ).
tcf(c_124739,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_123168]) ).
tcf(c_124740,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_122845]) ).
tcf(c_124741,plain,
! [X0: $i] :
( ( subtract(e,apply(g,sK2(g,b,X0)),subtract(e,apply(g,sK2(g,b,X0)),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_122848]) ).
tcf(c_124782,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(h,sK2(h,c,sK3(X0,X1,r))) = sK3(X0,X1,r) )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_122164]) ).
tcf(c_124783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( apply(h,sK2(h,c,sK5(X0,X2,X1,r,X3))) = sK5(X0,X2,X1,r,X3) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_122164]) ).
tcf(c_124784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( apply(h,sK2(h,c,sK5(X0,X2,X1,r,X3))) = sK5(X0,X2,X1,r,X3) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_122164]) ).
tcf(c_124785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( apply(h,sK2(h,c,sK6(X3,X0,r,X1,X2))) = sK6(X3,X0,r,X1,X2) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122164]) ).
tcf(c_124786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( apply(h,sK2(h,c,sK6(X3,X0,r,X1,X2))) = sK6(X3,X0,r,X1,X2) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122164]) ).
tcf(c_124787,plain,
! [X0: $i,X1: $i] :
( ( apply(h,sK2(h,c,subtract(r,X1,X0))) = subtract(r,X1,X0) )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_122164]) ).
tcf(c_124788,plain,
apply(h,sK2(h,c,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_122258,c_122164]) ).
tcf(c_124789,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(delta,X0))) = apply(delta,X0) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_122164]) ).
tcf(c_124790,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(h,X0))) = apply(h,X0) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_122164]) ).
tcf(c_124791,plain,
apply(h,sK2(h,c,zero(r))) = zero(r),
inference(superposition,[status(thm)],[c_122259,c_122164]) ).
tcf(c_124900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK2(h,c,iPr_def_10))) = sK2(h,c,iPr_def_10) )
| ~ exact(X2,h)
| ~ morphism(h,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(h,c,iPr_def_10),X1)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_124788,c_63]) ).
tcf(c_124901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X2,X3,sK2(h,c,iPr_def_10)),X3)
| ~ exact(X2,h)
| ~ morphism(h,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(h,c,iPr_def_10),X1)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_124788,c_62]) ).
tcf(c_124904,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(h,c,iPr_def_10) = X0 )
| ~ injection(h)
| ~ element(X0,X1)
| ~ morphism(h,X1,X2)
| ~ element(sK2(h,c,iPr_def_10),X1)
| ( apply(h,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_124788,c_51]) ).
tcf(c_124942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK2(h,c,zero(r)))) = sK2(h,c,zero(r)) )
| ~ exact(X2,h)
| ~ morphism(h,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(h,c,zero(r)),X1)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_124791,c_63]) ).
tcf(c_124943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X2,X3,sK2(h,c,zero(r))),X3)
| ~ exact(X2,h)
| ~ morphism(h,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(h,c,zero(r)),X1)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_124791,c_62]) ).
tcf(c_124946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(h,c,zero(r)) = X0 )
| ~ injection(h)
| ~ element(X0,X1)
| ~ morphism(h,X1,X2)
| ~ element(sK2(h,c,zero(r)),X1)
| ( apply(h,X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_124791,c_51]) ).
tcf(c_124995,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(f,sK2(f,a,sK3(X0,X1,d))) = sK3(X0,X1,d) )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_122170]) ).
tcf(c_124996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( apply(f,sK2(f,a,sK5(X0,X2,X1,d,X3))) = sK5(X0,X2,X1,d,X3) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_122170]) ).
tcf(c_124997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( apply(f,sK2(f,a,sK5(X0,X2,X1,d,X3))) = sK5(X0,X2,X1,d,X3) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_122170]) ).
tcf(c_124998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( apply(f,sK2(f,a,sK6(X3,X0,d,X1,X2))) = sK6(X3,X0,d,X1,X2) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122170]) ).
tcf(c_124999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( apply(f,sK2(f,a,sK6(X3,X0,d,X1,X2))) = sK6(X3,X0,d,X1,X2) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122170]) ).
tcf(c_125000,plain,
! [X0: $i,X1: $i] :
( ( apply(f,sK2(f,a,subtract(d,X1,X0))) = subtract(d,X1,X0) )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_122170]) ).
tcf(c_125001,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,apply(f,X0))) = apply(f,X0) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_122170]) ).
tcf(c_125002,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,sK2(gamma,d,X0))) = sK2(gamma,d,X0) )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_122170]) ).
tcf(c_125045,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(delta,sK2(delta,e,sK3(X0,X1,r))) = sK3(X0,X1,r) )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_122173]) ).
tcf(c_125046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( apply(delta,sK2(delta,e,sK5(X0,X2,X1,r,X3))) = sK5(X0,X2,X1,r,X3) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_122173]) ).
tcf(c_125047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( apply(delta,sK2(delta,e,sK5(X0,X2,X1,r,X3))) = sK5(X0,X2,X1,r,X3) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_122173]) ).
tcf(c_125048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( apply(delta,sK2(delta,e,sK6(X3,X0,r,X1,X2))) = sK6(X3,X0,r,X1,X2) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122173]) ).
tcf(c_125049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( apply(delta,sK2(delta,e,sK6(X3,X0,r,X1,X2))) = sK6(X3,X0,r,X1,X2) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122173]) ).
tcf(c_125050,plain,
! [X0: $i,X1: $i] :
( ( apply(delta,sK2(delta,e,subtract(r,X1,X0))) = subtract(r,X1,X0) )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_122173]) ).
tcf(c_125051,plain,
apply(delta,sK2(delta,e,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_122258,c_122173]) ).
tcf(c_125052,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,apply(delta,X0))) = apply(delta,X0) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_122173]) ).
tcf(c_125053,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,apply(h,X0))) = apply(h,X0) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_122173]) ).
tcf(c_125054,plain,
apply(delta,sK2(delta,e,zero(r))) = zero(r),
inference(superposition,[status(thm)],[c_122259,c_122173]) ).
tcf(c_125138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK2(delta,e,iPr_def_10))) = sK2(delta,e,iPr_def_10) )
| ~ exact(X2,delta)
| ~ morphism(delta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(delta,e,iPr_def_10),X1)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_125051,c_63]) ).
tcf(c_125139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X2,X3,sK2(delta,e,iPr_def_10)),X3)
| ~ exact(X2,delta)
| ~ morphism(delta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(delta,e,iPr_def_10),X1)
| ( zero(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_125051,c_62]) ).
tcf(c_125142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(delta,e,iPr_def_10) = X0 )
| ~ injection(delta)
| ~ element(X0,X1)
| ~ morphism(delta,X1,X2)
| ~ element(sK2(delta,e,iPr_def_10),X1)
| ( apply(delta,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_125051,c_51]) ).
tcf(c_125198,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_124061]) ).
tcf(c_125199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_124061]) ).
tcf(c_125200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_124061]) ).
tcf(c_125201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124061]) ).
tcf(c_125202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124061]) ).
tcf(c_125203,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_124061]) ).
tcf(c_125204,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_124061]) ).
tcf(c_125205,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_124061]) ).
tcf(c_125279,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_124062]) ).
tcf(c_125280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_124062]) ).
tcf(c_125281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_124062]) ).
tcf(c_125282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124062]) ).
tcf(c_125283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124062]) ).
tcf(c_125284,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_124062]) ).
tcf(c_125285,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_124062]) ).
tcf(c_125286,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_124062]) ).
tcf(c_125287,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_124062]) ).
tcf(c_125288,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_124062]) ).
tcf(c_125289,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_124062]) ).
tcf(c_125290,plain,
subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_124062]) ).
tcf(c_125291,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_124062]) ).
tcf(c_125292,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_124062]) ).
tcf(c_125364,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_124333]) ).
tcf(c_125365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_124333]) ).
tcf(c_125366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_124333]) ).
tcf(c_125367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124333]) ).
tcf(c_125368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124333]) ).
tcf(c_125369,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_124333]) ).
tcf(c_125370,plain,
subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_124333]) ).
tcf(c_125371,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_124333]) ).
tcf(c_125372,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_124333]) ).
tcf(c_125373,plain,
subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_124333]) ).
tcf(c_125457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(X1,X4,subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = sK5(X3,X0,e,X1,X2) )
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122543,c_74]) ).
tcf(c_125458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( subtract(X1,sK5(X3,X0,e,X1,X2),sK5(X3,X0,e,X1,X2)) = zero(X1) )
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122543,c_73]) ).
tcf(c_125459,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124062]) ).
tcf(c_125460,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123168]) ).
tcf(c_125461,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122845]) ).
tcf(c_125462,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122848]) ).
tcf(c_125463,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124061]) ).
tcf(c_125464,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK5(X2,X0,e,d,X1))) = sK5(X2,X0,e,d,X1) )
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122170]) ).
tcf(c_125465,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123167]) ).
tcf(c_125466,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122372]) ).
tcf(c_125467,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122110]) ).
tcf(c_125468,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123989]) ).
tcf(c_125469,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123984]) ).
tcf(c_125470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123164]) ).
tcf(c_125471,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123116]) ).
tcf(c_125472,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123111]) ).
tcf(c_125473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122369]) ).
tcf(c_125474,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122342]) ).
tcf(c_125475,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122338]) ).
tcf(c_125476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122045]) ).
tcf(c_125477,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122002]) ).
tcf(c_125478,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_121951]) ).
tcf(c_125479,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124333]) ).
tcf(c_125480,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122173]) ).
tcf(c_125481,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122164]) ).
tcf(c_125482,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124336]) ).
tcf(c_125483,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124339]) ).
tcf(c_125484,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124342]) ).
tcf(c_125485,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122265]) ).
tcf(c_125785,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(beta,sK2(beta,b,sK3(X0,X1,c))) = sK3(X0,X1,c) )
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_59,c_122179]) ).
tcf(c_125786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,c,X3)) = sK5(X0,X2,X1,c,X3) )
| ( apply(beta,sK2(beta,b,sK5(X0,X2,X1,c,X3))) = sK5(X0,X2,X1,c,X3) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_67,c_122179]) ).
tcf(c_125787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,c,X3),X1)
| ( apply(beta,sK2(beta,b,sK5(X0,X2,X1,c,X3))) = sK5(X0,X2,X1,c,X3) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_65,c_122179]) ).
tcf(c_125788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,c,X1,X2)) = zero(X2) )
| ( apply(beta,sK2(beta,b,sK6(X3,X0,c,X1,X2))) = sK6(X3,X0,c,X1,X2) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122179]) ).
tcf(c_125789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,c,X1,X2),X1)
| ( apply(beta,sK2(beta,b,sK6(X3,X0,c,X1,X2))) = sK6(X3,X0,c,X1,X2) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122179]) ).
tcf(c_125790,plain,
! [X0: $i,X1: $i] :
( ( apply(beta,sK2(beta,b,subtract(c,X1,X0))) = subtract(c,X1,X0) )
| ~ element(X1,c)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_72,c_122179]) ).
tcf(c_125791,plain,
( injection(h)
| ( apply(beta,sK2(beta,b,sK0(h,c))) = sK0(h,c) ) ),
inference(superposition,[status(thm)],[c_121728,c_122179]) ).
tcf(c_125792,plain,
! [X0: $i] :
( ( apply(beta,sK2(beta,b,apply(beta,X0))) = apply(beta,X0) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_122179]) ).
tcf(c_125793,plain,
( injection(h)
| ( apply(beta,sK2(beta,b,sK1(h,c))) = sK1(h,c) ) ),
inference(superposition,[status(thm)],[c_121790,c_122179]) ).
tcf(c_125794,plain,
! [X0: $i] :
( ( apply(beta,sK2(beta,b,sK2(h,c,X0))) = sK2(h,c,X0) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_122179]) ).
tcf(c_125795,plain,
apply(beta,sK2(beta,b,zero(c))) = zero(c),
inference(superposition,[status(thm)],[c_123669,c_122179]) ).
tcf(c_125796,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK5(X2,X0,e,c,X1))) = sK5(X2,X0,e,c,X1) )
| ( subtract(e,sK6(X2,X0,e,c,X1),subtract(e,sK6(X2,X0,e,c,X1),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122179]) ).
tcf(c_125896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK2(delta,e,zero(r)))) = sK2(delta,e,zero(r)) )
| ~ exact(X2,delta)
| ~ morphism(delta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(delta,e,zero(r)),X1)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_125054,c_63]) ).
tcf(c_125897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X2,X3,sK2(delta,e,zero(r))),X3)
| ~ exact(X2,delta)
| ~ morphism(delta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(delta,e,zero(r)),X1)
| ( zero(X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_125054,c_62]) ).
tcf(c_125900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(delta,e,zero(r)) = X0 )
| ~ injection(delta)
| ~ element(X0,X1)
| ~ morphism(delta,X1,X2)
| ~ element(sK2(delta,e,zero(r)),X1)
| ( apply(delta,X0) != zero(r) ) ),
inference(superposition,[status(thm)],[c_125054,c_51]) ).
tcf(c_125924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK2(beta,b,zero(c)))) = sK2(beta,b,zero(c)) )
| ~ exact(X2,beta)
| ~ morphism(beta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(beta,b,zero(c)),X1)
| ( zero(X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_125795,c_63]) ).
tcf(c_125925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X2,X3,sK2(beta,b,zero(c))),X3)
| ~ exact(X2,beta)
| ~ morphism(beta,X1,X0)
| ~ morphism(X2,X3,X1)
| ~ element(sK2(beta,b,zero(c)),X1)
| ( zero(X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_125795,c_62]) ).
tcf(c_125928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(beta,b,zero(c)) = X0 )
| ~ injection(beta)
| ~ element(X0,X1)
| ~ morphism(beta,X1,X2)
| ~ element(sK2(beta,b,zero(c)),X1)
| ( apply(beta,X0) != zero(c) ) ),
inference(superposition,[status(thm)],[c_125795,c_51]) ).
tcf(c_125970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(X1,X4,subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = sK6(X0,X2,X1,e,X3) )
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122552,c_74]) ).
tcf(c_125971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( subtract(X1,sK6(X0,X2,X1,e,X3),sK6(X0,X2,X1,e,X3)) = zero(X1) )
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122552,c_73]) ).
tcf(c_125972,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124062]) ).
tcf(c_125973,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123168]) ).
tcf(c_125974,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122845]) ).
tcf(c_125975,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122848]) ).
tcf(c_125976,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124061]) ).
tcf(c_125977,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK6(X2,X0,d,e,X1))) = sK6(X2,X0,d,e,X1) )
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122170]) ).
tcf(c_125978,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123167]) ).
tcf(c_125979,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122372]) ).
tcf(c_125980,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122110]) ).
tcf(c_125981,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123989]) ).
tcf(c_125982,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123984]) ).
tcf(c_125983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123164]) ).
tcf(c_125984,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123116]) ).
tcf(c_125985,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123111]) ).
tcf(c_125986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122369]) ).
tcf(c_125987,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122342]) ).
tcf(c_125988,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122338]) ).
tcf(c_125989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122045]) ).
tcf(c_125990,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122002]) ).
tcf(c_125992,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK6(X2,X0,c,e,X1))) = sK6(X2,X0,c,e,X1) )
| ( subtract(e,sK5(X2,X0,c,e,X1),subtract(e,sK5(X2,X0,c,e,X1),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122179]) ).
tcf(c_125993,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124333]) ).
tcf(c_125994,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122173]) ).
tcf(c_125995,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122164]) ).
tcf(c_125996,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124336]) ).
tcf(c_125997,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124339]) ).
tcf(c_125998,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124342]) ).
tcf(c_125999,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122265]) ).
tcf(c_126269,plain,
( surjection(gamma)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_124053]) ).
tcf(c_126270,plain,
( surjection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_124053]) ).
tcf(c_126285,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_124058]) ).
tcf(c_126286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_124058]) ).
tcf(c_126287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_124058]) ).
tcf(c_126288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124058]) ).
tcf(c_126289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124058]) ).
tcf(c_126290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_124058]) ).
tcf(c_126291,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_124058]) ).
tcf(c_126292,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_124058]) ).
tcf(c_126293,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_124058]) ).
tcf(c_126294,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_124058]) ).
tcf(c_126295,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_124058]) ).
tcf(c_126296,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_124058]) ).
tcf(c_126297,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_124058]) ).
tcf(c_126298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124058]) ).
tcf(c_126299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124058]) ).
tcf(c_126412,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_126291]) ).
tcf(c_126413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_126291]) ).
tcf(c_126414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_126291]) ).
tcf(c_126415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126291]) ).
tcf(c_126416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126291]) ).
tcf(c_126417,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_126291]) ).
tcf(c_126418,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_126291]) ).
tcf(c_126419,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_126291]) ).
tcf(c_126420,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_126291]) ).
tcf(c_126421,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_126291]) ).
tcf(c_126422,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_126291]) ).
tcf(c_126423,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_126291]) ).
tcf(c_126424,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_126291]) ).
tcf(c_126425,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126291]) ).
tcf(c_126426,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126291]) ).
tcf(c_126519,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_126296]) ).
tcf(c_126520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_126296]) ).
tcf(c_126521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_126296]) ).
tcf(c_126522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126296]) ).
tcf(c_126523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126296]) ).
tcf(c_126524,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_126296]) ).
tcf(c_126525,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_126296]) ).
tcf(c_126526,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_126296]) ).
tcf(c_126527,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_126296]) ).
tcf(c_126528,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_126296]) ).
tcf(c_126529,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_126296]) ).
tcf(c_126530,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_126296]) ).
tcf(c_126531,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_126296]) ).
tcf(c_126532,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126296]) ).
tcf(c_126533,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126296]) ).
tcf(c_126687,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_126420]) ).
tcf(c_126688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_126420]) ).
tcf(c_126689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_126420]) ).
tcf(c_126690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126420]) ).
tcf(c_126691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126420]) ).
tcf(c_126692,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_126420]) ).
tcf(c_126693,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_126420]) ).
tcf(c_126694,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_126420]) ).
tcf(c_126695,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126420]) ).
tcf(c_126696,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126420]) ).
tcf(c_126749,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_126421]) ).
tcf(c_126750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_126421]) ).
tcf(c_126751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_126421]) ).
tcf(c_126752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126421]) ).
tcf(c_126753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126421]) ).
tcf(c_126754,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_126421]) ).
tcf(c_126755,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_126421]) ).
tcf(c_126756,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_126421]) ).
tcf(c_126757,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_126421]) ).
tcf(c_126758,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_126421]) ).
tcf(c_126759,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_126421]) ).
tcf(c_126760,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_126421]) ).
tcf(c_126761,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_126421]) ).
tcf(c_126762,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_126421]) ).
tcf(c_126763,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126421]) ).
tcf(c_126764,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126421]) ).
tcf(c_126924,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_126424]) ).
tcf(c_126925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_126424]) ).
tcf(c_126926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_126424]) ).
tcf(c_126927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126424]) ).
tcf(c_126928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126424]) ).
tcf(c_126929,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_126424]) ).
tcf(c_126930,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_126424]) ).
tcf(c_126931,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_126424]) ).
tcf(c_126932,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_126424]) ).
tcf(c_126933,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_126424]) ).
tcf(c_126934,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126424]) ).
tcf(c_126935,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126424]) ).
tcf(c_127031,plain,
! [X0: $i] :
( exact(X0,alpha)
| ( apply(alpha,sK5(X0,alpha,e,a,b)) = zero(b) )
| ( subtract(e,sK6(X0,alpha,e,a,b),subtract(e,sK6(X0,alpha,e,a,b),sK8)) = sK8 )
| ~ morphism(X0,e,a) ),
inference(superposition,[status(thm)],[c_76,c_123247]) ).
tcf(c_127032,plain,
! [X0: $i] :
( exact(X0,beta)
| ( apply(beta,sK5(X0,beta,e,b,c)) = zero(c) )
| ( subtract(e,sK6(X0,beta,e,b,c),subtract(e,sK6(X0,beta,e,b,c),sK8)) = sK8 )
| ~ morphism(X0,e,b) ),
inference(superposition,[status(thm)],[c_77,c_123247]) ).
tcf(c_127033,plain,
! [X0: $i] :
( exact(X0,gamma)
| ( apply(gamma,sK5(X0,gamma,e,d,e)) = zero(e) )
| ( subtract(e,sK6(X0,gamma,e,d,e),subtract(e,sK6(X0,gamma,e,d,e),sK8)) = sK8 )
| ~ morphism(X0,e,d) ),
inference(superposition,[status(thm)],[c_78,c_123247]) ).
tcf(c_127034,plain,
! [X0: $i] :
( exact(X0,delta)
| ( apply(delta,sK5(X0,delta,e,e,r)) = zero(r) )
| ( subtract(e,sK6(X0,delta,e,e,r),subtract(e,sK6(X0,delta,e,e,r),sK8)) = sK8 )
| ~ morphism(X0,e,e) ),
inference(superposition,[status(thm)],[c_79,c_123247]) ).
tcf(c_127035,plain,
! [X0: $i] :
( exact(X0,f)
| ( apply(f,sK5(X0,f,e,a,d)) = zero(d) )
| ( subtract(e,sK6(X0,f,e,a,d),subtract(e,sK6(X0,f,e,a,d),sK8)) = sK8 )
| ~ morphism(X0,e,a) ),
inference(superposition,[status(thm)],[c_80,c_123247]) ).
tcf(c_127036,plain,
! [X0: $i] :
( exact(X0,g)
| ( apply(g,sK5(X0,g,e,b,e)) = zero(e) )
| ( subtract(e,sK6(X0,g,e,b,e),subtract(e,sK6(X0,g,e,b,e),sK8)) = sK8 )
| ~ morphism(X0,e,b) ),
inference(superposition,[status(thm)],[c_81,c_123247]) ).
tcf(c_127037,plain,
! [X0: $i] :
( exact(X0,h)
| ( apply(h,sK5(X0,h,e,c,r)) = zero(r) )
| ( subtract(e,sK6(X0,h,e,c,r),subtract(e,sK6(X0,h,e,c,r),sK8)) = sK8 )
| ~ morphism(X0,e,c) ),
inference(superposition,[status(thm)],[c_82,c_123247]) ).
tcf(c_127128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(X1,X4,subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = sK5(X3,X0,e,X1,X2) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122540,c_74]) ).
tcf(c_127129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( subtract(X1,sK5(X3,X0,e,X1,X2),sK5(X3,X0,e,X1,X2)) = zero(X1) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122540,c_73]) ).
tcf(c_127130,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126421]) ).
tcf(c_127131,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124062]) ).
tcf(c_127132,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123168]) ).
tcf(c_127133,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122845]) ).
tcf(c_127134,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122848]) ).
tcf(c_127135,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126420]) ).
tcf(c_127136,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124061]) ).
tcf(c_127137,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK5(X2,X0,e,d,X1))) = sK5(X2,X0,e,d,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122170]) ).
tcf(c_127138,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123167]) ).
tcf(c_127139,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122372]) ).
tcf(c_127140,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122110]) ).
tcf(c_127141,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126296]) ).
tcf(c_127142,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126291]) ).
tcf(c_127143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124058]) ).
tcf(c_127144,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123989]) ).
tcf(c_127145,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123984]) ).
tcf(c_127146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123164]) ).
tcf(c_127147,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123116]) ).
tcf(c_127148,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123111]) ).
tcf(c_127149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122369]) ).
tcf(c_127150,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122342]) ).
tcf(c_127151,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122338]) ).
tcf(c_127152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122045]) ).
tcf(c_127153,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122002]) ).
tcf(c_127155,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK5(X2,X0,e,c,X1))) = sK5(X2,X0,e,c,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122179]) ).
tcf(c_127156,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126424]) ).
tcf(c_127157,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124333]) ).
tcf(c_127158,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122173]) ).
tcf(c_127159,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122164]) ).
tcf(c_127160,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124336]) ).
tcf(c_127161,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124339]) ).
tcf(c_127162,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124342]) ).
tcf(c_127163,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122265]) ).
tcf(c_127511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(X1,X4,subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = sK6(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122549,c_74]) ).
tcf(c_127512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( subtract(X1,sK6(X0,X2,X1,e,X3),sK6(X0,X2,X1,e,X3)) = zero(X1) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122549,c_73]) ).
tcf(c_127513,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126421]) ).
tcf(c_127514,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124062]) ).
tcf(c_127515,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123168]) ).
tcf(c_127516,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122845]) ).
tcf(c_127517,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122848]) ).
tcf(c_127518,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126420]) ).
tcf(c_127519,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124061]) ).
tcf(c_127520,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK6(X2,X0,d,e,X1))) = sK6(X2,X0,d,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122170]) ).
tcf(c_127521,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123167]) ).
tcf(c_127522,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122372]) ).
tcf(c_127523,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122110]) ).
tcf(c_127524,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126296]) ).
tcf(c_127525,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126291]) ).
tcf(c_127526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124058]) ).
tcf(c_127527,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123989]) ).
tcf(c_127528,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123984]) ).
tcf(c_127529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123164]) ).
tcf(c_127530,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123116]) ).
tcf(c_127531,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123111]) ).
tcf(c_127532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122369]) ).
tcf(c_127533,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122342]) ).
tcf(c_127535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122045]) ).
tcf(c_127536,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122002]) ).
tcf(c_127538,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK6(X2,X0,c,e,X1))) = sK6(X2,X0,c,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122179]) ).
tcf(c_127539,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126424]) ).
tcf(c_127540,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124333]) ).
tcf(c_127541,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122173]) ).
tcf(c_127542,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122164]) ).
tcf(c_127543,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124336]) ).
tcf(c_127544,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124339]) ).
tcf(c_127545,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124342]) ).
tcf(c_127546,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122265]) ).
tcf(c_127941,plain,
( surjection(gamma)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_126412]) ).
tcf(c_127942,plain,
( surjection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_126412]) ).
tcf(c_127960,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(b,apply(alpha,sK3(X0,X1,a)),apply(alpha,sK3(X0,X1,a))) = zero(b) )
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_59,c_122012]) ).
tcf(c_127961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,a,X3)) = sK5(X0,X2,X1,a,X3) )
| ( subtract(b,apply(alpha,sK5(X0,X2,X1,a,X3)),apply(alpha,sK5(X0,X2,X1,a,X3))) = zero(b) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_67,c_122012]) ).
tcf(c_127962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,a,X3),X1)
| ( subtract(b,apply(alpha,sK5(X0,X2,X1,a,X3)),apply(alpha,sK5(X0,X2,X1,a,X3))) = zero(b) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_65,c_122012]) ).
tcf(c_127963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,a,X1,X2)) = zero(X2) )
| ( subtract(b,apply(alpha,sK6(X3,X0,a,X1,X2)),apply(alpha,sK6(X3,X0,a,X1,X2))) = zero(b) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122012]) ).
tcf(c_127964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,a,X1,X2),X1)
| ( subtract(b,apply(alpha,sK6(X3,X0,a,X1,X2)),apply(alpha,sK6(X3,X0,a,X1,X2))) = zero(b) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122012]) ).
tcf(c_127965,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,apply(alpha,subtract(a,X1,X0)),apply(alpha,subtract(a,X1,X0))) = zero(b) )
| ~ element(X1,a)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_72,c_122012]) ).
tcf(c_127966,plain,
( injection(f)
| ( subtract(b,apply(alpha,sK0(f,a)),apply(alpha,sK0(f,a))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121726,c_122012]) ).
tcf(c_127967,plain,
( injection(f)
| ( subtract(b,apply(alpha,sK1(f,a)),apply(alpha,sK1(f,a))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121788,c_122012]) ).
tcf(c_127968,plain,
! [X0: $i] :
( ( subtract(b,apply(alpha,sK2(alpha,a,X0)),apply(alpha,sK2(alpha,a,X0))) = zero(b) )
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_122012]) ).
tcf(c_127969,plain,
! [X0: $i] :
( ( subtract(b,apply(alpha,sK2(f,a,X0)),apply(alpha,sK2(f,a,X0))) = zero(b) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_122012]) ).
tcf(c_127970,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,apply(alpha,sK5(X2,X0,e,a,X1)),apply(alpha,sK5(X2,X0,e,a,X1))) = zero(b) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122012]) ).
tcf(c_127971,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,a,X1),subtract(e,sK6(X2,X0,e,a,X1),sK8)) = sK8 )
| ( subtract(b,apply(alpha,sK5(X2,X0,e,a,X1)),apply(alpha,sK5(X2,X0,e,a,X1))) = zero(b) )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122012]) ).
tcf(c_127972,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,apply(alpha,sK6(X2,X0,a,e,X1)),apply(alpha,sK6(X2,X0,a,e,X1))) = zero(b) )
| ( subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122012]) ).
tcf(c_127973,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,a,e,X1),subtract(e,sK5(X2,X0,a,e,X1),sK8)) = sK8 )
| ( subtract(b,apply(alpha,sK6(X2,X0,a,e,X1)),apply(alpha,sK6(X2,X0,a,e,X1))) = zero(b) )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122012]) ).
tcf(c_128064,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(c,apply(beta,sK3(X0,X1,b)),apply(beta,sK3(X0,X1,b))) = zero(c) )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_122032]) ).
tcf(c_128065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(c,apply(beta,sK5(X0,X2,X1,b,X3)),apply(beta,sK5(X0,X2,X1,b,X3))) = zero(c) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_122032]) ).
tcf(c_128066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(c,apply(beta,sK5(X0,X2,X1,b,X3)),apply(beta,sK5(X0,X2,X1,b,X3))) = zero(c) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_122032]) ).
tcf(c_128067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(c,apply(beta,sK6(X3,X0,b,X1,X2)),apply(beta,sK6(X3,X0,b,X1,X2))) = zero(c) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122032]) ).
tcf(c_128068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(c,apply(beta,sK6(X3,X0,b,X1,X2)),apply(beta,sK6(X3,X0,b,X1,X2))) = zero(c) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122032]) ).
tcf(c_128069,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,apply(beta,subtract(b,X1,X0)),apply(beta,subtract(b,X1,X0))) = zero(c) )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_122032]) ).
tcf(c_128070,plain,
( injection(beta)
| ( subtract(c,apply(beta,sK0(beta,b)),apply(beta,sK0(beta,b))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121723,c_122032]) ).
tcf(c_128071,plain,
( injection(g)
| ( subtract(c,apply(beta,sK0(g,b)),apply(beta,sK0(g,b))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121727,c_122032]) ).
tcf(c_128072,plain,
! [X0: $i] :
( ( subtract(c,apply(beta,apply(alpha,X0)),apply(beta,apply(alpha,X0))) = zero(c) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_122032]) ).
tcf(c_128073,plain,
( injection(beta)
| ( subtract(c,apply(beta,sK1(beta,b)),apply(beta,sK1(beta,b))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121785,c_122032]) ).
tcf(c_128074,plain,
( injection(g)
| ( subtract(c,apply(beta,sK1(g,b)),apply(beta,sK1(g,b))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121789,c_122032]) ).
tcf(c_128075,plain,
subtract(c,apply(beta,zero(b)),apply(beta,zero(b))) = zero(c),
inference(superposition,[status(thm)],[c_123652,c_122032]) ).
tcf(c_128076,plain,
! [X0: $i] :
( ( subtract(c,apply(beta,sK2(beta,b,X0)),apply(beta,sK2(beta,b,X0))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_122032]) ).
tcf(c_128077,plain,
! [X0: $i] :
( ( subtract(c,apply(beta,sK2(g,b,X0)),apply(beta,sK2(g,b,X0))) = zero(c) )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_122032]) ).
tcf(c_128078,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,apply(beta,sK5(X2,X0,e,b,X1)),apply(beta,sK5(X2,X0,e,b,X1))) = zero(c) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122032]) ).
tcf(c_128079,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(c,apply(beta,sK5(X2,X0,e,b,X1)),apply(beta,sK5(X2,X0,e,b,X1))) = zero(c) )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122032]) ).
tcf(c_128080,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,apply(beta,sK6(X2,X0,b,e,X1)),apply(beta,sK6(X2,X0,b,e,X1))) = zero(c) )
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122032]) ).
tcf(c_128081,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(c,apply(beta,sK6(X2,X0,b,e,X1)),apply(beta,sK6(X2,X0,b,e,X1))) = zero(c) )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122032]) ).
tcf(c_128219,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,apply(gamma,sK3(X0,X1,d)),apply(gamma,sK3(X0,X1,d))) = zero(e) )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_122108]) ).
tcf(c_128220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),apply(gamma,sK5(X0,X2,X1,d,X3))) = zero(e) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_122108]) ).
tcf(c_128221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),apply(gamma,sK5(X0,X2,X1,d,X3))) = zero(e) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_122108]) ).
tcf(c_128222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),apply(gamma,sK6(X3,X0,d,X1,X2))) = zero(e) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122108]) ).
tcf(c_128223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),apply(gamma,sK6(X3,X0,d,X1,X2))) = zero(e) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122108]) ).
tcf(c_128224,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(gamma,subtract(d,X1,X0)),apply(gamma,subtract(d,X1,X0))) = zero(e) )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_122108]) ).
tcf(c_128225,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,apply(f,X0)),apply(gamma,apply(f,X0))) = zero(e) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_122108]) ).
tcf(c_128226,plain,
! [X0: $i] :
( ( subtract(e,apply(gamma,sK2(gamma,d,X0)),apply(gamma,sK2(gamma,d,X0))) = zero(e) )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_122108]) ).
tcf(c_128227,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),apply(gamma,sK5(X2,X0,e,d,X1))) = zero(e) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122108]) ).
tcf(c_128228,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),apply(gamma,sK5(X2,X0,e,d,X1))) = zero(e) )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122108]) ).
tcf(c_128229,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),apply(gamma,sK6(X2,X0,d,e,X1))) = zero(e) )
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122108]) ).
tcf(c_128230,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),apply(gamma,sK6(X2,X0,d,e,X1))) = zero(e) )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122108]) ).
tcf(c_128344,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(alpha,sK2(alpha,a,sK3(X0,X1,b))) = sK3(X0,X1,b) )
| ~ surjection(alpha)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_122157]) ).
tcf(c_128345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( apply(alpha,sK2(alpha,a,sK5(X0,X2,X1,b,X3))) = sK5(X0,X2,X1,b,X3) )
| ~ surjection(alpha)
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_122157]) ).
tcf(c_128346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( apply(alpha,sK2(alpha,a,sK5(X0,X2,X1,b,X3))) = sK5(X0,X2,X1,b,X3) )
| ~ surjection(alpha)
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_122157]) ).
tcf(c_128347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( apply(alpha,sK2(alpha,a,sK6(X3,X0,b,X1,X2))) = sK6(X3,X0,b,X1,X2) )
| ~ surjection(alpha)
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122157]) ).
tcf(c_128348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( apply(alpha,sK2(alpha,a,sK6(X3,X0,b,X1,X2))) = sK6(X3,X0,b,X1,X2) )
| ~ surjection(alpha)
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122157]) ).
tcf(c_128349,plain,
! [X0: $i,X1: $i] :
( ( apply(alpha,sK2(alpha,a,subtract(b,X1,X0))) = subtract(b,X1,X0) )
| ~ surjection(alpha)
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_122157]) ).
tcf(c_128350,plain,
( injection(beta)
| ( apply(alpha,sK2(alpha,a,sK0(beta,b))) = sK0(beta,b) )
| ~ surjection(alpha) ),
inference(superposition,[status(thm)],[c_121723,c_122157]) ).
tcf(c_128351,plain,
( injection(g)
| ( apply(alpha,sK2(alpha,a,sK0(g,b))) = sK0(g,b) )
| ~ surjection(alpha) ),
inference(superposition,[status(thm)],[c_121727,c_122157]) ).
tcf(c_128352,plain,
! [X0: $i] :
( ( apply(alpha,sK2(alpha,a,apply(alpha,X0))) = apply(alpha,X0) )
| ~ surjection(alpha)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_122157]) ).
tcf(c_128353,plain,
( injection(beta)
| ( apply(alpha,sK2(alpha,a,sK1(beta,b))) = sK1(beta,b) )
| ~ surjection(alpha) ),
inference(superposition,[status(thm)],[c_121785,c_122157]) ).
tcf(c_128354,plain,
( injection(g)
| ( apply(alpha,sK2(alpha,a,sK1(g,b))) = sK1(g,b) )
| ~ surjection(alpha) ),
inference(superposition,[status(thm)],[c_121789,c_122157]) ).
tcf(c_128355,plain,
( ( apply(alpha,sK2(alpha,a,zero(b))) = zero(b) )
| ~ surjection(alpha) ),
inference(superposition,[status(thm)],[c_123652,c_122157]) ).
tcf(c_128356,plain,
! [X0: $i] :
( ( apply(alpha,sK2(alpha,a,sK2(beta,b,X0))) = sK2(beta,b,X0) )
| ~ surjection(alpha)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_122157]) ).
tcf(c_128357,plain,
! [X0: $i] :
( ( apply(alpha,sK2(alpha,a,sK2(g,b,X0))) = sK2(g,b,X0) )
| ~ surjection(g)
| ~ surjection(alpha)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_122157]) ).
tcf(c_128358,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK5(X2,X0,e,b,X1))) = sK5(X2,X0,e,b,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122157]) ).
tcf(c_128359,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK5(X2,X0,e,b,X1))) = sK5(X2,X0,e,b,X1) )
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122157]) ).
tcf(c_128360,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK6(X2,X0,b,e,X1))) = sK6(X2,X0,b,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122157]) ).
tcf(c_128361,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK6(X2,X0,b,e,X1))) = sK6(X2,X0,b,e,X1) )
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122157]) ).
tcf(c_128470,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_126417]) ).
tcf(c_128471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_126417]) ).
tcf(c_128472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_126417]) ).
tcf(c_128473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_126417]) ).
tcf(c_128474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_126417]) ).
tcf(c_128475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_126417]) ).
tcf(c_128476,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_126417]) ).
tcf(c_128477,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_126417]) ).
tcf(c_128478,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_126417]) ).
tcf(c_128479,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_126417]) ).
tcf(c_128480,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_126417]) ).
tcf(c_128481,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_126417]) ).
tcf(c_128482,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_126417]) ).
tcf(c_128483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_126417]) ).
tcf(c_128484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_126417]) ).
tcf(c_128485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_126417]) ).
tcf(c_128486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_126417]) ).
tcf(c_128642,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_128476]) ).
tcf(c_128643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_128476]) ).
tcf(c_128644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_128476]) ).
tcf(c_128645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128476]) ).
tcf(c_128646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128476]) ).
tcf(c_128647,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_128476]) ).
tcf(c_128648,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_128476]) ).
tcf(c_128649,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_128476]) ).
tcf(c_128650,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_128476]) ).
tcf(c_128651,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_128476]) ).
tcf(c_128652,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_128476]) ).
tcf(c_128653,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_128476]) ).
tcf(c_128654,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_128476]) ).
tcf(c_128655,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128476]) ).
tcf(c_128656,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128476]) ).
tcf(c_128657,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128476]) ).
tcf(c_128658,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128476]) ).
tcf(c_128828,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_128481]) ).
tcf(c_128829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_128481]) ).
tcf(c_128830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_128481]) ).
tcf(c_128831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128481]) ).
tcf(c_128832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128481]) ).
tcf(c_128833,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_128481]) ).
tcf(c_128834,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_128481]) ).
tcf(c_128835,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_128481]) ).
tcf(c_128836,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_128481]) ).
tcf(c_128837,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_128481]) ).
tcf(c_128838,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_128481]) ).
tcf(c_128839,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_128481]) ).
tcf(c_128840,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_128481]) ).
tcf(c_128841,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128481]) ).
tcf(c_128842,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128481]) ).
tcf(c_128843,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128481]) ).
tcf(c_128844,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128481]) ).
tcf(c_128940,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_128650]) ).
tcf(c_128941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_128650]) ).
tcf(c_128942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_128650]) ).
tcf(c_128943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128650]) ).
tcf(c_128944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128650]) ).
tcf(c_128945,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_128650]) ).
tcf(c_128946,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_128650]) ).
tcf(c_128947,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_128650]) ).
tcf(c_128948,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128650]) ).
tcf(c_128949,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128650]) ).
tcf(c_128950,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128650]) ).
tcf(c_128951,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128650]) ).
tcf(c_129082,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_128651]) ).
tcf(c_129083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_128651]) ).
tcf(c_129084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_128651]) ).
tcf(c_129085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128651]) ).
tcf(c_129086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128651]) ).
tcf(c_129087,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_128651]) ).
tcf(c_129088,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_128651]) ).
tcf(c_129089,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_128651]) ).
tcf(c_129090,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_128651]) ).
tcf(c_129091,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_128651]) ).
tcf(c_129092,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_128651]) ).
tcf(c_129093,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_128651]) ).
tcf(c_129094,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_128651]) ).
tcf(c_129095,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_128651]) ).
tcf(c_129096,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128651]) ).
tcf(c_129097,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128651]) ).
tcf(c_129098,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128651]) ).
tcf(c_129099,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128651]) ).
tcf(c_129272,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(gamma,sK2(gamma,d,sK3(X0,X1,e))) = sK3(X0,X1,e) )
| ~ surjection(gamma)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122159]) ).
tcf(c_129273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( apply(gamma,sK2(gamma,d,sK5(X0,X2,X1,e,X3))) = sK5(X0,X2,X1,e,X3) )
| ~ surjection(gamma)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122159]) ).
tcf(c_129274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( apply(gamma,sK2(gamma,d,sK5(X0,X2,X1,e,X3))) = sK5(X0,X2,X1,e,X3) )
| ~ surjection(gamma)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122159]) ).
tcf(c_129275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( apply(gamma,sK2(gamma,d,sK6(X3,X0,e,X1,X2))) = sK6(X3,X0,e,X1,X2) )
| ~ surjection(gamma)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122159]) ).
tcf(c_129276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( apply(gamma,sK2(gamma,d,sK6(X3,X0,e,X1,X2))) = sK6(X3,X0,e,X1,X2) )
| ~ surjection(gamma)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122159]) ).
tcf(c_129277,plain,
! [X0: $i,X1: $i] :
( ( apply(gamma,sK2(gamma,d,subtract(e,X1,X0))) = subtract(e,X1,X0) )
| ~ surjection(gamma)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122159]) ).
tcf(c_129278,plain,
( ( apply(gamma,sK2(gamma,d,sK8)) = sK8 )
| ~ surjection(gamma) ),
inference(superposition,[status(thm)],[c_3530,c_122159]) ).
tcf(c_129279,plain,
( injection(delta)
| ( apply(gamma,sK2(gamma,d,sK0(delta,e))) = sK0(delta,e) )
| ~ surjection(gamma) ),
inference(superposition,[status(thm)],[c_121725,c_122159]) ).
tcf(c_129280,plain,
! [X0: $i] :
( ( apply(gamma,sK2(gamma,d,apply(gamma,X0))) = apply(gamma,X0) )
| ~ surjection(gamma)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122159]) ).
tcf(c_129281,plain,
! [X0: $i] :
( ( apply(gamma,sK2(gamma,d,apply(g,X0))) = apply(g,X0) )
| ~ surjection(gamma)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122159]) ).
tcf(c_129282,plain,
( injection(delta)
| ( apply(gamma,sK2(gamma,d,sK1(delta,e))) = sK1(delta,e) )
| ~ surjection(gamma) ),
inference(superposition,[status(thm)],[c_121787,c_122159]) ).
tcf(c_129283,plain,
( ( apply(gamma,sK2(gamma,d,zero(e))) = zero(e) )
| ~ surjection(gamma) ),
inference(superposition,[status(thm)],[c_121897,c_122159]) ).
tcf(c_129284,plain,
! [X0: $i] :
( ( apply(gamma,sK2(gamma,d,sK2(delta,e,X0))) = sK2(delta,e,X0) )
| ~ surjection(gamma)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122159]) ).
tcf(c_129285,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122159]) ).
tcf(c_129286,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122159]) ).
tcf(c_129287,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122159]) ).
tcf(c_129288,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122159]) ).
tcf(c_129419,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(g,sK2(g,b,sK3(X0,X1,e))) = sK3(X0,X1,e) )
| ~ surjection(g)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122162]) ).
tcf(c_129420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( apply(g,sK2(g,b,sK5(X0,X2,X1,e,X3))) = sK5(X0,X2,X1,e,X3) )
| ~ surjection(g)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122162]) ).
tcf(c_129421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( apply(g,sK2(g,b,sK5(X0,X2,X1,e,X3))) = sK5(X0,X2,X1,e,X3) )
| ~ surjection(g)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122162]) ).
tcf(c_129422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( apply(g,sK2(g,b,sK6(X3,X0,e,X1,X2))) = sK6(X3,X0,e,X1,X2) )
| ~ surjection(g)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122162]) ).
tcf(c_129423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( apply(g,sK2(g,b,sK6(X3,X0,e,X1,X2))) = sK6(X3,X0,e,X1,X2) )
| ~ surjection(g)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122162]) ).
tcf(c_129424,plain,
! [X0: $i,X1: $i] :
( ( apply(g,sK2(g,b,subtract(e,X1,X0))) = subtract(e,X1,X0) )
| ~ surjection(g)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122162]) ).
tcf(c_129425,plain,
( ( apply(g,sK2(g,b,sK8)) = sK8 )
| ~ surjection(g) ),
inference(superposition,[status(thm)],[c_3530,c_122162]) ).
tcf(c_129426,plain,
( injection(delta)
| ( apply(g,sK2(g,b,sK0(delta,e))) = sK0(delta,e) )
| ~ surjection(g) ),
inference(superposition,[status(thm)],[c_121725,c_122162]) ).
tcf(c_129427,plain,
! [X0: $i] :
( ( apply(g,sK2(g,b,apply(gamma,X0))) = apply(gamma,X0) )
| ~ surjection(g)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122162]) ).
tcf(c_129428,plain,
! [X0: $i] :
( ( apply(g,sK2(g,b,apply(g,X0))) = apply(g,X0) )
| ~ surjection(g)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122162]) ).
tcf(c_129429,plain,
( injection(delta)
| ( apply(g,sK2(g,b,sK1(delta,e))) = sK1(delta,e) )
| ~ surjection(g) ),
inference(superposition,[status(thm)],[c_121787,c_122162]) ).
tcf(c_129430,plain,
( ( apply(g,sK2(g,b,zero(e))) = zero(e) )
| ~ surjection(g) ),
inference(superposition,[status(thm)],[c_121897,c_122162]) ).
tcf(c_129431,plain,
! [X0: $i] :
( ( apply(g,sK2(g,b,sK2(delta,e,X0))) = sK2(delta,e,X0) )
| ~ surjection(g)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122162]) ).
tcf(c_129432,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122162]) ).
tcf(c_129433,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122162]) ).
tcf(c_129434,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122162]) ).
tcf(c_129435,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122162]) ).
tcf(c_129576,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(r,apply(delta,sK3(X0,X1,e)),apply(delta,sK3(X0,X1,e))) = zero(r) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_122257]) ).
tcf(c_129577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(r,apply(delta,sK5(X0,X2,X1,e,X3)),apply(delta,sK5(X0,X2,X1,e,X3))) = zero(r) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_122257]) ).
tcf(c_129578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(r,apply(delta,sK5(X0,X2,X1,e,X3)),apply(delta,sK5(X0,X2,X1,e,X3))) = zero(r) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_122257]) ).
tcf(c_129579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(r,apply(delta,sK6(X3,X0,e,X1,X2)),apply(delta,sK6(X3,X0,e,X1,X2))) = zero(r) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122257]) ).
tcf(c_129580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(r,apply(delta,sK6(X3,X0,e,X1,X2)),apply(delta,sK6(X3,X0,e,X1,X2))) = zero(r) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122257]) ).
tcf(c_129581,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,apply(delta,subtract(e,X1,X0)),apply(delta,subtract(e,X1,X0))) = zero(r) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_122257]) ).
tcf(c_129582,plain,
subtract(r,apply(delta,sK8),apply(delta,sK8)) = zero(r),
inference(superposition,[status(thm)],[c_3530,c_122257]) ).
tcf(c_129583,plain,
( injection(delta)
| ( subtract(r,apply(delta,sK0(delta,e)),apply(delta,sK0(delta,e))) = zero(r) ) ),
inference(superposition,[status(thm)],[c_121725,c_122257]) ).
tcf(c_129584,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,apply(gamma,X0)),apply(delta,apply(gamma,X0))) = zero(r) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_122257]) ).
tcf(c_129585,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,apply(g,X0)),apply(delta,apply(g,X0))) = zero(r) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_122257]) ).
tcf(c_129586,plain,
( injection(delta)
| ( subtract(r,apply(delta,sK1(delta,e)),apply(delta,sK1(delta,e))) = zero(r) ) ),
inference(superposition,[status(thm)],[c_121787,c_122257]) ).
tcf(c_129587,plain,
subtract(r,apply(delta,zero(e)),apply(delta,zero(e))) = zero(r),
inference(superposition,[status(thm)],[c_121897,c_122257]) ).
tcf(c_129588,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,sK2(delta,e,X0)),apply(delta,sK2(delta,e,X0))) = zero(r) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_122257]) ).
tcf(c_129589,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(delta,sK5(X2,X0,e,e,X1)),apply(delta,sK5(X2,X0,e,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122257]) ).
tcf(c_129590,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(r,apply(delta,sK5(X2,X0,e,e,X1)),apply(delta,sK5(X2,X0,e,e,X1))) = zero(r) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122257]) ).
tcf(c_129591,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(delta,sK6(X2,X0,e,e,X1)),apply(delta,sK6(X2,X0,e,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122257]) ).
tcf(c_129592,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(r,apply(delta,sK6(X2,X0,e,e,X1)),apply(delta,sK6(X2,X0,e,e,X1))) = zero(r) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122257]) ).
tcf(c_129753,plain,
! [X0: $i,X1: $i] :
( exact(gamma,X0)
| ( apply(gamma,sK6(gamma,X0,d,e,X1)) = sK5(gamma,X0,d,e,X1) )
| ( subtract(e,sK5(gamma,X0,d,e,X1),subtract(e,sK5(gamma,X0,d,e,X1),sK8)) = sK8 )
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_78,c_123518]) ).
tcf(c_129754,plain,
! [X0: $i,X1: $i] :
( exact(g,X0)
| ( apply(g,sK6(g,X0,b,e,X1)) = sK5(g,X0,b,e,X1) )
| ( subtract(e,sK5(g,X0,b,e,X1),subtract(e,sK5(g,X0,b,e,X1),sK8)) = sK8 )
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_81,c_123518]) ).
tcf(c_129767,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK3(X0,X1,r)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_128654]) ).
tcf(c_129768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_128654]) ).
tcf(c_129769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X0,X2,X1,r,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_128654]) ).
tcf(c_129770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128654]) ).
tcf(c_129771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X3,X0,r,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128654]) ).
tcf(c_129772,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,subtract(r,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_128654]) ).
tcf(c_129773,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,iPr_def_10),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122258,c_128654]) ).
tcf(c_129774,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(delta,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_128654]) ).
tcf(c_129775,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,apply(h,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_128654]) ).
tcf(c_129776,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,zero(r)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_122259,c_128654]) ).
tcf(c_129777,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128654]) ).
tcf(c_129778,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128654]) ).
tcf(c_129779,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128654]) ).
tcf(c_129780,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128654]) ).
tcf(c_129881,plain,
! [X0: $i] :
( exact(X0,alpha)
| ( apply(alpha,sK5(X0,alpha,e,a,b)) = zero(b) )
| ( subtract(e,subtract(e,sK6(X0,alpha,e,a,b),sK8),subtract(e,subtract(e,sK6(X0,alpha,e,a,b),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,a) ),
inference(superposition,[status(thm)],[c_76,c_123244]) ).
tcf(c_129882,plain,
! [X0: $i] :
( exact(X0,beta)
| ( apply(beta,sK5(X0,beta,e,b,c)) = zero(c) )
| ( subtract(e,subtract(e,sK6(X0,beta,e,b,c),sK8),subtract(e,subtract(e,sK6(X0,beta,e,b,c),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,b) ),
inference(superposition,[status(thm)],[c_77,c_123244]) ).
tcf(c_129883,plain,
! [X0: $i] :
( exact(X0,gamma)
| ( apply(gamma,sK5(X0,gamma,e,d,e)) = zero(e) )
| ( subtract(e,subtract(e,sK6(X0,gamma,e,d,e),sK8),subtract(e,subtract(e,sK6(X0,gamma,e,d,e),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,d) ),
inference(superposition,[status(thm)],[c_78,c_123244]) ).
tcf(c_129884,plain,
! [X0: $i] :
( exact(X0,delta)
| ( apply(delta,sK5(X0,delta,e,e,r)) = zero(r) )
| ( subtract(e,subtract(e,sK6(X0,delta,e,e,r),sK8),subtract(e,subtract(e,sK6(X0,delta,e,e,r),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,e) ),
inference(superposition,[status(thm)],[c_79,c_123244]) ).
tcf(c_129885,plain,
! [X0: $i] :
( exact(X0,f)
| ( apply(f,sK5(X0,f,e,a,d)) = zero(d) )
| ( subtract(e,subtract(e,sK6(X0,f,e,a,d),sK8),subtract(e,subtract(e,sK6(X0,f,e,a,d),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,a) ),
inference(superposition,[status(thm)],[c_80,c_123244]) ).
tcf(c_129886,plain,
! [X0: $i] :
( exact(X0,g)
| ( apply(g,sK5(X0,g,e,b,e)) = zero(e) )
| ( subtract(e,subtract(e,sK6(X0,g,e,b,e),sK8),subtract(e,subtract(e,sK6(X0,g,e,b,e),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,b) ),
inference(superposition,[status(thm)],[c_81,c_123244]) ).
tcf(c_129887,plain,
! [X0: $i] :
( exact(X0,h)
| ( apply(h,sK5(X0,h,e,c,r)) = zero(r) )
| ( subtract(e,subtract(e,sK6(X0,h,e,c,r),sK8),subtract(e,subtract(e,sK6(X0,h,e,c,r),sK8),sK8)) = sK8 )
| ~ morphism(X0,e,c) ),
inference(superposition,[status(thm)],[c_82,c_123244]) ).
tcf(c_129942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(X1,X4,subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = sK6(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_123162,c_74]) ).
tcf(c_129943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( subtract(X1,sK6(X0,X2,X1,e,X3),sK6(X0,X2,X1,e,X3)) = zero(X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_123162,c_73]) ).
tcf(c_129944,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128651]) ).
tcf(c_129945,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK6(X2,X0,b,e,X1))) = sK6(X2,X0,b,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122157]) ).
tcf(c_129946,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,apply(beta,sK6(X2,X0,b,e,X1)),apply(beta,sK6(X2,X0,b,e,X1))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122032]) ).
tcf(c_129947,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126421]) ).
tcf(c_129948,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124062]) ).
tcf(c_129949,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123168]) ).
tcf(c_129950,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122845]) ).
tcf(c_129951,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122848]) ).
tcf(c_129952,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,apply(alpha,sK6(X2,X0,a,e,X1)),apply(alpha,sK6(X2,X0,a,e,X1))) = zero(b) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122012]) ).
tcf(c_129953,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128650]) ).
tcf(c_129954,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),apply(gamma,sK6(X2,X0,d,e,X1))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122108]) ).
tcf(c_129955,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126420]) ).
tcf(c_129956,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124061]) ).
tcf(c_129957,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK6(X2,X0,d,e,X1))) = sK6(X2,X0,d,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122170]) ).
tcf(c_129958,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123167]) ).
tcf(c_129959,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122372]) ).
tcf(c_129960,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122110]) ).
tcf(c_129961,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(delta,sK6(X2,X0,e,e,X1)),apply(delta,sK6(X2,X0,e,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122257]) ).
tcf(c_129962,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122162]) ).
tcf(c_129963,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK6(X2,X0,e,e,X1))) = sK6(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122159]) ).
tcf(c_129964,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128481]) ).
tcf(c_129965,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128476]) ).
tcf(c_129966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126417]) ).
tcf(c_129967,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126296]) ).
tcf(c_129968,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126291]) ).
tcf(c_129969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124058]) ).
tcf(c_129970,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123989]) ).
tcf(c_129971,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123984]) ).
tcf(c_129972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123164]) ).
tcf(c_129973,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123116]) ).
tcf(c_129974,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123111]) ).
tcf(c_129975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122369]) ).
tcf(c_129976,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122342]) ).
tcf(c_129978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122045]) ).
tcf(c_129979,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122002]) ).
tcf(c_129981,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK6(X2,X0,c,e,X1))) = sK6(X2,X0,c,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122179]) ).
tcf(c_129982,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128654]) ).
tcf(c_129983,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_126424]) ).
tcf(c_129984,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124333]) ).
tcf(c_129985,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122173]) ).
tcf(c_129986,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK6(X2,X0,r,e,X1))) = sK6(X2,X0,r,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122164]) ).
tcf(c_129987,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124336]) ).
tcf(c_129988,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124339]) ).
tcf(c_129989,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),subtract(e,sK2(delta,e,sK6(X2,X0,r,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124342]) ).
tcf(c_129990,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122265]) ).
tcf(c_130370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(X1,X4,subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = sK5(X3,X0,e,X1,X2) )
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_123163,c_74]) ).
tcf(c_130371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( subtract(X1,sK5(X3,X0,e,X1,X2),sK5(X3,X0,e,X1,X2)) = zero(X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_123163,c_73]) ).
tcf(c_130372,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128651]) ).
tcf(c_130373,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(alpha,sK2(alpha,a,sK5(X2,X0,e,b,X1))) = sK5(X2,X0,e,b,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(alpha)
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122157]) ).
tcf(c_130374,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,apply(beta,sK5(X2,X0,e,b,X1)),apply(beta,sK5(X2,X0,e,b,X1))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122032]) ).
tcf(c_130375,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126421]) ).
tcf(c_130376,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124062]) ).
tcf(c_130377,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123168]) ).
tcf(c_130378,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122845]) ).
tcf(c_130379,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122848]) ).
tcf(c_130380,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,apply(alpha,sK5(X2,X0,e,a,X1)),apply(alpha,sK5(X2,X0,e,a,X1))) = zero(b) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122012]) ).
tcf(c_130381,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128650]) ).
tcf(c_130382,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),apply(gamma,sK5(X2,X0,e,d,X1))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122108]) ).
tcf(c_130383,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126420]) ).
tcf(c_130384,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124061]) ).
tcf(c_130385,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,sK5(X2,X0,e,d,X1))) = sK5(X2,X0,e,d,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122170]) ).
tcf(c_130386,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123167]) ).
tcf(c_130387,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122372]) ).
tcf(c_130388,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122110]) ).
tcf(c_130389,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(delta,sK5(X2,X0,e,e,X1)),apply(delta,sK5(X2,X0,e,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122257]) ).
tcf(c_130390,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(g,sK2(g,b,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122162]) ).
tcf(c_130391,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(gamma,sK2(gamma,d,sK5(X2,X0,e,e,X1))) = sK5(X2,X0,e,e,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122159]) ).
tcf(c_130392,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128481]) ).
tcf(c_130393,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128476]) ).
tcf(c_130394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126417]) ).
tcf(c_130395,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126296]) ).
tcf(c_130396,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126291]) ).
tcf(c_130397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124058]) ).
tcf(c_130398,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123989]) ).
tcf(c_130399,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123984]) ).
tcf(c_130400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123164]) ).
tcf(c_130401,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123116]) ).
tcf(c_130403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122369]) ).
tcf(c_130404,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122342]) ).
tcf(c_130406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122045]) ).
tcf(c_130407,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122002]) ).
tcf(c_130409,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(beta,sK2(beta,b,sK5(X2,X0,e,c,X1))) = sK5(X2,X0,e,c,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122179]) ).
tcf(c_130410,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128654]) ).
tcf(c_130411,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_126424]) ).
tcf(c_130412,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124333]) ).
tcf(c_130413,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122173]) ).
tcf(c_130414,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,sK5(X2,X0,e,r,X1))) = sK5(X2,X0,e,r,X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122164]) ).
tcf(c_130415,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),subtract(e,subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124336]) ).
tcf(c_130416,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),subtract(e,subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124339]) ).
tcf(c_130417,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),subtract(e,sK2(delta,e,sK5(X2,X0,e,r,X1)),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124342]) ).
tcf(c_130418,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = iPr_def_10 )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122265]) ).
tcf(c_130792,plain,
! [X0: $i] :
( exact(X0,delta)
| ( subtract(e,sK6(X0,delta,e,e,r),subtract(e,sK6(X0,delta,e,e,r),sK8)) = sK8 )
| ( subtract(e,sK5(X0,delta,e,e,r),subtract(e,sK5(X0,delta,e,e,r),sK8)) = sK8 )
| ~ morphism(X0,e,e) ),
inference(superposition,[status(thm)],[c_79,c_125478]) ).
tcf(c_130803,plain,
( surjection(gamma)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(gamma,d,e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_78,c_128642]) ).
tcf(c_130804,plain,
( surjection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(g,b,e),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_81,c_128642]) ).
tcf(c_130824,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(r,sK3(X0,X1,r),subtract(r,sK3(X0,X1,r),zero(r))) = zero(r) )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_122275]) ).
tcf(c_130825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(r,sK5(X0,X2,X1,r,X3),subtract(r,sK5(X0,X2,X1,r,X3),zero(r))) = zero(r) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_122275]) ).
tcf(c_130826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(r,sK5(X0,X2,X1,r,X3),subtract(r,sK5(X0,X2,X1,r,X3),zero(r))) = zero(r) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_122275]) ).
tcf(c_130827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(r,sK6(X3,X0,r,X1,X2),subtract(r,sK6(X3,X0,r,X1,X2),zero(r))) = zero(r) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122275]) ).
tcf(c_130828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(r,sK6(X3,X0,r,X1,X2),subtract(r,sK6(X3,X0,r,X1,X2),zero(r))) = zero(r) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122275]) ).
tcf(c_130829,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,subtract(r,X1,X0),subtract(r,subtract(r,X1,X0),zero(r))) = zero(r) )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_122275]) ).
tcf(c_130830,plain,
subtract(r,iPr_def_10,subtract(r,iPr_def_10,zero(r))) = zero(r),
inference(superposition,[status(thm)],[c_122258,c_122275]) ).
tcf(c_130831,plain,
! [X0: $i] :
( ( subtract(r,apply(delta,X0),subtract(r,apply(delta,X0),zero(r))) = zero(r) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_122275]) ).
tcf(c_130832,plain,
! [X0: $i] :
( ( subtract(r,apply(h,X0),subtract(r,apply(h,X0),zero(r))) = zero(r) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_122275]) ).
tcf(c_130833,plain,
subtract(r,zero(r),subtract(r,zero(r),zero(r))) = zero(r),
inference(superposition,[status(thm)],[c_122259,c_122275]) ).
tcf(c_130834,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),zero(r))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122275]) ).
tcf(c_130835,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),zero(r))) = zero(r) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122275]) ).
tcf(c_130836,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(r,sK5(X2,X0,e,r,X1),subtract(r,sK5(X2,X0,e,r,X1),zero(r))) = zero(r) )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122275]) ).
tcf(c_130837,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),zero(r))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122275]) ).
tcf(c_130838,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),zero(r))) = zero(r) )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122275]) ).
tcf(c_130839,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(r,sK6(X2,X0,r,e,X1),subtract(r,sK6(X2,X0,r,e,X1),zero(r))) = zero(r) )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122275]) ).
tcf(c_130916,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(d,apply(f,sK3(X0,X1,a)),apply(f,sK3(X0,X1,a))) = zero(d) )
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_59,c_122798]) ).
tcf(c_130917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,a,X3)) = sK5(X0,X2,X1,a,X3) )
| ( subtract(d,apply(f,sK5(X0,X2,X1,a,X3)),apply(f,sK5(X0,X2,X1,a,X3))) = zero(d) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_67,c_122798]) ).
tcf(c_130918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,a,X3),X1)
| ( subtract(d,apply(f,sK5(X0,X2,X1,a,X3)),apply(f,sK5(X0,X2,X1,a,X3))) = zero(d) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_65,c_122798]) ).
tcf(c_130919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,a,X1,X2)) = zero(X2) )
| ( subtract(d,apply(f,sK6(X3,X0,a,X1,X2)),apply(f,sK6(X3,X0,a,X1,X2))) = zero(d) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122798]) ).
tcf(c_130920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,a,X1,X2),X1)
| ( subtract(d,apply(f,sK6(X3,X0,a,X1,X2)),apply(f,sK6(X3,X0,a,X1,X2))) = zero(d) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122798]) ).
tcf(c_130921,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,apply(f,subtract(a,X1,X0)),apply(f,subtract(a,X1,X0))) = zero(d) )
| ~ element(X1,a)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_72,c_122798]) ).
tcf(c_130922,plain,
( injection(f)
| ( subtract(d,apply(f,sK0(f,a)),apply(f,sK0(f,a))) = zero(d) ) ),
inference(superposition,[status(thm)],[c_121726,c_122798]) ).
tcf(c_130923,plain,
( injection(f)
| ( subtract(d,apply(f,sK1(f,a)),apply(f,sK1(f,a))) = zero(d) ) ),
inference(superposition,[status(thm)],[c_121788,c_122798]) ).
tcf(c_130924,plain,
! [X0: $i] :
( ( subtract(d,apply(f,sK2(alpha,a,X0)),apply(f,sK2(alpha,a,X0))) = zero(d) )
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_122798]) ).
tcf(c_130925,plain,
! [X0: $i] :
( ( subtract(d,apply(f,sK2(f,a,X0)),apply(f,sK2(f,a,X0))) = zero(d) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_122798]) ).
tcf(c_130926,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(d,apply(f,sK5(X2,X0,e,a,X1)),apply(f,sK5(X2,X0,e,a,X1))) = zero(d) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122798]) ).
tcf(c_130927,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(d,apply(f,sK5(X2,X0,e,a,X1)),apply(f,sK5(X2,X0,e,a,X1))) = zero(d) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122798]) ).
tcf(c_130928,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,a,X1),subtract(e,sK6(X2,X0,e,a,X1),sK8)) = sK8 )
| ( subtract(d,apply(f,sK5(X2,X0,e,a,X1)),apply(f,sK5(X2,X0,e,a,X1))) = zero(d) )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122798]) ).
tcf(c_130929,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(d,apply(f,sK6(X2,X0,a,e,X1)),apply(f,sK6(X2,X0,a,e,X1))) = zero(d) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122798]) ).
tcf(c_130930,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(d,apply(f,sK6(X2,X0,a,e,X1)),apply(f,sK6(X2,X0,a,e,X1))) = zero(d) )
| ( subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122798]) ).
tcf(c_130931,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,a,e,X1),subtract(e,sK5(X2,X0,a,e,X1),sK8)) = sK8 )
| ( subtract(d,apply(f,sK6(X2,X0,a,e,X1)),apply(f,sK6(X2,X0,a,e,X1))) = zero(d) )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122798]) ).
tcf(c_131086,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,apply(g,sK3(X0,X1,b)),apply(g,sK3(X0,X1,b))) = zero(e) )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_122843]) ).
tcf(c_131087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),apply(g,sK5(X0,X2,X1,b,X3))) = zero(e) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_122843]) ).
tcf(c_131088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),apply(g,sK5(X0,X2,X1,b,X3))) = zero(e) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_122843]) ).
tcf(c_131089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),apply(g,sK6(X3,X0,b,X1,X2))) = zero(e) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122843]) ).
tcf(c_131090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),apply(g,sK6(X3,X0,b,X1,X2))) = zero(e) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122843]) ).
tcf(c_131091,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,apply(g,subtract(b,X1,X0)),apply(g,subtract(b,X1,X0))) = zero(e) )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_122843]) ).
tcf(c_131092,plain,
( injection(beta)
| ( subtract(e,apply(g,sK0(beta,b)),apply(g,sK0(beta,b))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121723,c_122843]) ).
tcf(c_131093,plain,
( injection(g)
| ( subtract(e,apply(g,sK0(g,b)),apply(g,sK0(g,b))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121727,c_122843]) ).
tcf(c_131094,plain,
! [X0: $i] :
( ( subtract(e,apply(g,apply(alpha,X0)),apply(g,apply(alpha,X0))) = zero(e) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_122843]) ).
tcf(c_131095,plain,
( injection(beta)
| ( subtract(e,apply(g,sK1(beta,b)),apply(g,sK1(beta,b))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121785,c_122843]) ).
tcf(c_131096,plain,
( injection(g)
| ( subtract(e,apply(g,sK1(g,b)),apply(g,sK1(g,b))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121789,c_122843]) ).
tcf(c_131097,plain,
subtract(e,apply(g,zero(b)),apply(g,zero(b))) = zero(e),
inference(superposition,[status(thm)],[c_123652,c_122843]) ).
tcf(c_131098,plain,
! [X0: $i] :
( ( subtract(e,apply(g,sK2(beta,b,X0)),apply(g,sK2(beta,b,X0))) = zero(e) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_122843]) ).
tcf(c_131099,plain,
! [X0: $i] :
( ( subtract(e,apply(g,sK2(g,b,X0)),apply(g,sK2(g,b,X0))) = zero(e) )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_122843]) ).
tcf(c_131100,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),apply(g,sK5(X2,X0,e,b,X1))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122843]) ).
tcf(c_131101,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),apply(g,sK5(X2,X0,e,b,X1))) = zero(e) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122843]) ).
tcf(c_131102,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,apply(g,sK5(X2,X0,e,b,X1)),apply(g,sK5(X2,X0,e,b,X1))) = zero(e) )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122843]) ).
tcf(c_131103,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),apply(g,sK6(X2,X0,b,e,X1))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122843]) ).
tcf(c_131104,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),apply(g,sK6(X2,X0,b,e,X1))) = zero(e) )
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122843]) ).
tcf(c_131105,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,apply(g,sK6(X2,X0,b,e,X1)),apply(g,sK6(X2,X0,b,e,X1))) = zero(e) )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122843]) ).
tcf(c_131310,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(r,apply(h,sK3(X0,X1,c)),apply(h,sK3(X0,X1,c))) = zero(r) )
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_59,c_122871]) ).
tcf(c_131311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,c,X3)) = sK5(X0,X2,X1,c,X3) )
| ( subtract(r,apply(h,sK5(X0,X2,X1,c,X3)),apply(h,sK5(X0,X2,X1,c,X3))) = zero(r) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_67,c_122871]) ).
tcf(c_131312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,c,X3),X1)
| ( subtract(r,apply(h,sK5(X0,X2,X1,c,X3)),apply(h,sK5(X0,X2,X1,c,X3))) = zero(r) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_65,c_122871]) ).
tcf(c_131313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,c,X1,X2)) = zero(X2) )
| ( subtract(r,apply(h,sK6(X3,X0,c,X1,X2)),apply(h,sK6(X3,X0,c,X1,X2))) = zero(r) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_122871]) ).
tcf(c_131314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,c,X1,X2),X1)
| ( subtract(r,apply(h,sK6(X3,X0,c,X1,X2)),apply(h,sK6(X3,X0,c,X1,X2))) = zero(r) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_122871]) ).
tcf(c_131315,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,apply(h,subtract(c,X1,X0)),apply(h,subtract(c,X1,X0))) = zero(r) )
| ~ element(X1,c)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_72,c_122871]) ).
tcf(c_131316,plain,
( injection(h)
| ( subtract(r,apply(h,sK0(h,c)),apply(h,sK0(h,c))) = zero(r) ) ),
inference(superposition,[status(thm)],[c_121728,c_122871]) ).
tcf(c_131317,plain,
! [X0: $i] :
( ( subtract(r,apply(h,apply(beta,X0)),apply(h,apply(beta,X0))) = zero(r) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_122871]) ).
tcf(c_131318,plain,
( injection(h)
| ( subtract(r,apply(h,sK1(h,c)),apply(h,sK1(h,c))) = zero(r) ) ),
inference(superposition,[status(thm)],[c_121790,c_122871]) ).
tcf(c_131319,plain,
! [X0: $i] :
( ( subtract(r,apply(h,sK2(h,c,X0)),apply(h,sK2(h,c,X0))) = zero(r) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_122871]) ).
tcf(c_131320,plain,
subtract(r,apply(h,zero(c)),apply(h,zero(c))) = zero(r),
inference(superposition,[status(thm)],[c_123669,c_122871]) ).
tcf(c_131321,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(h,sK5(X2,X0,e,c,X1)),apply(h,sK5(X2,X0,e,c,X1))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_123163,c_122871]) ).
tcf(c_131322,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(h,sK5(X2,X0,e,c,X1)),apply(h,sK5(X2,X0,e,c,X1))) = zero(r) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122540,c_122871]) ).
tcf(c_131323,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,c,X1),subtract(e,sK6(X2,X0,e,c,X1),sK8)) = sK8 )
| ( subtract(r,apply(h,sK5(X2,X0,e,c,X1)),apply(h,sK5(X2,X0,e,c,X1))) = zero(r) )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122543,c_122871]) ).
tcf(c_131324,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(h,sK6(X2,X0,c,e,X1)),apply(h,sK6(X2,X0,c,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_122871]) ).
tcf(c_131325,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,apply(h,sK6(X2,X0,c,e,X1)),apply(h,sK6(X2,X0,c,e,X1))) = zero(r) )
| ( subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_122871]) ).
tcf(c_131326,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,c,e,X1),subtract(e,sK5(X2,X0,c,e,X1),sK8)) = sK8 )
| ( subtract(r,apply(h,sK6(X2,X0,c,e,X1)),apply(h,sK6(X2,X0,c,e,X1))) = zero(r) )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_122871]) ).
tcf(c_131408,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(b,sK3(X0,X1,b),subtract(b,sK3(X0,X1,b),zero(b))) = zero(b) )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_123654]) ).
tcf(c_131409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(b,sK5(X0,X2,X1,b,X3),subtract(b,sK5(X0,X2,X1,b,X3),zero(b))) = zero(b) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_123654]) ).
tcf(c_131410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(b,sK5(X0,X2,X1,b,X3),subtract(b,sK5(X0,X2,X1,b,X3),zero(b))) = zero(b) )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_123654]) ).
tcf(c_131411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(b,sK6(X3,X0,b,X1,X2),subtract(b,sK6(X3,X0,b,X1,X2),zero(b))) = zero(b) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123654]) ).
tcf(c_131412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(b,sK6(X3,X0,b,X1,X2),subtract(b,sK6(X3,X0,b,X1,X2),zero(b))) = zero(b) )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123654]) ).
tcf(c_131413,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,subtract(b,X1,X0),subtract(b,subtract(b,X1,X0),zero(b))) = zero(b) )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_123654]) ).
tcf(c_131414,plain,
( injection(beta)
| ( subtract(b,sK0(beta,b),subtract(b,sK0(beta,b),zero(b))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121723,c_123654]) ).
tcf(c_131415,plain,
( injection(g)
| ( subtract(b,sK0(g,b),subtract(b,sK0(g,b),zero(b))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121727,c_123654]) ).
tcf(c_131416,plain,
! [X0: $i] :
( ( subtract(b,apply(alpha,X0),subtract(b,apply(alpha,X0),zero(b))) = zero(b) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_123654]) ).
tcf(c_131417,plain,
( injection(beta)
| ( subtract(b,sK1(beta,b),subtract(b,sK1(beta,b),zero(b))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121785,c_123654]) ).
tcf(c_131418,plain,
( injection(g)
| ( subtract(b,sK1(g,b),subtract(b,sK1(g,b),zero(b))) = zero(b) ) ),
inference(superposition,[status(thm)],[c_121789,c_123654]) ).
tcf(c_131419,plain,
subtract(b,zero(b),subtract(b,zero(b),zero(b))) = zero(b),
inference(superposition,[status(thm)],[c_123652,c_123654]) ).
tcf(c_131420,plain,
! [X0: $i] :
( ( subtract(b,sK2(beta,b,X0),subtract(b,sK2(beta,b,X0),zero(b))) = zero(b) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_123654]) ).
tcf(c_131421,plain,
! [X0: $i] :
( ( subtract(b,sK2(g,b,X0),subtract(b,sK2(g,b,X0),zero(b))) = zero(b) )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_123654]) ).
tcf(c_131422,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,sK5(X2,X0,e,b,X1),subtract(b,sK5(X2,X0,e,b,X1),zero(b))) = zero(b) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123654]) ).
tcf(c_131423,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,sK5(X2,X0,e,b,X1),subtract(b,sK5(X2,X0,e,b,X1),zero(b))) = zero(b) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123654]) ).
tcf(c_131424,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(b,sK5(X2,X0,e,b,X1),subtract(b,sK5(X2,X0,e,b,X1),zero(b))) = zero(b) )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123654]) ).
tcf(c_131425,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,sK6(X2,X0,b,e,X1),subtract(b,sK6(X2,X0,b,e,X1),zero(b))) = zero(b) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123654]) ).
tcf(c_131426,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(b,sK6(X2,X0,b,e,X1),subtract(b,sK6(X2,X0,b,e,X1),zero(b))) = zero(b) )
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123654]) ).
tcf(c_131427,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(b,sK6(X2,X0,b,e,X1),subtract(b,sK6(X2,X0,b,e,X1),zero(b))) = zero(b) )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123654]) ).
tcf(c_131549,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(c,sK3(X0,X1,c),subtract(c,sK3(X0,X1,c),zero(c))) = zero(c) )
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_59,c_123671]) ).
tcf(c_131550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,c,X3)) = sK5(X0,X2,X1,c,X3) )
| ( subtract(c,sK5(X0,X2,X1,c,X3),subtract(c,sK5(X0,X2,X1,c,X3),zero(c))) = zero(c) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_67,c_123671]) ).
tcf(c_131551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,c,X3),X1)
| ( subtract(c,sK5(X0,X2,X1,c,X3),subtract(c,sK5(X0,X2,X1,c,X3),zero(c))) = zero(c) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_65,c_123671]) ).
tcf(c_131552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,c,X1,X2)) = zero(X2) )
| ( subtract(c,sK6(X3,X0,c,X1,X2),subtract(c,sK6(X3,X0,c,X1,X2),zero(c))) = zero(c) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123671]) ).
tcf(c_131553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,c,X1,X2),X1)
| ( subtract(c,sK6(X3,X0,c,X1,X2),subtract(c,sK6(X3,X0,c,X1,X2),zero(c))) = zero(c) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123671]) ).
tcf(c_131554,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,subtract(c,X1,X0),subtract(c,subtract(c,X1,X0),zero(c))) = zero(c) )
| ~ element(X1,c)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_72,c_123671]) ).
tcf(c_131555,plain,
( injection(h)
| ( subtract(c,sK0(h,c),subtract(c,sK0(h,c),zero(c))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121728,c_123671]) ).
tcf(c_131556,plain,
! [X0: $i] :
( ( subtract(c,apply(beta,X0),subtract(c,apply(beta,X0),zero(c))) = zero(c) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_123671]) ).
tcf(c_131557,plain,
( injection(h)
| ( subtract(c,sK1(h,c),subtract(c,sK1(h,c),zero(c))) = zero(c) ) ),
inference(superposition,[status(thm)],[c_121790,c_123671]) ).
tcf(c_131558,plain,
! [X0: $i] :
( ( subtract(c,sK2(h,c,X0),subtract(c,sK2(h,c,X0),zero(c))) = zero(c) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_123671]) ).
tcf(c_131559,plain,
subtract(c,zero(c),subtract(c,zero(c),zero(c))) = zero(c),
inference(superposition,[status(thm)],[c_123669,c_123671]) ).
tcf(c_131560,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK5(X2,X0,e,c,X1),subtract(c,sK5(X2,X0,e,c,X1),zero(c))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123671]) ).
tcf(c_131561,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK5(X2,X0,e,c,X1),subtract(c,sK5(X2,X0,e,c,X1),zero(c))) = zero(c) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123671]) ).
tcf(c_131562,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,c,X1),subtract(e,sK6(X2,X0,e,c,X1),sK8)) = sK8 )
| ( subtract(c,sK5(X2,X0,e,c,X1),subtract(c,sK5(X2,X0,e,c,X1),zero(c))) = zero(c) )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123671]) ).
tcf(c_131563,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK6(X2,X0,c,e,X1),subtract(c,sK6(X2,X0,c,e,X1),zero(c))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123671]) ).
tcf(c_131564,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK6(X2,X0,c,e,X1),subtract(c,sK6(X2,X0,c,e,X1),zero(c))) = zero(c) )
| ( subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123671]) ).
tcf(c_131565,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,c,e,X1),subtract(e,sK5(X2,X0,c,e,X1),sK8)) = sK8 )
| ( subtract(c,sK6(X2,X0,c,e,X1),subtract(c,sK6(X2,X0,c,e,X1),zero(c))) = zero(c) )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123671]) ).
tcf(c_131713,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(h,sK2(h,c,apply(delta,sK3(X0,X1,e)))) = apply(delta,sK3(X0,X1,e)) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_124789]) ).
tcf(c_131714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( apply(h,sK2(h,c,apply(delta,sK5(X0,X2,X1,e,X3)))) = apply(delta,sK5(X0,X2,X1,e,X3)) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_124789]) ).
tcf(c_131715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( apply(h,sK2(h,c,apply(delta,sK5(X0,X2,X1,e,X3)))) = apply(delta,sK5(X0,X2,X1,e,X3)) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_124789]) ).
tcf(c_131716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( apply(h,sK2(h,c,apply(delta,sK6(X3,X0,e,X1,X2)))) = apply(delta,sK6(X3,X0,e,X1,X2)) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124789]) ).
tcf(c_131717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( apply(h,sK2(h,c,apply(delta,sK6(X3,X0,e,X1,X2)))) = apply(delta,sK6(X3,X0,e,X1,X2)) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124789]) ).
tcf(c_131718,plain,
! [X0: $i,X1: $i] :
( ( apply(h,sK2(h,c,apply(delta,subtract(e,X1,X0)))) = apply(delta,subtract(e,X1,X0)) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_124789]) ).
tcf(c_131719,plain,
apply(h,sK2(h,c,apply(delta,sK8))) = apply(delta,sK8),
inference(superposition,[status(thm)],[c_3530,c_124789]) ).
tcf(c_131720,plain,
( injection(delta)
| ( apply(h,sK2(h,c,apply(delta,sK0(delta,e)))) = apply(delta,sK0(delta,e)) ) ),
inference(superposition,[status(thm)],[c_121725,c_124789]) ).
tcf(c_131721,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(delta,apply(gamma,X0)))) = apply(delta,apply(gamma,X0)) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_124789]) ).
tcf(c_131722,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(delta,apply(g,X0)))) = apply(delta,apply(g,X0)) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_124789]) ).
tcf(c_131723,plain,
( injection(delta)
| ( apply(h,sK2(h,c,apply(delta,sK1(delta,e)))) = apply(delta,sK1(delta,e)) ) ),
inference(superposition,[status(thm)],[c_121787,c_124789]) ).
tcf(c_131724,plain,
apply(h,sK2(h,c,apply(delta,zero(e)))) = apply(delta,zero(e)),
inference(superposition,[status(thm)],[c_121897,c_124789]) ).
tcf(c_131725,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(delta,sK2(delta,e,X0)))) = apply(delta,sK2(delta,e,X0)) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_124789]) ).
tcf(c_131726,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124789]) ).
tcf(c_131727,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124789]) ).
tcf(c_131728,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124789]) ).
tcf(c_131729,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124789]) ).
tcf(c_131730,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124789]) ).
tcf(c_131731,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124789]) ).
tcf(c_131887,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(h,sK2(h,c,apply(h,sK3(X0,X1,c)))) = apply(h,sK3(X0,X1,c)) )
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_59,c_124790]) ).
tcf(c_131888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,c,X3)) = sK5(X0,X2,X1,c,X3) )
| ( apply(h,sK2(h,c,apply(h,sK5(X0,X2,X1,c,X3)))) = apply(h,sK5(X0,X2,X1,c,X3)) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_67,c_124790]) ).
tcf(c_131889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,c,X3),X1)
| ( apply(h,sK2(h,c,apply(h,sK5(X0,X2,X1,c,X3)))) = apply(h,sK5(X0,X2,X1,c,X3)) )
| ~ morphism(X2,c,X3)
| ~ morphism(X0,X1,c) ),
inference(superposition,[status(thm)],[c_65,c_124790]) ).
tcf(c_131890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,c,X1,X2)) = zero(X2) )
| ( apply(h,sK2(h,c,apply(h,sK6(X3,X0,c,X1,X2)))) = apply(h,sK6(X3,X0,c,X1,X2)) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124790]) ).
tcf(c_131891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,c,X1,X2),X1)
| ( apply(h,sK2(h,c,apply(h,sK6(X3,X0,c,X1,X2)))) = apply(h,sK6(X3,X0,c,X1,X2)) )
| ~ morphism(X3,c,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124790]) ).
tcf(c_131892,plain,
! [X0: $i,X1: $i] :
( ( apply(h,sK2(h,c,apply(h,subtract(c,X1,X0)))) = apply(h,subtract(c,X1,X0)) )
| ~ element(X1,c)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_72,c_124790]) ).
tcf(c_131893,plain,
( injection(h)
| ( apply(h,sK2(h,c,apply(h,sK0(h,c)))) = apply(h,sK0(h,c)) ) ),
inference(superposition,[status(thm)],[c_121728,c_124790]) ).
tcf(c_131894,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(h,apply(beta,X0)))) = apply(h,apply(beta,X0)) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_124790]) ).
tcf(c_131895,plain,
( injection(h)
| ( apply(h,sK2(h,c,apply(h,sK1(h,c)))) = apply(h,sK1(h,c)) ) ),
inference(superposition,[status(thm)],[c_121790,c_124790]) ).
tcf(c_131896,plain,
! [X0: $i] :
( ( apply(h,sK2(h,c,apply(h,sK2(h,c,X0)))) = apply(h,sK2(h,c,X0)) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_124790]) ).
tcf(c_131897,plain,
apply(h,sK2(h,c,apply(h,zero(c)))) = apply(h,zero(c)),
inference(superposition,[status(thm)],[c_123669,c_124790]) ).
tcf(c_131898,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK5(X2,X0,e,c,X1)))) = apply(h,sK5(X2,X0,e,c,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124790]) ).
tcf(c_131899,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK5(X2,X0,e,c,X1)))) = apply(h,sK5(X2,X0,e,c,X1)) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,c,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124790]) ).
tcf(c_131900,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK5(X2,X0,e,c,X1)))) = apply(h,sK5(X2,X0,e,c,X1)) )
| ( subtract(e,sK6(X2,X0,e,c,X1),subtract(e,sK6(X2,X0,e,c,X1),sK8)) = sK8 )
| ~ morphism(X2,e,c)
| ~ morphism(X0,c,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124790]) ).
tcf(c_131901,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK6(X2,X0,c,e,X1)))) = apply(h,sK6(X2,X0,c,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124790]) ).
tcf(c_131902,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK6(X2,X0,c,e,X1)))) = apply(h,sK6(X2,X0,c,e,X1)) )
| ( subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,c,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124790]) ).
tcf(c_131903,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(h,sK2(h,c,apply(h,sK6(X2,X0,c,e,X1)))) = apply(h,sK6(X2,X0,c,e,X1)) )
| ( subtract(e,sK5(X2,X0,c,e,X1),subtract(e,sK5(X2,X0,c,e,X1),sK8)) = sK8 )
| ~ morphism(X2,c,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124790]) ).
tcf(c_132057,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,sK3(X0,X1,e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_128647]) ).
tcf(c_132058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_128647]) ).
tcf(c_132059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK5(X0,X2,X1,e,X3)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_128647]) ).
tcf(c_132060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_128647]) ).
tcf(c_132061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X4,sK6(X3,X0,e,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,e)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_128647]) ).
tcf(c_132062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X2,subtract(e,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X2,e)
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_128647]) ).
tcf(c_132063,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_128647]) ).
tcf(c_132064,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK0(delta,e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_128647]) ).
tcf(c_132065,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(gamma,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_128647]) ).
tcf(c_132066,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,apply(g,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_128647]) ).
tcf(c_132067,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,sK1(delta,e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_128647]) ).
tcf(c_132068,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X0,zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_128647]) ).
tcf(c_132069,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,sK2(delta,e,X0)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_128647]) ).
tcf(c_132070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_128647]) ).
tcf(c_132071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_128647]) ).
tcf(c_132072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK5(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_128647]) ).
tcf(c_132073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_128647]) ).
tcf(c_132074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_128647]) ).
tcf(c_132075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X3,sK6(X2,X0,e,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X3,e)
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_128647]) ).
tcf(c_132331,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_132063]) ).
tcf(c_132332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_132063]) ).
tcf(c_132333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_132063]) ).
tcf(c_132334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132063]) ).
tcf(c_132335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132063]) ).
tcf(c_132336,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_132063]) ).
tcf(c_132337,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_132063]) ).
tcf(c_132338,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_132063]) ).
tcf(c_132339,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_132063]) ).
tcf(c_132340,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_132063]) ).
tcf(c_132341,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_132063]) ).
tcf(c_132342,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_132063]) ).
tcf(c_132343,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_132063]) ).
tcf(c_132344,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132063]) ).
tcf(c_132345,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132063]) ).
tcf(c_132346,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132063]) ).
tcf(c_132347,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132063]) ).
tcf(c_132348,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132063]) ).
tcf(c_132349,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132063]) ).
tcf(c_132561,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_132068]) ).
tcf(c_132562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_132068]) ).
tcf(c_132563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_132068]) ).
tcf(c_132564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132068]) ).
tcf(c_132565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132068]) ).
tcf(c_132566,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_132068]) ).
tcf(c_132567,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK8,zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_3530,c_132068]) ).
tcf(c_132568,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK0(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121725,c_132068]) ).
tcf(c_132569,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_132068]) ).
tcf(c_132570,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_132068]) ).
tcf(c_132571,plain,
( injection(delta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK1(delta,e),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121787,c_132068]) ).
tcf(c_132572,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,zero(e),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_121897,c_132068]) ).
tcf(c_132573,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_132068]) ).
tcf(c_132574,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132068]) ).
tcf(c_132575,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132068]) ).
tcf(c_132576,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132068]) ).
tcf(c_132577,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132068]) ).
tcf(c_132578,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132068]) ).
tcf(c_132579,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132068]) ).
tcf(c_132711,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_132339]) ).
tcf(c_132712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_132339]) ).
tcf(c_132713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_132339]) ).
tcf(c_132714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132339]) ).
tcf(c_132715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132339]) ).
tcf(c_132716,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_132339]) ).
tcf(c_132717,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_132339]) ).
tcf(c_132718,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_132339]) ).
tcf(c_132719,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132339]) ).
tcf(c_132720,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132339]) ).
tcf(c_132721,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132339]) ).
tcf(c_132722,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132339]) ).
tcf(c_132723,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132339]) ).
tcf(c_132724,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132339]) ).
tcf(c_132807,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK3(X0,X1,b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_59,c_132340]) ).
tcf(c_132808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,b,X3)) = sK5(X0,X2,X1,b,X3) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_67,c_132340]) ).
tcf(c_132809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,b,X3),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X0,X2,X1,b,X3)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,X3)
| ~ morphism(X0,X1,b) ),
inference(superposition,[status(thm)],[c_65,c_132340]) ).
tcf(c_132810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,b,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132340]) ).
tcf(c_132811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,b,X1,X2),X1)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X3,X0,b,X1,X2)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X3,b,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132340]) ).
tcf(c_132812,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,subtract(b,X1,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_72,c_132340]) ).
tcf(c_132813,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121723,c_132340]) ).
tcf(c_132814,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK0(g,b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121727,c_132340]) ).
tcf(c_132815,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,apply(alpha,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_132340]) ).
tcf(c_132816,plain,
( injection(beta)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(beta,b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121785,c_132340]) ).
tcf(c_132817,plain,
( injection(g)
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK1(g,b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_121789,c_132340]) ).
tcf(c_132818,plain,
subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,zero(b)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8,
inference(superposition,[status(thm)],[c_123652,c_132340]) ).
tcf(c_132819,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(beta,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_132340]) ).
tcf(c_132820,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK2(g,b,X0)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ surjection(g)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_132340]) ).
tcf(c_132821,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132340]) ).
tcf(c_132822,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,b,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132340]) ).
tcf(c_132823,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,b,X1),subtract(e,sK6(X2,X0,e,b,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK5(X2,X0,e,b,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,b)
| ~ morphism(X0,b,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132340]) ).
tcf(c_132824,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132340]) ).
tcf(c_132825,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,b,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132340]) ).
tcf(c_132826,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,b,e,X1),subtract(e,sK5(X2,X0,b,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,subtract(e,apply(g,sK6(X2,X0,b,e,X1)),sK8),sK8),sK8),sK8),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,b,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132340]) ).
tcf(c_132939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjection(X0)
| ( subtract(X2,subtract(X2,X3,sK3(X0,X1,X2)),subtract(X2,X3,sK3(X0,X1,X2))) = zero(X2) )
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_59,c_121896]) ).
tcf(c_132940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| ( apply(X0,sK6(X0,X3,X1,X2,X4)) = sK5(X0,X3,X1,X2,X4) )
| ( subtract(X2,subtract(X2,X5,sK5(X0,X3,X1,X2,X4)),subtract(X2,X5,sK5(X0,X3,X1,X2,X4))) = zero(X2) )
| ~ element(X5,X2)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_67,c_121896]) ).
tcf(c_132941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| element(sK6(X0,X3,X1,X2,X4),X1)
| ( subtract(X2,subtract(X2,X5,sK5(X0,X3,X1,X2,X4)),subtract(X2,X5,sK5(X0,X3,X1,X2,X4))) = zero(X2) )
| ~ element(X5,X2)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_121896]) ).
tcf(c_132942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| ( apply(X3,sK5(X0,X3,X1,X2,X4)) = zero(X4) )
| ( subtract(X1,subtract(X1,X5,sK6(X0,X3,X1,X2,X4)),subtract(X1,X5,sK6(X0,X3,X1,X2,X4))) = zero(X1) )
| ~ element(X5,X1)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_121896]) ).
tcf(c_132943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( exact(X0,X3)
| element(sK5(X0,X3,X1,X2,X4),X2)
| ( subtract(X1,subtract(X1,X5,sK6(X0,X3,X1,X2,X4)),subtract(X1,X5,sK6(X0,X3,X1,X2,X4))) = zero(X1) )
| ~ element(X5,X1)
| ~ morphism(X3,X2,X4)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_121896]) ).
tcf(c_132944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(X1,subtract(X1,X3,subtract(X1,X2,X0)),subtract(X1,X3,subtract(X1,X2,X0))) = zero(X1) )
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_72,c_121896]) ).
tcf(c_132945,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,X0,sK8),subtract(e,X0,sK8)) = zero(e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_3530,c_121896]) ).
tcf(c_132946,plain,
! [X0: $i] :
( ( subtract(r,subtract(r,X0,iPr_def_10),subtract(r,X0,iPr_def_10)) = zero(r) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_122258,c_121896]) ).
tcf(c_132947,plain,
! [X0: $i] :
( injection(beta)
| ( subtract(b,subtract(b,X0,sK0(beta,b)),subtract(b,X0,sK0(beta,b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121723,c_121896]) ).
tcf(c_132948,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,X0,sK0(delta,e)),subtract(e,X0,sK0(delta,e))) = zero(e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121725,c_121896]) ).
tcf(c_132949,plain,
! [X0: $i] :
( injection(f)
| ( subtract(a,subtract(a,X0,sK0(f,a)),subtract(a,X0,sK0(f,a))) = zero(a) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121726,c_121896]) ).
tcf(c_132950,plain,
! [X0: $i] :
( injection(g)
| ( subtract(b,subtract(b,X0,sK0(g,b)),subtract(b,X0,sK0(g,b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121727,c_121896]) ).
tcf(c_132951,plain,
! [X0: $i] :
( injection(h)
| ( subtract(c,subtract(c,X0,sK0(h,c)),subtract(c,X0,sK0(h,c))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121728,c_121896]) ).
tcf(c_132952,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,subtract(b,X1,apply(alpha,X0)),subtract(b,X1,apply(alpha,X0))) = zero(b) )
| ~ element(X1,b)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121757,c_121896]) ).
tcf(c_132953,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,subtract(c,X1,apply(beta,X0)),subtract(c,X1,apply(beta,X0))) = zero(c) )
| ~ element(X1,c)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121758,c_121896]) ).
tcf(c_132954,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,apply(gamma,X0)),subtract(e,X1,apply(gamma,X0))) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_121896]) ).
tcf(c_132955,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,subtract(r,X1,apply(delta,X0)),subtract(r,X1,apply(delta,X0))) = zero(r) )
| ~ element(X1,r)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_121896]) ).
tcf(c_132956,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,subtract(d,X1,apply(f,X0)),subtract(d,X1,apply(f,X0))) = zero(d) )
| ~ element(X1,d)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_121896]) ).
tcf(c_132957,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,apply(g,X0)),subtract(e,X1,apply(g,X0))) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_121896]) ).
tcf(c_132958,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,subtract(r,X1,apply(h,X0)),subtract(r,X1,apply(h,X0))) = zero(r) )
| ~ element(X1,r)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_121896]) ).
tcf(c_132959,plain,
! [X0: $i] :
( injection(beta)
| ( subtract(b,subtract(b,X0,sK1(beta,b)),subtract(b,X0,sK1(beta,b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121785,c_121896]) ).
tcf(c_132960,plain,
! [X0: $i] :
( injection(delta)
| ( subtract(e,subtract(e,X0,sK1(delta,e)),subtract(e,X0,sK1(delta,e))) = zero(e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121787,c_121896]) ).
tcf(c_132961,plain,
! [X0: $i] :
( injection(f)
| ( subtract(a,subtract(a,X0,sK1(f,a)),subtract(a,X0,sK1(f,a))) = zero(a) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121788,c_121896]) ).
tcf(c_132962,plain,
! [X0: $i] :
( injection(g)
| ( subtract(b,subtract(b,X0,sK1(g,b)),subtract(b,X0,sK1(g,b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121789,c_121896]) ).
tcf(c_132963,plain,
! [X0: $i] :
( injection(h)
| ( subtract(c,subtract(c,X0,sK1(h,c)),subtract(c,X0,sK1(h,c))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121790,c_121896]) ).
tcf(c_132964,plain,
! [X0: $i] :
( ( subtract(b,subtract(b,X0,zero(b)),subtract(b,X0,zero(b))) = zero(b) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_123652,c_121896]) ).
tcf(c_132965,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,X0,zero(e)),subtract(e,X0,zero(e))) = zero(e) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121897,c_121896]) ).
tcf(c_132966,plain,
! [X0: $i,X1: $i] :
( ( subtract(a,subtract(a,X1,sK2(alpha,a,X0)),subtract(a,X1,sK2(alpha,a,X0))) = zero(a) )
| ~ surjection(alpha)
| ~ element(X1,a)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_121896]) ).
tcf(c_132967,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,subtract(b,X1,sK2(beta,b,X0)),subtract(b,X1,sK2(beta,b,X0))) = zero(b) )
| ~ element(X1,b)
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121937,c_121896]) ).
tcf(c_132968,plain,
! [X0: $i,X1: $i] :
( ( subtract(d,subtract(d,X1,sK2(gamma,d,X0)),subtract(d,X1,sK2(gamma,d,X0))) = zero(d) )
| ~ surjection(gamma)
| ~ element(X1,d)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_121896]) ).
tcf(c_132969,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,X1,sK2(delta,e,X0)),subtract(e,X1,sK2(delta,e,X0))) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_121896]) ).
tcf(c_132970,plain,
! [X0: $i,X1: $i] :
( ( subtract(a,subtract(a,X1,sK2(f,a,X0)),subtract(a,X1,sK2(f,a,X0))) = zero(a) )
| ~ element(X1,a)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_121896]) ).
tcf(c_132971,plain,
! [X0: $i,X1: $i] :
( ( subtract(b,subtract(b,X1,sK2(g,b,X0)),subtract(b,X1,sK2(g,b,X0))) = zero(b) )
| ~ surjection(g)
| ~ element(X1,b)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121920,c_121896]) ).
tcf(c_132972,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,subtract(c,X1,sK2(h,c,X0)),subtract(c,X1,sK2(h,c,X0))) = zero(c) )
| ~ element(X1,c)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121922,c_121896]) ).
tcf(c_132973,plain,
! [X0: $i] :
( ( subtract(c,subtract(c,X0,zero(c)),subtract(c,X0,zero(c))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_123669,c_121896]) ).
tcf(c_132974,plain,
! [X0: $i] :
( ( subtract(r,subtract(r,X0,zero(r)),subtract(r,X0,zero(r))) = zero(r) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_122259,c_121896]) ).
tcf(c_132975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(X1,subtract(X1,X4,sK5(X3,X0,e,X1,X2)),subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = zero(X1) )
| ( subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_123163,c_121896]) ).
tcf(c_132976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(X1,subtract(X1,X4,sK5(X3,X0,e,X1,X2)),subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = zero(X1) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122540,c_121896]) ).
tcf(c_132977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X3,X0)
| ( subtract(e,sK6(X3,X0,e,X1,X2),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = sK8 )
| ( subtract(X1,subtract(X1,X4,sK5(X3,X0,e,X1,X2)),subtract(X1,X4,sK5(X3,X0,e,X1,X2))) = zero(X1) )
| ~ element(X4,X1)
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122543,c_121896]) ).
tcf(c_132978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(X1,subtract(X1,X4,sK6(X0,X2,X1,e,X3)),subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = zero(X1) )
| ( subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_123162,c_121896]) ).
tcf(c_132979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(X1,subtract(X1,X4,sK6(X0,X2,X1,e,X3)),subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = zero(X1) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),sK8)) = sK8 )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122549,c_121896]) ).
tcf(c_132980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( exact(X0,X2)
| ( subtract(e,sK5(X0,X2,X1,e,X3),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = sK8 )
| ( subtract(X1,subtract(X1,X4,sK6(X0,X2,X1,e,X3)),subtract(X1,X4,sK6(X0,X2,X1,e,X3))) = zero(X1) )
| ~ element(X4,X1)
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_122552,c_121896]) ).
tcf(c_133341,plain,
( ( apply(gamma,sK2(gamma,d,zero(e))) = zero(e) )
| ( subtract(e,sK3(gamma,d,e),subtract(e,sK3(gamma,d,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_122318,c_129283]) ).
tcf(c_133342,plain,
( ( apply(gamma,sK2(gamma,d,sK8)) = sK8 )
| ( subtract(e,sK3(gamma,d,e),subtract(e,sK3(gamma,d,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_122318,c_129278]) ).
tcf(c_133351,plain,
( ( apply(g,sK2(g,b,zero(e))) = zero(e) )
| ( subtract(e,sK3(g,b,e),subtract(e,sK3(g,b,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_122319,c_129430]) ).
tcf(c_133352,plain,
( ( apply(g,sK2(g,b,sK8)) = sK8 )
| ( subtract(e,sK3(g,b,e),subtract(e,sK3(g,b,e),sK8)) = sK8 ) ),
inference(superposition,[status(thm)],[c_122319,c_129425]) ).
tcf(c_133361,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(c,sK2(h,c,sK3(X0,X1,r)),sK2(h,c,sK3(X0,X1,r))) = zero(c) )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_123701]) ).
tcf(c_133362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(c,sK2(h,c,sK5(X0,X2,X1,r,X3)),sK2(h,c,sK5(X0,X2,X1,r,X3))) = zero(c) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_123701]) ).
tcf(c_133363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(c,sK2(h,c,sK5(X0,X2,X1,r,X3)),sK2(h,c,sK5(X0,X2,X1,r,X3))) = zero(c) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_123701]) ).
tcf(c_133364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(c,sK2(h,c,sK6(X3,X0,r,X1,X2)),sK2(h,c,sK6(X3,X0,r,X1,X2))) = zero(c) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_123701]) ).
tcf(c_133365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(c,sK2(h,c,sK6(X3,X0,r,X1,X2)),sK2(h,c,sK6(X3,X0,r,X1,X2))) = zero(c) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_123701]) ).
tcf(c_133366,plain,
! [X0: $i,X1: $i] :
( ( subtract(c,sK2(h,c,subtract(r,X1,X0)),sK2(h,c,subtract(r,X1,X0))) = zero(c) )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_123701]) ).
tcf(c_133367,plain,
subtract(c,sK2(h,c,iPr_def_10),sK2(h,c,iPr_def_10)) = zero(c),
inference(superposition,[status(thm)],[c_122258,c_123701]) ).
tcf(c_133368,plain,
! [X0: $i] :
( ( subtract(c,sK2(h,c,apply(delta,X0)),sK2(h,c,apply(delta,X0))) = zero(c) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_123701]) ).
tcf(c_133369,plain,
! [X0: $i] :
( ( subtract(c,sK2(h,c,apply(h,X0)),sK2(h,c,apply(h,X0))) = zero(c) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_123701]) ).
tcf(c_133370,plain,
subtract(c,sK2(h,c,zero(r)),sK2(h,c,zero(r))) = zero(c),
inference(superposition,[status(thm)],[c_122259,c_123701]) ).
tcf(c_133371,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK2(h,c,sK5(X2,X0,e,r,X1)),sK2(h,c,sK5(X2,X0,e,r,X1))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_123701]) ).
tcf(c_133372,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK2(h,c,sK5(X2,X0,e,r,X1)),sK2(h,c,sK5(X2,X0,e,r,X1))) = zero(c) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_123701]) ).
tcf(c_133373,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(c,sK2(h,c,sK5(X2,X0,e,r,X1)),sK2(h,c,sK5(X2,X0,e,r,X1))) = zero(c) )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_123701]) ).
tcf(c_133374,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK2(h,c,sK6(X2,X0,r,e,X1)),sK2(h,c,sK6(X2,X0,r,e,X1))) = zero(c) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_123701]) ).
tcf(c_133375,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(c,sK2(h,c,sK6(X2,X0,r,e,X1)),sK2(h,c,sK6(X2,X0,r,e,X1))) = zero(c) )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_123701]) ).
tcf(c_133376,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(c,sK2(h,c,sK6(X2,X0,r,e,X1)),sK2(h,c,sK6(X2,X0,r,e,X1))) = zero(c) )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_123701]) ).
tcf(c_133466,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(a,sK2(f,a,sK3(X0,X1,d)),sK2(f,a,sK3(X0,X1,d))) = zero(a) )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_124315]) ).
tcf(c_133467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(a,sK2(f,a,sK5(X0,X2,X1,d,X3)),sK2(f,a,sK5(X0,X2,X1,d,X3))) = zero(a) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_124315]) ).
tcf(c_133468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(a,sK2(f,a,sK5(X0,X2,X1,d,X3)),sK2(f,a,sK5(X0,X2,X1,d,X3))) = zero(a) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_124315]) ).
tcf(c_133469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(a,sK2(f,a,sK6(X3,X0,d,X1,X2)),sK2(f,a,sK6(X3,X0,d,X1,X2))) = zero(a) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_124315]) ).
tcf(c_133470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(a,sK2(f,a,sK6(X3,X0,d,X1,X2)),sK2(f,a,sK6(X3,X0,d,X1,X2))) = zero(a) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_124315]) ).
tcf(c_133471,plain,
! [X0: $i,X1: $i] :
( ( subtract(a,sK2(f,a,subtract(d,X1,X0)),sK2(f,a,subtract(d,X1,X0))) = zero(a) )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_124315]) ).
tcf(c_133472,plain,
! [X0: $i] :
( ( subtract(a,sK2(f,a,apply(f,X0)),sK2(f,a,apply(f,X0))) = zero(a) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_124315]) ).
tcf(c_133473,plain,
! [X0: $i] :
( ( subtract(a,sK2(f,a,sK2(gamma,d,X0)),sK2(f,a,sK2(gamma,d,X0))) = zero(a) )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_124315]) ).
tcf(c_133474,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(a,sK2(f,a,sK5(X2,X0,e,d,X1)),sK2(f,a,sK5(X2,X0,e,d,X1))) = zero(a) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_124315]) ).
tcf(c_133475,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(a,sK2(f,a,sK5(X2,X0,e,d,X1)),sK2(f,a,sK5(X2,X0,e,d,X1))) = zero(a) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_124315]) ).
tcf(c_133476,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(a,sK2(f,a,sK5(X2,X0,e,d,X1)),sK2(f,a,sK5(X2,X0,e,d,X1))) = zero(a) )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_124315]) ).
tcf(c_133477,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(a,sK2(f,a,sK6(X2,X0,d,e,X1)),sK2(f,a,sK6(X2,X0,d,e,X1))) = zero(a) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_124315]) ).
tcf(c_133478,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(a,sK2(f,a,sK6(X2,X0,d,e,X1)),sK2(f,a,sK6(X2,X0,d,e,X1))) = zero(a) )
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_124315]) ).
tcf(c_133479,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(a,sK2(f,a,sK6(X2,X0,d,e,X1)),sK2(f,a,sK6(X2,X0,d,e,X1))) = zero(a) )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_124315]) ).
tcf(c_133616,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(f,sK2(f,a,apply(f,sK3(X0,X1,a)))) = apply(f,sK3(X0,X1,a)) )
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_59,c_125001]) ).
tcf(c_133617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,a,X3)) = sK5(X0,X2,X1,a,X3) )
| ( apply(f,sK2(f,a,apply(f,sK5(X0,X2,X1,a,X3)))) = apply(f,sK5(X0,X2,X1,a,X3)) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_67,c_125001]) ).
tcf(c_133618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,a,X3),X1)
| ( apply(f,sK2(f,a,apply(f,sK5(X0,X2,X1,a,X3)))) = apply(f,sK5(X0,X2,X1,a,X3)) )
| ~ morphism(X2,a,X3)
| ~ morphism(X0,X1,a) ),
inference(superposition,[status(thm)],[c_65,c_125001]) ).
tcf(c_133619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,a,X1,X2)) = zero(X2) )
| ( apply(f,sK2(f,a,apply(f,sK6(X3,X0,a,X1,X2)))) = apply(f,sK6(X3,X0,a,X1,X2)) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_125001]) ).
tcf(c_133620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,a,X1,X2),X1)
| ( apply(f,sK2(f,a,apply(f,sK6(X3,X0,a,X1,X2)))) = apply(f,sK6(X3,X0,a,X1,X2)) )
| ~ morphism(X3,a,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_125001]) ).
tcf(c_133621,plain,
! [X0: $i,X1: $i] :
( ( apply(f,sK2(f,a,apply(f,subtract(a,X1,X0)))) = apply(f,subtract(a,X1,X0)) )
| ~ element(X1,a)
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_72,c_125001]) ).
tcf(c_133622,plain,
( injection(f)
| ( apply(f,sK2(f,a,apply(f,sK0(f,a)))) = apply(f,sK0(f,a)) ) ),
inference(superposition,[status(thm)],[c_121726,c_125001]) ).
tcf(c_133623,plain,
( injection(f)
| ( apply(f,sK2(f,a,apply(f,sK1(f,a)))) = apply(f,sK1(f,a)) ) ),
inference(superposition,[status(thm)],[c_121788,c_125001]) ).
tcf(c_133624,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,apply(f,sK2(alpha,a,X0)))) = apply(f,sK2(alpha,a,X0)) )
| ~ surjection(alpha)
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121915,c_125001]) ).
tcf(c_133625,plain,
! [X0: $i] :
( ( apply(f,sK2(f,a,apply(f,sK2(f,a,X0)))) = apply(f,sK2(f,a,X0)) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121928,c_125001]) ).
tcf(c_133626,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK5(X2,X0,e,a,X1)))) = apply(f,sK5(X2,X0,e,a,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_123163,c_125001]) ).
tcf(c_133627,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK5(X2,X0,e,a,X1)))) = apply(f,sK5(X2,X0,e,a,X1)) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,a,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122540,c_125001]) ).
tcf(c_133628,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK5(X2,X0,e,a,X1)))) = apply(f,sK5(X2,X0,e,a,X1)) )
| ( subtract(e,sK6(X2,X0,e,a,X1),subtract(e,sK6(X2,X0,e,a,X1),sK8)) = sK8 )
| ~ morphism(X2,e,a)
| ~ morphism(X0,a,X1) ),
inference(superposition,[status(thm)],[c_122543,c_125001]) ).
tcf(c_133629,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK6(X2,X0,a,e,X1)))) = apply(f,sK6(X2,X0,a,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_125001]) ).
tcf(c_133630,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK6(X2,X0,a,e,X1)))) = apply(f,sK6(X2,X0,a,e,X1)) )
| ( subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,a,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_125001]) ).
tcf(c_133631,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(f,sK2(f,a,apply(f,sK6(X2,X0,a,e,X1)))) = apply(f,sK6(X2,X0,a,e,X1)) )
| ( subtract(e,sK5(X2,X0,a,e,X1),subtract(e,sK5(X2,X0,a,e,X1),sK8)) = sK8 )
| ~ morphism(X2,a,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_125001]) ).
tcf(c_133712,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK3(X0,X1,e)))) = apply(delta,sK3(X0,X1,e)) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_125052]) ).
tcf(c_133713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( apply(delta,sK2(delta,e,apply(delta,sK5(X0,X2,X1,e,X3)))) = apply(delta,sK5(X0,X2,X1,e,X3)) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_125052]) ).
tcf(c_133714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( apply(delta,sK2(delta,e,apply(delta,sK5(X0,X2,X1,e,X3)))) = apply(delta,sK5(X0,X2,X1,e,X3)) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_125052]) ).
tcf(c_133715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( apply(delta,sK2(delta,e,apply(delta,sK6(X3,X0,e,X1,X2)))) = apply(delta,sK6(X3,X0,e,X1,X2)) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_125052]) ).
tcf(c_133716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( apply(delta,sK2(delta,e,apply(delta,sK6(X3,X0,e,X1,X2)))) = apply(delta,sK6(X3,X0,e,X1,X2)) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_125052]) ).
tcf(c_133717,plain,
! [X0: $i,X1: $i] :
( ( apply(delta,sK2(delta,e,apply(delta,subtract(e,X1,X0)))) = apply(delta,subtract(e,X1,X0)) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_125052]) ).
tcf(c_133718,plain,
apply(delta,sK2(delta,e,apply(delta,sK8))) = apply(delta,sK8),
inference(superposition,[status(thm)],[c_3530,c_125052]) ).
tcf(c_133719,plain,
( injection(delta)
| ( apply(delta,sK2(delta,e,apply(delta,sK0(delta,e)))) = apply(delta,sK0(delta,e)) ) ),
inference(superposition,[status(thm)],[c_121725,c_125052]) ).
tcf(c_133720,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,apply(delta,apply(gamma,X0)))) = apply(delta,apply(gamma,X0)) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_125052]) ).
tcf(c_133721,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,apply(delta,apply(g,X0)))) = apply(delta,apply(g,X0)) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_125052]) ).
tcf(c_133722,plain,
( injection(delta)
| ( apply(delta,sK2(delta,e,apply(delta,sK1(delta,e)))) = apply(delta,sK1(delta,e)) ) ),
inference(superposition,[status(thm)],[c_121787,c_125052]) ).
tcf(c_133723,plain,
apply(delta,sK2(delta,e,apply(delta,zero(e)))) = apply(delta,zero(e)),
inference(superposition,[status(thm)],[c_121897,c_125052]) ).
tcf(c_133724,plain,
! [X0: $i] :
( ( apply(delta,sK2(delta,e,apply(delta,sK2(delta,e,X0)))) = apply(delta,sK2(delta,e,X0)) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_125052]) ).
tcf(c_133725,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_125052]) ).
tcf(c_133726,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_125052]) ).
tcf(c_133727,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK5(X2,X0,e,e,X1)))) = apply(delta,sK5(X2,X0,e,e,X1)) )
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_125052]) ).
tcf(c_133728,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_125052]) ).
tcf(c_133729,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_125052]) ).
tcf(c_133730,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( apply(delta,sK2(delta,e,apply(delta,sK6(X2,X0,e,e,X1)))) = apply(delta,sK6(X2,X0,e,e,X1)) )
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_125052]) ).
tcf(c_133878,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,sK3(X0,X1,e),sK8),subtract(e,sK3(X0,X1,e),sK8)) = zero(e) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_132945]) ).
tcf(c_133879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_132945]) ).
tcf(c_133880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),sK8),subtract(e,sK5(X0,X2,X1,e,X3),sK8)) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_132945]) ).
tcf(c_133881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132945]) ).
tcf(c_133882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),sK8),subtract(e,sK6(X3,X0,e,X1,X2),sK8)) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132945]) ).
tcf(c_133883,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,X0),sK8),subtract(e,subtract(e,X1,X0),sK8)) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_132945]) ).
tcf(c_133884,plain,
subtract(e,subtract(e,sK8,sK8),subtract(e,sK8,sK8)) = zero(e),
inference(superposition,[status(thm)],[c_3530,c_132945]) ).
tcf(c_133885,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK0(delta,e),sK8),subtract(e,sK0(delta,e),sK8)) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121725,c_132945]) ).
tcf(c_133886,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,X0),sK8),subtract(e,apply(gamma,X0),sK8)) = zero(e) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_132945]) ).
tcf(c_133887,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,X0),sK8),subtract(e,apply(g,X0),sK8)) = zero(e) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_132945]) ).
tcf(c_133888,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK1(delta,e),sK8),subtract(e,sK1(delta,e),sK8)) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121787,c_132945]) ).
tcf(c_133889,plain,
subtract(e,subtract(e,zero(e),sK8),subtract(e,zero(e),sK8)) = zero(e),
inference(superposition,[status(thm)],[c_121897,c_132945]) ).
tcf(c_133890,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,X0),sK8),subtract(e,sK2(delta,e,X0),sK8)) = zero(e) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_132945]) ).
tcf(c_133891,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132945]) ).
tcf(c_133892,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = zero(e) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132945]) ).
tcf(c_133893,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132945]) ).
tcf(c_133894,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132945]) ).
tcf(c_133895,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = zero(e) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132945]) ).
tcf(c_133896,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132945]) ).
tcf(c_133990,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(r,subtract(r,sK3(X0,X1,r),iPr_def_10),subtract(r,sK3(X0,X1,r),iPr_def_10)) = zero(r) )
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_59,c_132946]) ).
tcf(c_133991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,r,X3)) = sK5(X0,X2,X1,r,X3) )
| ( subtract(r,subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10),subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10)) = zero(r) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_67,c_132946]) ).
tcf(c_133992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,r,X3),X1)
| ( subtract(r,subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10),subtract(r,sK5(X0,X2,X1,r,X3),iPr_def_10)) = zero(r) )
| ~ morphism(X2,r,X3)
| ~ morphism(X0,X1,r) ),
inference(superposition,[status(thm)],[c_65,c_132946]) ).
tcf(c_133993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,r,X1,X2)) = zero(X2) )
| ( subtract(r,subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10),subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10)) = zero(r) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132946]) ).
tcf(c_133994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,r,X1,X2),X1)
| ( subtract(r,subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10),subtract(r,sK6(X3,X0,r,X1,X2),iPr_def_10)) = zero(r) )
| ~ morphism(X3,r,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132946]) ).
tcf(c_133995,plain,
! [X0: $i,X1: $i] :
( ( subtract(r,subtract(r,subtract(r,X1,X0),iPr_def_10),subtract(r,subtract(r,X1,X0),iPr_def_10)) = zero(r) )
| ~ element(X1,r)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_72,c_132946]) ).
tcf(c_133996,plain,
subtract(r,subtract(r,iPr_def_10,iPr_def_10),subtract(r,iPr_def_10,iPr_def_10)) = zero(r),
inference(superposition,[status(thm)],[c_122258,c_132946]) ).
tcf(c_133997,plain,
! [X0: $i] :
( ( subtract(r,subtract(r,apply(delta,X0),iPr_def_10),subtract(r,apply(delta,X0),iPr_def_10)) = zero(r) )
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121760,c_132946]) ).
tcf(c_133998,plain,
! [X0: $i] :
( ( subtract(r,subtract(r,apply(h,X0),iPr_def_10),subtract(r,apply(h,X0),iPr_def_10)) = zero(r) )
| ~ element(X0,c) ),
inference(superposition,[status(thm)],[c_121763,c_132946]) ).
tcf(c_133999,plain,
subtract(r,subtract(r,zero(r),iPr_def_10),subtract(r,zero(r),iPr_def_10)) = zero(r),
inference(superposition,[status(thm)],[c_122259,c_132946]) ).
tcf(c_134000,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132946]) ).
tcf(c_134001,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = zero(r) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,r,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132946]) ).
tcf(c_134002,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,r,X1),subtract(e,sK6(X2,X0,e,r,X1),sK8)) = sK8 )
| ( subtract(r,subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10),subtract(r,sK5(X2,X0,e,r,X1),iPr_def_10)) = zero(r) )
| ~ morphism(X2,e,r)
| ~ morphism(X0,r,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132946]) ).
tcf(c_134003,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = zero(r) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132946]) ).
tcf(c_134004,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(r,subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = zero(r) )
| ( subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,r,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132946]) ).
tcf(c_134005,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,r,e,X1),subtract(e,sK5(X2,X0,r,e,X1),sK8)) = sK8 )
| ( subtract(r,subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10),subtract(r,sK6(X2,X0,r,e,X1),iPr_def_10)) = zero(r) )
| ~ morphism(X2,r,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132946]) ).
tcf(c_134131,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,sK3(X0,X1,e),zero(e)),subtract(e,sK3(X0,X1,e),zero(e))) = zero(e) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_59,c_132965]) ).
tcf(c_134132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,e,X3)) = sK5(X0,X2,X1,e,X3) )
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),subtract(e,sK5(X0,X2,X1,e,X3),zero(e))) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_67,c_132965]) ).
tcf(c_134133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,e,X3),X1)
| ( subtract(e,subtract(e,sK5(X0,X2,X1,e,X3),zero(e)),subtract(e,sK5(X0,X2,X1,e,X3),zero(e))) = zero(e) )
| ~ morphism(X2,e,X3)
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_65,c_132965]) ).
tcf(c_134134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,e,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),subtract(e,sK6(X3,X0,e,X1,X2),zero(e))) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_132965]) ).
tcf(c_134135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,e,X1,X2),X1)
| ( subtract(e,subtract(e,sK6(X3,X0,e,X1,X2),zero(e)),subtract(e,sK6(X3,X0,e,X1,X2),zero(e))) = zero(e) )
| ~ morphism(X3,e,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_132965]) ).
tcf(c_134136,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,subtract(e,X1,X0),zero(e)),subtract(e,subtract(e,X1,X0),zero(e))) = zero(e) )
| ~ element(X1,e)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_72,c_132965]) ).
tcf(c_134137,plain,
subtract(e,subtract(e,sK8,zero(e)),subtract(e,sK8,zero(e))) = zero(e),
inference(superposition,[status(thm)],[c_3530,c_132965]) ).
tcf(c_134138,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK0(delta,e),zero(e)),subtract(e,sK0(delta,e),zero(e))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121725,c_132965]) ).
tcf(c_134139,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,X0),zero(e)),subtract(e,apply(gamma,X0),zero(e))) = zero(e) )
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_121759,c_132965]) ).
tcf(c_134140,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(g,X0),zero(e)),subtract(e,apply(g,X0),zero(e))) = zero(e) )
| ~ element(X0,b) ),
inference(superposition,[status(thm)],[c_121762,c_132965]) ).
tcf(c_134141,plain,
( injection(delta)
| ( subtract(e,subtract(e,sK1(delta,e),zero(e)),subtract(e,sK1(delta,e),zero(e))) = zero(e) ) ),
inference(superposition,[status(thm)],[c_121787,c_132965]) ).
tcf(c_134142,plain,
subtract(e,subtract(e,zero(e),zero(e)),subtract(e,zero(e),zero(e))) = zero(e),
inference(superposition,[status(thm)],[c_121897,c_132965]) ).
tcf(c_134143,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,sK2(delta,e,X0),zero(e)),subtract(e,sK2(delta,e,X0),zero(e))) = zero(e) )
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_121931,c_132965]) ).
tcf(c_134144,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123163,c_132965]) ).
tcf(c_134145,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122540,c_132965]) ).
tcf(c_134146,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,e,X1),subtract(e,sK6(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),zero(e)),subtract(e,sK5(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122543,c_132965]) ).
tcf(c_134147,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_132965]) ).
tcf(c_134148,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ( subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,e,e,X1),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_132965]) ).
tcf(c_134149,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,e,e,X1),subtract(e,sK5(X2,X0,e,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,sK6(X2,X0,e,e,X1),zero(e)),subtract(e,sK6(X2,X0,e,e,X1),zero(e))) = zero(e) )
| ~ morphism(X2,e,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_132965]) ).
tcf(c_134332,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( subtract(e,subtract(e,apply(gamma,sK3(X0,X1,d)),sK8),subtract(e,apply(gamma,sK3(X0,X1,d)),sK8)) = zero(e) )
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_59,c_133886]) ).
tcf(c_134333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| ( apply(X0,sK6(X0,X2,X1,d,X3)) = sK5(X0,X2,X1,d,X3) )
| ( subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8)) = zero(e) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_67,c_133886]) ).
tcf(c_134334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X0,X2)
| element(sK6(X0,X2,X1,d,X3),X1)
| ( subtract(e,subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8),subtract(e,apply(gamma,sK5(X0,X2,X1,d,X3)),sK8)) = zero(e) )
| ~ morphism(X2,d,X3)
| ~ morphism(X0,X1,d) ),
inference(superposition,[status(thm)],[c_65,c_133886]) ).
tcf(c_134335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| ( apply(X0,sK5(X3,X0,d,X1,X2)) = zero(X2) )
| ( subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8)) = zero(e) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_66,c_133886]) ).
tcf(c_134336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( exact(X3,X0)
| element(sK5(X3,X0,d,X1,X2),X1)
| ( subtract(e,subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8),subtract(e,apply(gamma,sK6(X3,X0,d,X1,X2)),sK8)) = zero(e) )
| ~ morphism(X3,d,X1)
| ~ morphism(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_65,c_133886]) ).
tcf(c_134337,plain,
! [X0: $i,X1: $i] :
( ( subtract(e,subtract(e,apply(gamma,subtract(d,X1,X0)),sK8),subtract(e,apply(gamma,subtract(d,X1,X0)),sK8)) = zero(e) )
| ~ element(X1,d)
| ~ element(X0,d) ),
inference(superposition,[status(thm)],[c_72,c_133886]) ).
tcf(c_134338,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,apply(f,X0)),sK8),subtract(e,apply(gamma,apply(f,X0)),sK8)) = zero(e) )
| ~ element(X0,a) ),
inference(superposition,[status(thm)],[c_121761,c_133886]) ).
tcf(c_134339,plain,
! [X0: $i] :
( ( subtract(e,subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8),subtract(e,apply(gamma,sK2(gamma,d,X0)),sK8)) = zero(e) )
| ~ surjection(gamma)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_121917,c_133886]) ).
tcf(c_134340,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_123163,c_133886]) ).
tcf(c_134341,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),subtract(e,subtract(e,sK6(X2,X0,e,d,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = zero(e) )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122540,c_133886]) ).
tcf(c_134342,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK6(X2,X0,e,d,X1),subtract(e,sK6(X2,X0,e,d,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8),subtract(e,apply(gamma,sK5(X2,X0,e,d,X1)),sK8)) = zero(e) )
| ~ morphism(X2,e,d)
| ~ morphism(X0,d,X1) ),
inference(superposition,[status(thm)],[c_122543,c_133886]) ).
tcf(c_134343,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = zero(e) )
| ( subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),subtract(e,subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8),sK8)) = sK8 )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_123162,c_133886]) ).
tcf(c_134344,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),subtract(e,subtract(e,sK5(X2,X0,d,e,X1),sK8),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = zero(e) )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122549,c_133886]) ).
tcf(c_134345,plain,
! [X0: $i,X1: $i,X2: $i] :
( exact(X2,X0)
| ( subtract(e,sK5(X2,X0,d,e,X1),subtract(e,sK5(X2,X0,d,e,X1),sK8)) = sK8 )
| ( subtract(e,subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8),subtract(e,apply(gamma,sK6(X2,X0,d,e,X1)),sK8)) = zero(e) )
| ~ morphism(X2,d,e)
| ~ morphism(X0,e,X1) ),
inference(superposition,[status(thm)],[c_122552,c_133886]) ).
tcf(c_134424,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_132826,c_132825,c_132824,c_132823,c_132822,c_132821,c_132820,c_132819,c_132818,c_132817,c_132816,c_132815,c_132814,c_132813,c_132812,c_132811,c_132810,c_132809,c_132808,c_132807,c_132724,c_132723,c_132722,c_132721,c_132720,c_132719,c_132718,c_132717,c_132716,c_132715,c_132714,c_132713,c_132712,c_132711,c_132579,c_132578,c_132577,c_132576,c_132575,c_132574,c_132573,c_132572,c_132571,c_132570,c_132569,c_132568,c_132567,c_132566,c_132565,c_132564,c_132563,c_132562,c_132561,c_132349,c_132348,c_132347,c_132346,c_132345,c_132344,c_132343,c_132342,c_132341,c_132340,c_132339,c_132338,c_132337,c_132336,c_132335,c_132334,c_132333,c_132332,c_132331,c_132075,c_132074,c_132073,c_132072,c_132071,c_132070,c_132069,c_132068,c_132067,c_132066,c_132065,c_132064,c_132063,c_132062,c_132061,c_132060,c_132059,c_132058,c_132057,c_130804,c_130803,c_130792,c_130418,c_134000,c_130417,c_130414,c_130413,c_130416,c_130415,c_130834,c_133371,c_130412,c_130411,c_130410,c_130409,c_131321,c_131560,c_131898,c_130407,c_130406,c_130404,c_130403,c_130401,c_134144,c_130391,c_130400,c_130399,c_130390,c_130389,c_130398,c_130397,c_130396,c_130395,c_131726,c_133725,c_130394,c_130393,c_130392,c_130388,c_130387,c_130386,c_130385,c_134340,c_130382,c_130384,c_133474,c_130383,c_130381,c_130380,c_130926,c_133626,c_130379,c_130378,c_130377,c_130374,c_130373,c_131100,c_130376,c_131422,c_130375,c_130372,c_130371,c_130370,c_132975,c_129990,c_134003,c_129989,c_129986,c_129985,c_129988,c_129987,c_130837,c_133374,c_129984,c_129983,c_129982,c_129981,c_131324,c_131563,c_131901,c_129979,c_129978,c_129976,c_129975,c_129974,c_129973,c_134147,c_129963,c_129972,c_129971,c_129962,c_129961,c_129970,c_129969,c_129968,c_129967,c_131729,c_133728,c_129966,c_129965,c_129964,c_129960,c_129959,c_129958,c_129957,c_134343,c_129954,c_129956,c_133477,c_129955,c_129953,c_129952,c_130929,c_133629,c_129951,c_129950,c_129949,c_129946,c_129945,c_131103,c_129948,c_131425,c_129947,c_129944,c_129943,c_129942,c_132978,c_129887,c_129886,c_129885,c_129884,c_129883,c_129882,c_129881,c_129780,c_129779,c_129778,c_129777,c_129776,c_129775,c_129774,c_129773,c_129772,c_129771,c_129770,c_129769,c_129768,c_129767,c_129754,c_129753,c_129099,c_129098,c_129097,c_129096,c_129095,c_129094,c_129093,c_129092,c_129091,c_129090,c_129089,c_129088,c_129087,c_129086,c_129085,c_129084,c_129083,c_129082,c_128951,c_128950,c_128949,c_128948,c_128947,c_128946,c_128945,c_128944,c_128943,c_128942,c_128941,c_128940,c_128844,c_128843,c_128842,c_128841,c_128840,c_128839,c_128838,c_128837,c_128836,c_128835,c_128834,c_128833,c_128832,c_128831,c_128830,c_128829,c_128828,c_128658,c_128657,c_128656,c_128655,c_128654,c_128653,c_128652,c_128651,c_128650,c_128649,c_128648,c_128647,c_128646,c_128645,c_128644,c_128643,c_128642,c_128486,c_128485,c_128484,c_128483,c_128482,c_128481,c_128480,c_128479,c_128478,c_128477,c_128476,c_128475,c_128474,c_128473,c_128472,c_128471,c_128470,c_127942,c_127941,c_127546,c_134004,c_127545,c_127542,c_127541,c_127544,c_127543,c_130838,c_133375,c_127540,c_127539,c_127538,c_131325,c_131564,c_131902,c_127536,c_127535,c_127533,c_127532,c_127531,c_127530,c_134148,c_129287,c_127529,c_127528,c_129434,c_129591,c_127527,c_127526,c_127525,c_127524,c_131730,c_133729,c_127523,c_127522,c_127521,c_127520,c_134344,c_128229,c_127519,c_133478,c_127518,c_127972,c_130930,c_133630,c_127517,c_127516,c_127515,c_128080,c_128360,c_131104,c_127514,c_131426,c_127513,c_127512,c_127511,c_132979,c_127163,c_134001,c_127162,c_127159,c_127158,c_127161,c_127160,c_130835,c_133372,c_127157,c_127156,c_127155,c_131322,c_131561,c_131899,c_127153,c_127152,c_127151,c_127150,c_127149,c_127148,c_127147,c_134145,c_129285,c_127146,c_127145,c_129432,c_129589,c_127144,c_127143,c_127142,c_127141,c_131727,c_133726,c_127140,c_127139,c_127138,c_127137,c_134341,c_128227,c_127136,c_133475,c_127135,c_127970,c_130927,c_133627,c_127134,c_127133,c_127132,c_128078,c_128358,c_131101,c_127131,c_131423,c_127130,c_127129,c_127128,c_132976,c_133730,c_133727,c_133724,c_133723,c_133722,c_133721,c_133720,c_133719,c_133718,c_133717,c_133716,c_133715,c_133714,c_133713,c_133712,c_133895,c_133894,c_133892,c_133891,c_127037,c_127036,c_127035,c_127034,c_127033,c_127032,c_127031,c_126935,c_126934,c_126933,c_126932,c_126931,c_126930,c_126929,c_126928,c_126927,c_126926,c_126925,c_126924,c_126764,c_126763,c_126762,c_126761,c_126760,c_126759,c_126758,c_126757,c_126756,c_126755,c_126754,c_126753,c_126752,c_126751,c_126750,c_126749,c_126696,c_126695,c_126694,c_126693,c_126692,c_126691,c_126690,c_126689,c_126688,c_126687,c_133631,c_133628,c_133625,c_133624,c_133623,c_133622,c_133621,c_133620,c_133619,c_133618,c_133617,c_133616,c_131903,c_131900,c_131897,c_131896,c_131895,c_131894,c_131893,c_131892,c_131891,c_131890,c_131889,c_131888,c_131887,c_131731,c_131728,c_131725,c_131724,c_131723,c_131722,c_131721,c_131720,c_131719,c_131718,c_131717,c_131716,c_131715,c_131714,c_131713,c_131427,c_131424,c_131421,c_131420,c_131419,c_131418,c_131417,c_131416,c_131415,c_131414,c_131413,c_131412,c_131411,c_131410,c_131409,c_131408,c_126533,c_126532,c_126531,c_126530,c_126529,c_126528,c_126527,c_126526,c_126525,c_126524,c_126523,c_126522,c_126521,c_126520,c_126519,c_126426,c_126425,c_126424,c_126423,c_126422,c_126421,c_126420,c_126419,c_126418,c_126417,c_126416,c_126415,c_126414,c_126413,c_126412,c_126299,c_126298,c_126297,c_126296,c_126295,c_126294,c_126293,c_126292,c_126291,c_126290,c_126289,c_126288,c_126287,c_126286,c_126285,c_123657,c_123656,c_123869,c_128075,c_128355,c_131097,c_125290,c_123655,c_123654,c_132964,c_122069,c_123652,c_126270,c_126269,c_125999,c_134005,c_125998,c_125995,c_125994,c_125997,c_125996,c_130839,c_133376,c_125993,c_125992,c_131326,c_131565,c_125990,c_125989,c_125988,c_125987,c_125986,c_125985,c_125984,c_133896,c_134149,c_129288,c_125983,c_125982,c_129435,c_129592,c_125981,c_125980,c_125979,c_125978,c_125977,c_134345,c_128230,c_125976,c_133479,c_127973,c_130931,c_125975,c_125974,c_125973,c_128081,c_128361,c_131105,c_125972,c_125971,c_125970,c_132980,c_125485,c_134002,c_125484,c_125481,c_125480,c_125483,c_125482,c_130836,c_133373,c_125479,c_125796,c_131323,c_131562,c_125478,c_125477,c_125476,c_125475,c_125474,c_125473,c_125472,c_125471,c_133893,c_134146,c_129286,c_125470,c_125469,c_129433,c_129590,c_125468,c_125467,c_125466,c_125465,c_125464,c_134342,c_128228,c_125463,c_133476,c_127971,c_130928,c_125462,c_125461,c_125460,c_128079,c_128359,c_131102,c_125459,c_125458,c_125457,c_132977,c_125928,c_125925,c_125924,c_131559,c_131558,c_131557,c_131556,c_131555,c_131554,c_131553,c_131552,c_131551,c_131550,c_131549,c_125373,c_125372,c_125371,c_125370,c_125369,c_125368,c_125367,c_125366,c_125365,c_125364,c_125795,c_131320,c_123672,c_123671,c_132973,c_123669,c_133473,c_133472,c_133471,c_133470,c_133469,c_133468,c_133467,c_133466,c_133370,c_133369,c_133368,c_133367,c_133366,c_133365,c_133364,c_133363,c_133362,c_133361,c_133352,c_133351,c_133342,c_133341,c_125292,c_125291,c_125289,c_125288,c_125287,c_125286,c_125285,c_125284,c_125283,c_125282,c_125281,c_125280,c_125279,c_125205,c_125204,c_125203,c_125202,c_125201,c_125200,c_125199,c_125198,c_124615,c_124614,c_124613,c_124612,c_124611,c_124610,c_124609,c_124608,c_124607,c_124606,c_124605,c_124604,c_124603,c_131319,c_131318,c_131317,c_131316,c_131315,c_131314,c_131313,c_131312,c_131311,c_131310,c_131099,c_131098,c_131096,c_131095,c_131094,c_131093,c_131092,c_131091,c_131090,c_131089,c_131088,c_131087,c_131086,c_130925,c_130924,c_130923,c_130922,c_130921,c_130920,c_130919,c_130918,c_130917,c_130916,c_130833,c_130832,c_130831,c_130830,c_130829,c_130828,c_130827,c_130826,c_130825,c_130824,c_129588,c_129587,c_129586,c_129585,c_129584,c_129583,c_129582,c_129581,c_129580,c_129579,c_129578,c_129577,c_129576,c_129431,c_129430,c_129429,c_129428,c_129427,c_129426,c_129425,c_129424,c_129423,c_129422,c_129421,c_129420,c_129419,c_124333,c_124064,c_124063,c_124062,c_124061,c_124060,c_124059,c_124058,c_124057,c_124056,c_124055,c_124054,c_124053,c_124334,c_123989,c_123988,c_123987,c_123986,c_123985,c_123984,c_123983,c_123982,c_123981,c_123980,c_123979,c_123978,c_129284,c_129283,c_129282,c_129281,c_129280,c_129279,c_129278,c_129277,c_129276,c_129275,c_129274,c_129273,c_129272,c_128357,c_128356,c_128354,c_128353,c_128352,c_128351,c_128350,c_128349,c_128348,c_128347,c_128346,c_128345,c_128344,c_128226,c_128225,c_128224,c_128223,c_128222,c_128221,c_128220,c_128219,c_128077,c_128076,c_128074,c_128073,c_128072,c_128071,c_128070,c_128069,c_128068,c_128067,c_128066,c_128065,c_128064,c_127969,c_127968,c_127967,c_127966,c_127965,c_127964,c_127963,c_127962,c_127961,c_127960,c_124544,c_124543,c_124542,c_124541,c_124540,c_124539,c_124538,c_124537,c_124536,c_124535,c_125900,c_125897,c_125896,c_125794,c_125793,c_125792,c_125791,c_125790,c_125789,c_125788,c_125787,c_125786,c_125785,c_124477,c_124476,c_124475,c_124474,c_124473,c_124472,c_124471,c_124470,c_124469,c_124468,c_134339,c_134338,c_134337,c_134336,c_134335,c_134334,c_134333,c_134332,c_125142,c_125139,c_125138,c_125054,c_125053,c_125052,c_125051,c_125050,c_125049,c_125048,c_125047,c_125046,c_125045,c_124946,c_124943,c_124942,c_124904,c_124901,c_124900,c_125002,c_125001,c_125000,c_124999,c_124998,c_124997,c_124996,c_124995,c_124791,c_124790,c_124789,c_124788,c_124787,c_124786,c_124785,c_124784,c_124783,c_124782,c_124741,c_124740,c_124739,c_124738,c_124737,c_132971,c_124709,c_124708,c_124707,c_124706,c_124705,c_132968,c_124427,c_124426,c_124425,c_124424,c_124423,c_124422,c_124421,c_124420,c_124419,c_124418,c_134143,c_134142,c_134141,c_134140,c_134139,c_134138,c_134137,c_134136,c_134135,c_134134,c_134133,c_134132,c_134131,c_133999,c_133998,c_133997,c_133996,c_133995,c_133994,c_133993,c_133992,c_133991,c_133990,c_133890,c_133889,c_133888,c_133887,c_133886,c_133885,c_133884,c_133883,c_133882,c_133881,c_133880,c_133879,c_133878,c_124691,c_124690,c_132966,c_124390,c_124389,c_124388,c_124387,c_124386,c_132967,c_124342,c_124341,c_124340,c_124339,c_124338,c_124337,c_124336,c_124335,c_124332,c_124331,c_132969,c_124315,c_124314,c_132970,c_124288,c_124263,c_124262,c_124219,c_124218,c_124217,c_124216,c_124215,c_124214,c_124213,c_132974,c_132972,c_132965,c_132963,c_132962,c_132961,c_132960,c_132959,c_132958,c_132957,c_132956,c_132955,c_132954,c_132953,c_132952,c_132951,c_132950,c_132949,c_132948,c_132947,c_132946,c_132945,c_132944,c_132943,c_132942,c_132941,c_132940,c_132939,c_123967,c_123966,c_123868,c_123867,c_123866,c_123865,c_123864,c_123863,c_123862,c_123861,c_123860,c_123859,c_123858,c_123802,c_123801,c_123800,c_123799,c_123798,c_123797,c_123796,c_123722,c_123721,c_123720,c_123719,c_123718,c_123717,c_123716,c_123715,c_123714,c_123713,c_123712,c_123711,c_123170,c_123169,c_123168,c_123167,c_123166,c_123165,c_123164,c_123163,c_123241,c_123162,c_123512,c_123161,c_123701,c_123700,c_123519,c_123518,c_123517,c_123516,c_123515,c_123514,c_123513,c_123511,c_123510,c_123509,c_123508,c_123507,c_123506,c_123439,c_123438,c_123437,c_123436,c_123435,c_123434,c_123433,c_123432,c_123372,c_123371,c_123370,c_123369,c_123368,c_123367,c_123366,c_123248,c_123247,c_123246,c_123245,c_123244,c_123243,c_123242,c_123240,c_123239,c_123238,c_123237,c_123236,c_123235,c_123116,c_123115,c_123114,c_123113,c_123112,c_123111,c_123110,c_123109,c_123108,c_123107,c_123069,c_123068,c_123030,c_123029,c_123028,c_123027,c_123026,c_123025,c_123024,c_123023,c_123022,c_122986,c_122985,c_122984,c_122983,c_122982,c_122405,c_122404,c_122844,c_122403,c_122402,c_122401,c_122400,c_122539,c_122548,c_122399,c_122906,c_122905,c_122904,c_122903,c_122902,c_122901,c_122900,c_122899,c_122898,c_122872,c_122871,c_122870,c_122848,c_122847,c_122846,c_122845,c_122843,c_122842,c_122799,c_122798,c_122797,c_122796,c_122728,c_122727,c_122726,c_122725,c_122724,c_122723,c_122722,c_122721,c_122675,c_122674,c_122673,c_122672,c_122671,c_122670,c_122669,c_122553,c_122552,c_122551,c_122550,c_122549,c_122547,c_122546,c_122545,c_122544,c_122543,c_122542,c_122541,c_122540,c_122538,c_122537,c_122536,c_122508,c_122496,c_122464,c_122463,c_122462,c_122461,c_122460,c_122459,c_122458,c_122457,c_122374,c_122373,c_122372,c_122371,c_122370,c_122369,c_122368,c_122342,c_122341,c_122340,c_122339,c_122338,c_122337,c_122336,c_122319,c_122318,c_122303,c_122302,c_122289,c_122288,c_122287,c_122286,c_122285,c_122284,c_121885,c_122276,c_122275,c_122266,c_122265,c_121712,c_121886,c_122259,c_122258,c_122257,c_122256,c_122255,c_122254,c_122215,c_122214,c_122213,c_122212,c_122211,c_122210,c_122209,c_122179,c_122173,c_122170,c_122164,c_122163,c_122162,c_122161,c_122160,c_122159,c_122158,c_122157,c_122135,c_122134,c_122133,c_122132,c_122130,c_122110,c_122109,c_122108,c_122107,c_122081,c_122080,c_122079,c_122078,c_122077,c_122076,c_122050,c_122049,c_122048,c_122047,c_122046,c_122045,c_122044,c_122032,c_122031,c_122030,c_122012,c_122011,c_122010,c_122003,c_122002,c_121961,c_121960,c_121959,c_121958,c_121957,c_121956,c_121955,c_121954,c_121953,c_121952,c_121951,c_121950,c_121949,c_121937,c_121931,c_121928,c_121922,c_121921,c_121920,c_121919,c_121918,c_121917,c_121916,c_121915,c_121897,c_121896,c_121895,c_121882,c_121875,c_121868,c_121861,c_121854,c_121847,c_121832,c_121825,c_121824,c_121823,c_121822,c_121821,c_121820,c_121819,c_121840,c_121808,c_121807,c_121806,c_5820,c_121790,c_121789,c_121788,c_121787,c_121785,c_121763,c_121762,c_121761,c_121760,c_121759,c_121758,c_121757,c_121728,c_121727,c_121726,c_121725,c_121723,c_3531,c_3529,c_3530,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL004+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 16:09:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 72.45/12.29 % SZS status Started for theBenchmark.p
% 72.45/12.29 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_98 (s_0 s_0 s_0) Bool) supplied sort is s_130")
% 72.45/12.29 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun f_98 (s_0 s_0 s_0) Bool) supplied sort is s_130")
% 72.45/12.29 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.67" --time_out_real 2.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_mw5y_ecq/f_hitr_9 2>> /export/starexec/sandbox2/tmp/iprover_out_mw5y_ecq/f_hitr_9_error
% 72.45/12.29 % SZS status Theorem for theBenchmark.p
% 72.45/12.29
% 72.45/12.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 72.45/12.29
% 72.45/12.29 % ------ iProver source info
% 72.45/12.29
% 72.45/12.29 % git: date: 2026-07-19 20:42:38 +0200
% 72.45/12.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 72.45/12.29 % git: non_committed_changes: false
% 72.45/12.29
% 72.45/12.29 % ------ Parsing...
% 72.45/12.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 72.45/12.29
% 72.45/12.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 72.45/12.29
% 72.45/12.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 72.45/12.29
% 72.45/12.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 72.45/12.29 % ------ Proving...
% 72.45/12.29 % ------ Problem Properties
% 72.45/12.29
% 72.45/12.29 %
% 72.45/12.29 % clauses 46
% 72.45/12.29 % conjectures 2
% 72.45/12.29 % EPR 18
% 72.45/12.29 % Horn 37
% 72.45/12.29 % unary 19
% 72.45/12.29 % binary 2
% 72.45/12.29 % lits 136
% 72.45/12.29 % lits eq 25
% 72.45/12.29 % fd_pure 0
% 72.45/12.29 % fd_pseudo 0
% 72.45/12.29 % fd_cond 0
% 72.45/12.29 % fd_pseudo_cond 1
% 72.45/12.29 % AC symbols 0
% 72.45/12.29
% 72.45/12.29 % ------ Schedule dynamic 5 is on
% 72.45/12.29
% 72.45/12.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 72.45/12.29
% 72.45/12.29
% 72.45/12.29 % ------
% 72.45/12.29 % Current options:
% 72.45/12.29 % ------
% 72.45/12.29
% 72.45/12.29
% 72.45/12.29 %
% 72.45/12.29
% 72.45/12.29 % ------ Proving...
% 72.45/12.29 % Proof_search_loop: time out after: 3547 full_loop iterations
% 72.45/12.29
% 72.45/12.29 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 72.45/12.29
% 72.45/12.29
% 72.45/12.29 % ------
% 72.45/12.29 % Current options:
% 72.45/12.29 % ------
% 72.45/12.29
% 72.45/12.29
% 72.45/12.29 %
% 72.45/12.29
% 72.45/12.29 % ------ Proving...
% 72.45/12.29 %
% 72.45/12.29
% 72.45/12.29 % SZS status Theorem for theBenchmark.p
% 72.45/12.29
% 72.45/12.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 73.14/12.32
% 73.14/12.32
%------------------------------------------------------------------------------