%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 5.98s 2.33s
% Output : CNFRefutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 1409 ( 8 unt; 0 def)
% Number of atoms : 4089 (2524 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3854 (1174 ~;2631 |; 31 &)
% ( 2 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 901 ( 0 sgn 895 !; 6 ?; 746 :)
% 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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection_2(X0) )
=> ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> X3 = zero(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> X3 = zero(X1) )
& morphism(X0,X1,X2) )
=> injection_2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_morphism) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',my) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ? [X3] :
( apply(X0,X3) = zero(X2)
& element(X3,X1)
& zero(X1) != X3 )
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ? [X3] :
( apply(X0,X3) = zero(X2)
& element(X3,X1)
& zero(X1) != X3 )
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ injection_2(X0)
| ! [X3] :
( apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| X3 = zero(X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ injection_2(X0)
| ! [X3] :
( apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| X3 = zero(X1) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f29,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(f30,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(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(ennf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
( ( injection(x)
| injection_2(x) )
& ( ~ injection(x)
| ~ injection_2(x) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f37,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))],[f21]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1)
& zero(X1) != sK2(X0,X1,X2) )
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f25]) ).
fof(f39,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
( injection(x)
| injection_2(x) ),
inference(cnf_transformation,[],[f36]) ).
fof(f41,plain,
( ~ injection(x)
| ~ injection_2(x) ),
inference(cnf_transformation,[],[f36]) ).
fof(f42,plain,
! [X2,X0,X1] :
( apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f43,plain,
! [X2,X0,X1] :
( element(sK1(X0,X1),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f44,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f45,plain,
! [X2,X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f46,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,[],[f23]) ).
fof(f47,plain,
! [X2,X0,X1] :
( zero(X2) = apply(X0,sK2(X0,X1,X2))
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f48,plain,
! [X2,X0,X1] :
( element(sK2(X0,X1,X2),X1)
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f49,plain,
! [X2,X0,X1] :
( zero(X1) != sK2(X0,X1,X2)
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ injection_2(X0)
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| zero(X1) = X3 ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,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,[],[f31]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_49,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_50,negated_conjecture,
( ~ injection(x)
| ~ injection_2(x) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_51,negated_conjecture,
( injection(x)
| injection_2(x) ),
inference(cnf_transformation,[],[f40]) ).
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,[],[f45]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK1(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
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,[],[f42]) ).
tcf(c_56,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,[],[f46]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| ~ morphism(X0,X1,X2)
| ( sK2(X0,X1,X2) != zero(X1) ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| element(sK2(X0,X1,X2),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| ( apply(X0,sK2(X0,X1,X2)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zero(X3) = X1 )
| ~ injection_2(X0)
| ~ element(X1,X3)
| ~ morphism(X0,X3,X2)
| ( apply(X0,X1) != zero(X2) ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( subtract(X1,X0,X0) = zero(X1) )
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,zero(X1)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,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,[],[f54]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(X1,X0,subtract(X1,X0,X2)) = X2 )
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subtract(X1,X0,X2),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_82,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_83,plain,
( ~ injection(x)
| ~ injection_2(x) ),
inference(renaming,[status(thm)],[c_82]) ).
tcf(c_84,plain,
( injection_2(x)
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_85,plain,
( injection(x)
| injection_2(x) ),
inference(renaming,[status(thm)],[c_84]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,zero(X1)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_352,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)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_64]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,X0),apply(x,X1)) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(unflattening,[status(thm)],[c_352]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,zero(X1)) = zero(X2) )
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_86]) ).
tcf(c_365,plain,
apply(x,zero(any1)) = zero(any2),
inference(unflattening,[status(thm)],[c_364]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_370,plain,
! [X0: $i] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) ),
inference(unflattening,[status(thm)],[c_369]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| ( apply(X0,sK2(X0,X1,X2)) = zero(X2) )
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_379,plain,
( injection_2(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(unflattening,[status(thm)],[c_378]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| element(sK2(X0,X1,X2),X1)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_387,plain,
( injection_2(x)
| element(sK2(x,any1,any2),any1) ),
inference(unflattening,[status(thm)],[c_386]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection_2(X0)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x )
| ( sK2(X0,X1,X2) != zero(X1) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_395,plain,
( injection_2(x)
| ( sK2(x,any1,any2) != zero(any1) ) ),
inference(unflattening,[status(thm)],[c_394]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| ( apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) )
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_403,plain,
( injection(x)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ) ),
inference(unflattening,[status(thm)],[c_402]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK1(X0,X1),X1)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_54]) ).
tcf(c_411,plain,
( injection(x)
| element(sK1(x,any1),any1) ),
inference(unflattening,[status(thm)],[c_410]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK0(X0,X1),X1)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_419,plain,
( injection(x)
| element(sK0(x,any1),any1) ),
inference(unflattening,[status(thm)],[c_418]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| ( X2 != any2 )
| ( X1 != any1 )
| ( X0 != x )
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
tcf(c_427,plain,
( injection(x)
| ( sK0(x,any1) != sK1(x,any1) ) ),
inference(unflattening,[status(thm)],[c_426]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ~ injection(X0)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ( X4 != any2 )
| ( X3 != any1 )
| ( X0 != x )
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1)
| ( apply(x,X0) != apply(x,X1) ) ),
inference(unflattening,[status(thm)],[c_434]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zero(X3) = X1 )
| ~ injection_2(X0)
| ~ element(X1,X3)
| ( X3 != any1 )
| ( X2 != any2 )
| ( X0 != x )
| ( apply(X0,X1) != zero(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_453,plain,
! [X0: $i] :
( ( zero(any1) = X0 )
| ~ injection_2(x)
| ~ element(X0,any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(unflattening,[status(thm)],[c_452]) ).
tcf(c_510,plain,
( ~ injection(x)
| ( sK2(x,any1,any2) != zero(any1) ) ),
inference(resolution,[status(thm)],[c_395,c_83]) ).
tcf(c_531,plain,
( element(sK2(x,any1,any2),any1)
| ~ injection(x) ),
inference(resolution,[status(thm)],[c_387,c_83]) ).
tcf(c_552,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ injection(x) ),
inference(resolution,[status(thm)],[c_379,c_83]) ).
tcf(c_559,plain,
! [X0: $i] :
( injection(x)
| ( zero(any1) = X0 )
| ~ element(X0,any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(resolution,[status(thm)],[c_85,c_453]) ).
tcf(c_745,plain,
( injection_2(x)
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_746,plain,
( injection(x)
| injection_2(x) ),
inference(renaming,[status(thm)],[c_745]) ).
tcf(c_747,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ injection(x) ),
inference(prop_impl_just,[status(thm)],[c_552]) ).
tcf(c_749,plain,
( element(sK2(x,any1,any2),any1)
| ~ injection(x) ),
inference(prop_impl_just,[status(thm)],[c_531]) ).
tcf(c_751,plain,
( ( sK2(x,any1,any2) != zero(any1) )
| ~ injection(x) ),
inference(prop_impl_just,[status(thm)],[c_510]) ).
tcf(c_752,plain,
( ~ injection(x)
| ( sK2(x,any1,any2) != zero(any1) ) ),
inference(renaming,[status(thm)],[c_751]) ).
tcf(c_753,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_403]) ).
tcf(c_754,plain,
( injection(x)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ) ),
inference(renaming,[status(thm)],[c_753]) ).
tcf(c_755,plain,
( element(sK1(x,any1),any1)
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_411]) ).
tcf(c_756,plain,
( injection(x)
| element(sK1(x,any1),any1) ),
inference(renaming,[status(thm)],[c_755]) ).
tcf(c_757,plain,
( element(sK0(x,any1),any1)
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_419]) ).
tcf(c_758,plain,
( injection(x)
| element(sK0(x,any1),any1) ),
inference(renaming,[status(thm)],[c_757]) ).
tcf(c_759,plain,
( ( sK0(x,any1) != sK1(x,any1) )
| injection(x) ),
inference(prop_impl_just,[status(thm)],[c_427]) ).
tcf(c_760,plain,
( injection(x)
| ( sK0(x,any1) != sK1(x,any1) ) ),
inference(renaming,[status(thm)],[c_759]) ).
tcf(c_765,plain,
! [X0: $i] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) ),
inference(prop_impl_just,[status(thm)],[c_370]) ).
tcf(c_810,plain,
! [X0: $i] :
( injection(x)
| ( zero(any1) = X0 )
| ~ element(X0,any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(bin_hyper_res,[status(thm)],[c_453,c_746]) ).
tcf(c_1083,plain,
( element(sK0(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(resolution,[status(thm)],[c_758,c_747]) ).
tcf(c_1120,plain,
( element(sK1(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(resolution,[status(thm)],[c_756,c_747]) ).
tcf(c_1164,plain,
( element(sK2(x,any1,any2),any1)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ) ),
inference(resolution,[status(thm)],[c_754,c_749]) ).
tcf(c_1171,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( sK2(x,any1,any2) != zero(any1) ) ),
inference(resolution,[status(thm)],[c_754,c_752]) ).
tcf(c_1987,plain,
( element(zero(any2),any2)
| ~ element(zero(any1),any1) ),
inference(superposition,[status(thm)],[c_365,c_765]) ).
tcf(c_2002,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,X0),apply(x,X0)) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_61]) ).
tcf(c_2003,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_61]) ).
tcf(c_2004,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_61]) ).
tcf(c_2005,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_61]) ).
tcf(c_2025,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(X1,subtract(X1,X0,X2),subtract(X1,X0,X2)) = zero(X1) )
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_61]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(X1,subtract(X1,X0,X2),subtract(X1,subtract(X1,X0,X2),X3)) = X3 )
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_65]) ).
tcf(c_2037,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,X0),subtract(any2,apply(x,X0),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_65]) ).
tcf(c_2038,plain,
! [X0: $i] :
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),X0)) = X0 )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_65]) ).
tcf(c_2039,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_65]) ).
tcf(c_2040,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_65]) ).
tcf(c_2070,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_754,c_747]) ).
tcf(c_2077,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2004,c_747]) ).
tcf(c_2084,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2005,c_747]) ).
tcf(c_2091,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,subtract(any1,X0,X1)),apply(x,subtract(any1,X0,X1))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2002]) ).
tcf(c_2092,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2002]) ).
tcf(c_2093,plain,
( injection(x)
| ( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_756,c_2002]) ).
tcf(c_2094,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_758,c_2002]) ).
tcf(c_2109,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2005,c_2003]) ).
tcf(c_2110,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2004,c_2003]) ).
tcf(c_2111,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_754,c_2003]) ).
tcf(c_2122,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2093,c_2003]) ).
tcf(c_2123,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2093,c_747]) ).
tcf(c_2132,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2094,c_2003]) ).
tcf(c_2133,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2094,c_747]) ).
tcf(c_2153,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2039]) ).
tcf(c_2155,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_2039]) ).
tcf(c_2156,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2039]) ).
tcf(c_2166,plain,
( element(apply(x,sK2(x,any1,any2)),any2)
| ~ element(sK2(x,any1,any2),any1) ),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_2174,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2040]) ).
tcf(c_2176,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_2040]) ).
tcf(c_2177,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2040]) ).
tcf(c_2193,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2155,c_2003]) ).
tcf(c_2194,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2155,c_747]) ).
tcf(c_2204,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2156,c_2003]) ).
tcf(c_2205,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2156,c_747]) ).
tcf(c_2218,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2176,c_2003]) ).
tcf(c_2219,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2176,c_747]) ).
tcf(c_2232,plain,
( injection(x)
| ( sK2(x,any1,any2) = zero(any1) )
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2070,c_810]) ).
tcf(c_2233,plain,
( element(zero(any2),any2)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2070,c_765]) ).
tcf(c_2252,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2176,c_2092]) ).
tcf(c_2253,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2156,c_2092]) ).
tcf(c_2254,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2155,c_2092]) ).
tcf(c_2255,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2094,c_2092]) ).
tcf(c_2256,plain,
( ( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2093,c_2092]) ).
tcf(c_2257,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2005,c_2092]) ).
tcf(c_2258,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2004,c_2092]) ).
tcf(c_2259,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_754,c_2092]) ).
tcf(c_2294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(X1,subtract(X1,subtract(X1,X0,X2),X3),subtract(X1,subtract(X1,X0,X2),X3)) = zero(X1) )
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_2025]) ).
tcf(c_2295,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,subtract(any2,apply(x,X0),X1),subtract(any2,apply(x,X0),X1)) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2025]) ).
tcf(c_2296,plain,
! [X0: $i] :
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),X0),subtract(any1,sK2(x,any1,any2),X0)) = zero(any1) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2025]) ).
tcf(c_2297,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,sK1(x,any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2025]) ).
tcf(c_2298,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,sK0(x,any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2025]) ).
tcf(c_2347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,apply(x,subtract(any1,X0,X1)),subtract(any2,apply(x,subtract(any1,X0,X1)),X2)) = X2 )
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2037]) ).
tcf(c_2348,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = X0 )
| ~ injection(x)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_749,c_2037]) ).
tcf(c_2349,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_756,c_2037]) ).
tcf(c_2350,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_758,c_2037]) ).
tcf(c_2400,plain,
( element(zero(any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_2077,c_66]) ).
tcf(c_2408,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2177,c_2092]) ).
tcf(c_2409,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2177,c_2003]) ).
tcf(c_2410,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2177,c_747]) ).
tcf(c_2417,plain,
( element(zero(any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_2400,c_1120,c_2400]) ).
tcf(c_2423,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,zero(any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2025]) ).
tcf(c_2424,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_65]) ).
tcf(c_2425,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_61]) ).
tcf(c_2426,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,zero(any1)),subtract(any2,apply(x,zero(any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2417,c_2037]) ).
tcf(c_2427,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2040]) ).
tcf(c_2428,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2039]) ).
tcf(c_2429,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_2002]) ).
tcf(c_2430,plain,
( element(zero(any2),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_1987]) ).
tcf(c_2435,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(light_normalisation,[status(thm)],[c_2429,c_365]) ).
tcf(c_2447,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ~ element(X0,any2) ),
inference(light_normalisation,[status(thm)],[c_2426,c_365]) ).
tcf(c_2479,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2430,c_2025]) ).
tcf(c_2517,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2038]) ).
tcf(c_2518,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2038]) ).
tcf(c_2521,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2417,c_2038]) ).
tcf(c_2559,plain,
( element(zero(any2),any2)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2233,c_1164,c_2233]) ).
tcf(c_2565,plain,
! [X0: $i] :
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2559,c_2025]) ).
tcf(c_2566,plain,
! [X0: $i] :
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2559,c_65]) ).
tcf(c_2567,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2559,c_61]) ).
tcf(c_2603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,apply(x,subtract(any1,X0,X1)),apply(x,X2)) = apply(x,subtract(any1,subtract(any1,X0,X1),X2)) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_353]) ).
tcf(c_2604,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0)) = apply(x,subtract(any1,sK2(x,any1,any2),X0)) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_353]) ).
tcf(c_2605,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK1(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK1(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_353]) ).
tcf(c_2606,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK0(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_353]) ).
tcf(c_2607,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,X0)) = apply(x,subtract(any1,zero(any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_353]) ).
tcf(c_2617,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),X0)) = subtract(any2,zero(any2),apply(x,X0)) )
| ~ element(X0,any1) ),
inference(light_normalisation,[status(thm)],[c_2607,c_365]) ).
tcf(c_2644,plain,
! [X0: $i] :
( ( zero(any1) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(zero(any1),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_365,c_435]) ).
tcf(c_2645,plain,
! [X0: $i] :
( ( sK2(x,any1,any2) = X0 )
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(sK2(x,any1,any2),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_2070,c_435]) ).
tcf(c_2667,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2297]) ).
tcf(c_2669,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_2297]) ).
tcf(c_2670,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2297]) ).
tcf(c_2671,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2297]) ).
tcf(c_2702,plain,
( element(zero(any1),any1)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2109,c_66]) ).
tcf(c_2710,plain,
( element(zero(any1),any1)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_2702,c_531,c_2005,c_2702]) ).
tcf(c_2716,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,zero(any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2025]) ).
tcf(c_2717,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_65]) ).
tcf(c_2718,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2710,c_61]) ).
tcf(c_2720,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,X0)) = apply(x,subtract(any1,zero(any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_353]) ).
tcf(c_2721,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2710,c_2038]) ).
tcf(c_2722,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),subtract(any2,apply(x,zero(any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2710,c_2037]) ).
tcf(c_2725,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2710,c_2002]) ).
tcf(c_2726,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2710,c_1987]) ).
tcf(c_2731,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(light_normalisation,[status(thm)],[c_2725,c_365]) ).
tcf(c_2737,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ~ element(X0,any2) ),
inference(light_normalisation,[status(thm)],[c_2722,c_365]) ).
tcf(c_2747,plain,
! [X0: $i] :
( ( apply(x,subtract(any1,zero(any1),X0)) = subtract(any2,zero(any2),apply(x,X0)) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ~ element(X0,any1) ),
inference(light_normalisation,[status(thm)],[c_2720,c_365]) ).
tcf(c_2791,plain,
( element(zero(any1),any1)
| ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ~ element(sK0(x,any1),any1) ),
inference(superposition,[status(thm)],[c_2718,c_66]) ).
tcf(c_2798,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ~ element(sK0(x,any1),any1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2791,c_61]) ).
tcf(c_2805,plain,
( injection(x)
| ( subtract(any1,zero(any1),zero(any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2798]) ).
tcf(c_2813,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2177,c_2518]) ).
tcf(c_2814,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2176,c_2518]) ).
tcf(c_2815,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2156,c_2518]) ).
tcf(c_2816,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2155,c_2518]) ).
tcf(c_2817,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2094,c_2518]) ).
tcf(c_2818,plain,
( ( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2093,c_2518]) ).
tcf(c_2819,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2005,c_2518]) ).
tcf(c_2820,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2004,c_2518]) ).
tcf(c_2821,plain,
( ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_754,c_2518]) ).
tcf(c_2877,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2805,c_2518]) ).
tcf(c_2878,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2805,c_2092]) ).
tcf(c_2879,plain,
( ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2805,c_2003]) ).
tcf(c_2891,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2726,c_2025]) ).
tcf(c_2908,plain,
( element(zero(any1),any1)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ~ element(sK0(x,any1),any1) ),
inference(superposition,[status(thm)],[c_2731,c_66]) ).
tcf(c_2920,plain,
( injection(x)
| element(zero(any1),any1)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_758,c_2908]) ).
tcf(c_2941,plain,
( injection(x)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2920,c_2002]) ).
tcf(c_2949,plain,
( injection(x)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) ) ),
inference(light_normalisation,[status(thm)],[c_2941,c_365]) ).
tcf(c_2958,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2949,c_2518]) ).
tcf(c_2959,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2949,c_2092]) ).
tcf(c_2960,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2949,c_2003]) ).
tcf(c_2996,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2298]) ).
tcf(c_2998,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_2298]) ).
tcf(c_2999,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2298]) ).
tcf(c_3001,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2298]) ).
tcf(c_3020,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2349]) ).
tcf(c_3021,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2349]) ).
tcf(c_3024,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2430,c_2349]) ).
tcf(c_3043,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2350]) ).
tcf(c_3044,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2350]) ).
tcf(c_3047,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2430,c_2350]) ).
tcf(c_3082,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_2518]) ).
tcf(c_3083,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_2092]) ).
tcf(c_3084,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_2003]) ).
tcf(c_3085,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_747]) ).
tcf(c_3108,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_2518]) ).
tcf(c_3109,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_2092]) ).
tcf(c_3110,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_2003]) ).
tcf(c_3111,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_747]) ).
tcf(c_3124,plain,
( element(zero(any1),any1)
| ( subtract(any1,zero(any1),zero(any1)) = zero(any1) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2879,c_66]) ).
tcf(c_3142,plain,
( element(zero(any1),any1)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2110,c_66]) ).
tcf(c_3146,plain,
( element(zero(any1),any1)
| ( subtract(any1,zero(any1),zero(any1)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_3124,c_531,c_2805,c_3124]) ).
tcf(c_3150,plain,
subtract(any1,zero(any1),zero(any1)) = zero(any1),
inference(forward_subsumption_resolution,[status(thm)],[c_3146,c_61]) ).
tcf(c_3156,plain,
( element(zero(any1),any1)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_3142,c_531,c_2004,c_3142]) ).
tcf(c_3162,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,zero(any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2025]) ).
tcf(c_3163,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_65]) ).
tcf(c_3167,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,X0)) = apply(x,subtract(any1,zero(any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_353]) ).
tcf(c_3168,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3156,c_2038]) ).
tcf(c_3169,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),subtract(any2,apply(x,zero(any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3156,c_2037]) ).
tcf(c_3172,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3156,c_2002]) ).
tcf(c_3173,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3156,c_1987]) ).
tcf(c_3176,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(light_normalisation,[status(thm)],[c_3172,c_365]) ).
tcf(c_3182,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ~ element(X0,any2) ),
inference(light_normalisation,[status(thm)],[c_3169,c_365]) ).
tcf(c_3192,plain,
! [X0: $i] :
( ( apply(x,subtract(any1,zero(any1),X0)) = subtract(any2,zero(any2),apply(x,X0)) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ~ element(X0,any1) ),
inference(light_normalisation,[status(thm)],[c_3167,c_365]) ).
tcf(c_3227,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,apply(x,subtract(any1,subtract(any1,X0,X1),X2)),apply(x,subtract(any1,subtract(any1,X0,X1),X2))) = zero(any2) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2091]) ).
tcf(c_3228,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,subtract(any1,sK2(x,any1,any2),X0))) = zero(any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2091]) ).
tcf(c_3229,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),apply(x,subtract(any1,sK1(x,any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2091]) ).
tcf(c_3230,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),apply(x,subtract(any1,sK0(x,any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2091]) ).
tcf(c_3231,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,subtract(any1,zero(any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2091]) ).
tcf(c_3232,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,subtract(any1,zero(any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2091]) ).
tcf(c_3233,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,subtract(any1,zero(any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2091]) ).
tcf(c_3299,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3173,c_2025]) ).
tcf(c_3312,plain,
( element(zero(any1),any1)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3176,c_66]) ).
tcf(c_3327,plain,
( element(zero(any1),any1)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2960,c_66]) ).
tcf(c_3335,plain,
( element(zero(any1),any1)
| ( subtract(any2,zero(any2),zero(any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3327,c_531,c_2949,c_3327]) ).
tcf(c_3352,plain,
( ( subtract(any2,zero(any2),zero(any2)) = zero(any2) )
| ( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3335,c_2002]) ).
tcf(c_3356,plain,
subtract(any2,zero(any2),zero(any2)) = zero(any2),
inference(light_normalisation,[status(thm)],[c_3352,c_365]) ).
tcf(c_3362,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_2518]) ).
tcf(c_3363,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_2092]) ).
tcf(c_3364,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_2003]) ).
tcf(c_3365,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_747]) ).
tcf(c_3378,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_2518]) ).
tcf(c_3379,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_2092]) ).
tcf(c_3380,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_2003]) ).
tcf(c_3381,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_747]) ).
tcf(c_3390,plain,
! [X0: $i] :
( ( zero(any1) = X0 )
| ( apply(x,X0) != zero(any2) )
| ~ element(zero(any1),any1)
| ~ element(X0,any1) ),
inference(global_subsumption_just,[status(thm)],[c_2644,c_559,c_2644]) ).
tcf(c_3391,plain,
! [X0: $i] :
( ( zero(any1) = X0 )
| ~ element(X0,any1)
| ~ element(zero(any1),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(renaming,[status(thm)],[c_3390]) ).
tcf(c_3402,plain,
( ( sK2(x,any1,any2) = zero(any1) )
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ~ element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2070,c_3391]) ).
tcf(c_3411,plain,
( element(zero(any1),any1)
| ( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) )
| ~ element(sK2(x,any1,any2),any1) ),
inference(superposition,[status(thm)],[c_2111,c_66]) ).
tcf(c_3425,plain,
apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)),
inference(global_subsumption_just,[status(thm)],[c_3411,c_1164,c_1171,c_3402,c_3411]) ).
tcf(c_3432,plain,
( ( sK1(x,any1) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(sK1(x,any1),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_3425,c_3391]) ).
tcf(c_3434,plain,
( injection(x)
| ( sK1(x,any1) = zero(any1) )
| ~ element(sK1(x,any1),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_3425,c_810]) ).
tcf(c_3435,plain,
( element(apply(x,sK0(x,any1)),any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3425,c_765]) ).
tcf(c_3436,plain,
! [X0: $i] :
( ( sK1(x,any1) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(sK1(x,any1),any1)
| ( apply(x,sK0(x,any1)) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_3425,c_435]) ).
tcf(c_3462,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),X0),subtract(any2,apply(x,sK0(x,any1)),X0)) = zero(any2) )
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2025]) ).
tcf(c_3463,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),X0)) = X0 )
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_65]) ).
tcf(c_3464,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_61]) ).
tcf(c_3465,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2350]) ).
tcf(c_3518,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,subtract(any2,apply(x,subtract(any1,X0,X1)),X2),subtract(any2,apply(x,subtract(any1,X0,X1)),X2)) = zero(any2) )
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2295]) ).
tcf(c_3519,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),X0),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = zero(any2) )
| ~ injection(x)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_749,c_2295]) ).
tcf(c_3520,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK1(x,any1)),X0),subtract(any2,apply(x,sK1(x,any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_756,c_2295]) ).
tcf(c_3521,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),X0),subtract(any2,apply(x,sK0(x,any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_758,c_2295]) ).
tcf(c_3522,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,zero(any1)),X0),subtract(any2,apply(x,zero(any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3156,c_2295]) ).
tcf(c_3523,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,zero(any1)),X0),subtract(any2,apply(x,zero(any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2710,c_2295]) ).
tcf(c_3524,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,zero(any1)),X0),subtract(any2,apply(x,zero(any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2417,c_2295]) ).
tcf(c_3548,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2424]) ).
tcf(c_3549,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2424]) ).
tcf(c_3550,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_2424]) ).
tcf(c_3551,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2424]) ).
tcf(c_3554,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2424]) ).
tcf(c_3580,plain,
( injection(x)
| ( sK1(x,any1) = zero(any1) )
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3434,c_411,c_3434]) ).
tcf(c_3594,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2447]) ).
tcf(c_3595,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2447]) ).
tcf(c_3598,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2430,c_2447]) ).
tcf(c_3599,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2447]) ).
tcf(c_3615,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK1(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(light_normalisation,[status(thm)],[c_2605,c_3425]) ).
tcf(c_3625,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1))) = apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3615]) ).
tcf(c_3627,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_756,c_3615]) ).
tcf(c_3628,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_758,c_3615]) ).
tcf(c_3631,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2417,c_3615]) ).
tcf(c_3634,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(light_normalisation,[status(thm)],[c_3627,c_3425]) ).
tcf(c_3637,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) ) ),
inference(light_normalisation,[status(thm)],[c_3631,c_365]) ).
tcf(c_3674,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1))) = apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2606]) ).
tcf(c_3676,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_756,c_2606]) ).
tcf(c_3677,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_758,c_2606]) ).
tcf(c_3680,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2417,c_2606]) ).
tcf(c_3683,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(light_normalisation,[status(thm)],[c_3676,c_3425]) ).
tcf(c_3686,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) ) ),
inference(light_normalisation,[status(thm)],[c_3680,c_365]) ).
tcf(c_3699,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_3628,c_2518]) ).
tcf(c_3700,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3628,c_2092]) ).
tcf(c_3701,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3628,c_2003]) ).
tcf(c_3702,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3628,c_747]) ).
tcf(c_3725,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_3634,c_2518]) ).
tcf(c_3726,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3634,c_2092]) ).
tcf(c_3727,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3634,c_2003]) ).
tcf(c_3728,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3634,c_747]) ).
tcf(c_3744,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_3677,c_2518]) ).
tcf(c_3745,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3677,c_2092]) ).
tcf(c_3746,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3677,c_2003]) ).
tcf(c_3747,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3677,c_747]) ).
tcf(c_3772,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_3683,c_2518]) ).
tcf(c_3773,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3683,c_2092]) ).
tcf(c_3774,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3683,c_2003]) ).
tcf(c_3775,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3683,c_747]) ).
tcf(c_3800,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1)),subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))) = zero(any1) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2296]) ).
tcf(c_3801,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2296]) ).
tcf(c_3804,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),zero(any1)),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3156,c_2296]) ).
tcf(c_3805,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),zero(any1)),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2710,c_2296]) ).
tcf(c_3806,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),zero(any1)),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2417,c_2296]) ).
tcf(c_3851,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ injection(x)
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2348]) ).
tcf(c_3852,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0))) = apply(x,X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2348]) ).
tcf(c_3853,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3173,c_2348]) ).
tcf(c_3854,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2726,c_2348]) ).
tcf(c_3855,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2430,c_2348]) ).
tcf(c_3856,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2348]) ).
tcf(c_3900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( subtract(X1,subtract(X1,X3,X4),subtract(X1,subtract(X1,X3,X4),subtract(X1,X0,X2))) = subtract(X1,X0,X2) )
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_2036]) ).
tcf(c_3901,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,subtract(any2,X1,X2),subtract(any2,subtract(any2,X1,X2),apply(x,X0))) = apply(x,X0) )
| ~ element(X2,any2)
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2036]) ).
tcf(c_3902,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2036]) ).
tcf(c_3903,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2036]) ).
tcf(c_3904,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2036]) ).
tcf(c_3905,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3173,c_2036]) ).
tcf(c_3906,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2726,c_2036]) ).
tcf(c_3907,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2430,c_2036]) ).
tcf(c_3908,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2036]) ).
tcf(c_3909,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2036]) ).
tcf(c_3910,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2036]) ).
tcf(c_3911,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2036]) ).
tcf(c_4029,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),zero(any1)) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2077,c_2194]) ).
tcf(c_4046,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_2132,c_66]) ).
tcf(c_4050,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_4046,c_411,c_2003,c_3435,c_4046]) ).
tcf(c_4056,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_2036]) ).
tcf(c_4057,plain,
! [X0: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_2025]) ).
tcf(c_4058,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_65]) ).
tcf(c_4060,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4050,c_2348]) ).
tcf(c_4061,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4050,c_2447]) ).
tcf(c_4062,plain,
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4050,c_2350]) ).
tcf(c_4087,plain,
( element(sK0(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_2205,c_66]) ).
tcf(c_4096,plain,
( element(sK1(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(sK0(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_2219,c_66]) ).
tcf(c_4129,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),zero(any1)) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2084,c_2410]) ).
tcf(c_4143,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_2427,c_552,c_2427]) ).
tcf(c_4144,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) ) ),
inference(renaming,[status(thm)],[c_4143]) ).
tcf(c_4151,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_2428,c_552,c_2428]) ).
tcf(c_4152,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) ) ),
inference(renaming,[status(thm)],[c_4151]) ).
tcf(c_4167,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2717]) ).
tcf(c_4168,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2717]) ).
tcf(c_4171,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3156,c_2717]) ).
tcf(c_4172,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2710,c_2717]) ).
tcf(c_4190,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2737]) ).
tcf(c_4191,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2737]) ).
tcf(c_4192,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4050,c_2737]) ).
tcf(c_4193,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3173,c_2737]) ).
tcf(c_4194,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2726,c_2737]) ).
tcf(c_4196,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2737]) ).
tcf(c_4227,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3044]) ).
tcf(c_4229,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_3044]) ).
tcf(c_4230,plain,
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_3044]) ).
tcf(c_4233,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_3044]) ).
tcf(c_4249,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3163]) ).
tcf(c_4250,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3163]) ).
tcf(c_4253,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3156,c_3163]) ).
tcf(c_4284,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,X0,X1))) = apply(x,subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2604]) ).
tcf(c_4285,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2604]) ).
tcf(c_4288,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1))) = apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3156,c_2604]) ).
tcf(c_4289,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1))) = apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2710,c_2604]) ).
tcf(c_4290,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1))) = apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2417,c_2604]) ).
tcf(c_4293,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) = subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)) )
| ~ injection(x) ),
inference(light_normalisation,[status(thm)],[c_4290,c_365]) ).
tcf(c_4297,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) = subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)) )
| ~ injection(x) ),
inference(light_normalisation,[status(thm)],[c_4289,c_365]) ).
tcf(c_4301,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))) = subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)) )
| ~ injection(x) ),
inference(light_normalisation,[status(thm)],[c_4288,c_365]) ).
tcf(c_4345,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3683,c_3801]) ).
tcf(c_4346,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3677,c_3801]) ).
tcf(c_4347,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3634,c_3801]) ).
tcf(c_4348,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3628,c_3801]) ).
tcf(c_4349,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_3801]) ).
tcf(c_4350,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_3801]) ).
tcf(c_4351,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_3801]) ).
tcf(c_4352,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_3801]) ).
tcf(c_4353,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2177,c_3801]) ).
tcf(c_4354,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2176,c_3801]) ).
tcf(c_4355,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2156,c_3801]) ).
tcf(c_4356,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2155,c_3801]) ).
tcf(c_4357,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2094,c_3801]) ).
tcf(c_4358,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2005,c_3801]) ).
tcf(c_4359,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2004,c_3801]) ).
tcf(c_4426,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,subtract(any1,X0,X1),X2))) = subtract(any1,subtract(any1,X0,X1),X2) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2153]) ).
tcf(c_4428,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0))) = subtract(any1,sK1(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2153]) ).
tcf(c_4429,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0))) = subtract(any1,sK0(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2153]) ).
tcf(c_4432,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,zero(any1),X0))) = subtract(any1,zero(any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2153]) ).
tcf(c_4467,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_3182]) ).
tcf(c_4468,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_3182]) ).
tcf(c_4469,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4050,c_3182]) ).
tcf(c_4470,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3173,c_3182]) ).
tcf(c_4473,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_3182]) ).
tcf(c_4494,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1))),apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3229]) ).
tcf(c_4496,plain,
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_756,c_3229]) ).
tcf(c_4497,plain,
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_758,c_3229]) ).
tcf(c_4500,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),apply(x,subtract(any1,sK1(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_3229]) ).
tcf(c_4519,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1))),apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3230]) ).
tcf(c_4521,plain,
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_756,c_3230]) ).
tcf(c_4522,plain,
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_758,c_3230]) ).
tcf(c_4525,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),apply(x,subtract(any1,sK0(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_3230]) ).
tcf(c_4578,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,X1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,X1))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_3521]) ).
tcf(c_4579,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,X0)),subtract(any2,apply(x,sK0(x,any1)),apply(x,X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_3521]) ).
tcf(c_4580,plain,
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),zero(any2)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4050,c_3521]) ).
tcf(c_4583,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),zero(any2)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2430,c_3521]) ).
tcf(c_4584,plain,
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_3521]) ).
tcf(c_4603,plain,
( ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3550,c_552,c_3550]) ).
tcf(c_4604,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(renaming,[status(thm)],[c_4603]) ).
tcf(c_4609,plain,
( element(sK1(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_4604,c_66]) ).
tcf(c_4627,plain,
( ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3551,c_552,c_3551]) ).
tcf(c_4628,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(renaming,[status(thm)],[c_4627]) ).
tcf(c_4633,plain,
( element(sK0(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK0(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_4628,c_66]) ).
tcf(c_4642,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4230,c_3801]) ).
tcf(c_4643,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4230,c_2518]) ).
tcf(c_4644,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4230,c_2092]) ).
tcf(c_4645,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4230,c_2003]) ).
tcf(c_4646,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4230,c_747]) ).
tcf(c_4669,plain,
( ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4496,c_3801]) ).
tcf(c_4670,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_2518]) ).
tcf(c_4671,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_2092]) ).
tcf(c_4672,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_2003]) ).
tcf(c_4673,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_747]) ).
tcf(c_4725,plain,
( ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4497,c_3801]) ).
tcf(c_4726,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_2518]) ).
tcf(c_4727,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_2092]) ).
tcf(c_4728,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_2003]) ).
tcf(c_4729,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_747]) ).
tcf(c_4764,plain,
( ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4521,c_3801]) ).
tcf(c_4765,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_2518]) ).
tcf(c_4766,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_2092]) ).
tcf(c_4767,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_2003]) ).
tcf(c_4768,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_747]) ).
tcf(c_4783,plain,
( ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4522,c_3801]) ).
tcf(c_4784,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_2518]) ).
tcf(c_4785,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_2092]) ).
tcf(c_4786,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_2003]) ).
tcf(c_4787,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_747]) ).
tcf(c_4802,plain,
( element(sK0(x,any1),any1)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_2204,c_66]) ).
tcf(c_4815,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,subtract(any1,X0,X1),X2))) = subtract(any1,subtract(any1,X0,X1),X2) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2174]) ).
tcf(c_4817,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0))) = subtract(any1,sK1(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2174]) ).
tcf(c_4818,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0))) = subtract(any1,sK0(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2174]) ).
tcf(c_4821,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,zero(any1),X0))) = subtract(any1,zero(any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2174]) ).
tcf(c_4847,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3595]) ).
tcf(c_4848,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3595]) ).
tcf(c_4849,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_3595]) ).
tcf(c_4850,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_3595]) ).
tcf(c_4853,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_3595]) ).
tcf(c_4876,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_4058]) ).
tcf(c_4877,plain,
! [X0: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_4058]) ).
tcf(c_4878,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4050,c_4058]) ).
tcf(c_4882,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_4058]) ).
tcf(c_4899,plain,
( element(sK1(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_4609,c_1120]) ).
tcf(c_4905,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2036]) ).
tcf(c_4906,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,sK1(x,any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2025]) ).
tcf(c_4907,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_65]) ).
tcf(c_4909,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_3595]) ).
tcf(c_4910,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0))) = subtract(any1,sK1(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2174]) ).
tcf(c_4913,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0))) = subtract(any1,sK1(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2153]) ).
tcf(c_4914,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK2(x,any1,any2),sK1(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4899,c_2604]) ).
tcf(c_4916,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_3044]) ).
tcf(c_4918,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK1(x,any1)),subtract(any1,sK2(x,any1,any2),sK1(x,any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4899,c_2296]) ).
tcf(c_4919,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_4899,c_2606]) ).
tcf(c_4920,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_4899,c_3615]) ).
tcf(c_4922,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK1(x,any1)),X0),subtract(any2,apply(x,sK1(x,any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4899,c_2295]) ).
tcf(c_4923,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),apply(x,subtract(any1,sK1(x,any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2091]) ).
tcf(c_4926,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK1(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK1(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_353]) ).
tcf(c_4927,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK1(x,any1))) = sK1(x,any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4899,c_2038]) ).
tcf(c_4928,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4899,c_2037]) ).
tcf(c_4932,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4899,c_3463]) ).
tcf(c_4937,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(light_normalisation,[status(thm)],[c_4909,c_3425]) ).
tcf(c_4950,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK1(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(light_normalisation,[status(thm)],[c_4926,c_3425]) ).
tcf(c_4957,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),X0),subtract(any2,apply(x,sK0(x,any1)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(light_normalisation,[status(thm)],[c_4922,c_3425]) ).
tcf(c_4971,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK2(x,any1,any2),sK1(x,any1))) )
| ~ injection(x) ),
inference(light_normalisation,[status(thm)],[c_4914,c_3425]) ).
tcf(c_5028,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4907]) ).
tcf(c_5029,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4907]) ).
tcf(c_5097,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),subtract(any1,X0,X1)),subtract(any1,zero(any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2423]) ).
tcf(c_5098,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),sK2(x,any1,any2)),subtract(any1,zero(any1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2423]) ).
tcf(c_5099,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),sK1(x,any1)),subtract(any1,zero(any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_2423]) ).
tcf(c_5101,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),sK0(x,any1)),subtract(any1,zero(any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_2423]) ).
tcf(c_5104,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),zero(any1)),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_2423]) ).
tcf(c_5156,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),subtract(any2,X0,X1)),subtract(any2,zero(any2),subtract(any2,X0,X1))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2479]) ).
tcf(c_5157,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,X0)),subtract(any2,zero(any2),apply(x,X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2479]) ).
tcf(c_5158,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4050,c_2479]) ).
tcf(c_5161,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2430,c_2479]) ).
tcf(c_5162,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2479]) ).
tcf(c_5183,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2617]) ).
tcf(c_5184,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))) = subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2617]) ).
tcf(c_5185,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK1(x,any1))) = subtract(any2,zero(any2),apply(x,sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_4899,c_2617]) ).
tcf(c_5186,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK1(x,any1))) = subtract(any2,zero(any2),apply(x,sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_756,c_2617]) ).
tcf(c_5187,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) = subtract(any2,zero(any2),apply(x,sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_758,c_2617]) ).
tcf(c_5190,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),zero(any1))) = subtract(any2,zero(any2),apply(x,zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2417,c_2617]) ).
tcf(c_5192,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK1(x,any1))) = subtract(any2,zero(any2),apply(x,sK0(x,any1))) ) ),
inference(light_normalisation,[status(thm)],[c_5185,c_3425]) ).
tcf(c_5248,plain,
( ( sK0(x,any1) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(sK0(x,any1),any1) ),
inference(equality_resolution,[status(thm)],[c_3436]) ).
tcf(c_5271,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3903]) ).
tcf(c_5273,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_3903]) ).
tcf(c_5274,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_3903]) ).
tcf(c_5275,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_3903]) ).
tcf(c_5278,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,subtract(any1,zero(any1),X0),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_3903]) ).
tcf(c_5315,plain,
( element(apply(x,sK0(x,any1)),any2)
| ~ element(sK0(x,any1),any1) ),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_5331,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3904]) ).
tcf(c_5333,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_3904]) ).
tcf(c_5334,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_3904]) ).
tcf(c_5335,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_3904]) ).
tcf(c_5338,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,subtract(any1,zero(any1),X0),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_3904]) ).
tcf(c_5367,plain,
( element(sK1(x,any1),any1)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ~ element(sK0(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_2218,c_66]) ).
tcf(c_5372,plain,
( element(sK0(x,any1),any1)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_4633,c_1083]) ).
tcf(c_5378,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2036]) ).
tcf(c_5379,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,sK0(x,any1),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2025]) ).
tcf(c_5380,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_65]) ).
tcf(c_5382,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_3904]) ).
tcf(c_5383,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_3903]) ).
tcf(c_5384,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) = subtract(any2,zero(any2),apply(x,sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_5372,c_2617]) ).
tcf(c_5385,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),sK0(x,any1)),subtract(any1,zero(any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_2423]) ).
tcf(c_5388,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0))) = subtract(any1,sK0(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2174]) ).
tcf(c_5391,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0))) = subtract(any1,sK0(x,any1),X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2153]) ).
tcf(c_5392,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK2(x,any1,any2),sK0(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_5372,c_2604]) ).
tcf(c_5396,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK0(x,any1)),subtract(any1,sK2(x,any1,any2),sK0(x,any1))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_5372,c_2296]) ).
tcf(c_5401,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),apply(x,subtract(any1,sK0(x,any1),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2091]) ).
tcf(c_5404,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,X0)) = apply(x,subtract(any1,sK0(x,any1),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_353]) ).
tcf(c_5405,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK0(x,any1))) = sK0(x,any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_5372,c_2038]) ).
tcf(c_5498,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5380]) ).
tcf(c_5499,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_5380]) ).
tcf(c_5531,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))),apply(x,subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1)))) = zero(any2) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3228]) ).
tcf(c_5532,plain,
( ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3228]) ).
tcf(c_5533,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK1(x,any1))),apply(x,subtract(any1,sK2(x,any1,any2),sK1(x,any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4899,c_3228]) ).
tcf(c_5535,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK0(x,any1))),apply(x,subtract(any1,sK2(x,any1,any2),sK0(x,any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_5372,c_3228]) ).
tcf(c_5537,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))),apply(x,subtract(any1,sK2(x,any1,any2),zero(any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3156,c_3228]) ).
tcf(c_5538,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))),apply(x,subtract(any1,sK2(x,any1,any2),zero(any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2710,c_3228]) ).
tcf(c_5539,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),zero(any1))),apply(x,subtract(any1,sK2(x,any1,any2),zero(any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2417,c_3228]) ).
tcf(c_5590,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,X0,X1)),subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,X0,X1))) = zero(any2) )
| ~ injection(x)
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_3519]) ).
tcf(c_5591,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0))) = zero(any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_3519]) ).
tcf(c_5592,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4050,c_3519]) ).
tcf(c_5593,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3173,c_3519]) ).
tcf(c_5594,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2726,c_3519]) ).
tcf(c_5595,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2430,c_3519]) ).
tcf(c_5596,plain,
( ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_3519]) ).
tcf(c_5629,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1)))) = subtract(any1,sK1(x,any1),subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4428]) ).
tcf(c_5631,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_4428]) ).
tcf(c_5632,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_4428]) ).
tcf(c_5633,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5372,c_4428]) ).
tcf(c_5634,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_4428]) ).
tcf(c_5637,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1)))) = subtract(any1,sK1(x,any1),zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_4428]) ).
tcf(c_5676,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1)))) = subtract(any1,sK0(x,any1),subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4429]) ).
tcf(c_5678,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_4429]) ).
tcf(c_5679,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_4429]) ).
tcf(c_5680,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5372,c_4429]) ).
tcf(c_5681,plain,
( injection(x)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_4429]) ).
tcf(c_5684,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),zero(any1)))) = subtract(any1,sK0(x,any1),zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_4429]) ).
tcf(c_5754,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1)))) = subtract(any1,sK1(x,any1),subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4817]) ).
tcf(c_5756,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_4817]) ).
tcf(c_5757,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_4817]) ).
tcf(c_5758,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5372,c_4817]) ).
tcf(c_5759,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_4817]) ).
tcf(c_5762,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),zero(any1)))) = subtract(any1,sK1(x,any1),zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_4817]) ).
tcf(c_5812,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1)))) = subtract(any1,sK0(x,any1),subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4818]) ).
tcf(c_5814,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_4818]) ).
tcf(c_5815,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_4818]) ).
tcf(c_5816,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5372,c_4818]) ).
tcf(c_5817,plain,
( injection(x)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_4818]) ).
tcf(c_5820,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1)))) = subtract(any1,sK0(x,any1),zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_4818]) ).
tcf(c_5843,plain,
( element(apply(x,sK0(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(subtract(any2,zero(any2),apply(x,sK0(x,any1))),any2) ),
inference(superposition,[status(thm)],[c_4937,c_66]) ).
tcf(c_5865,plain,
( element(apply(x,subtract(any1,zero(any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_5192,c_66]) ).
tcf(c_5866,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5192,c_4937]) ).
tcf(c_5889,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5274]) ).
tcf(c_5891,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_5274]) ).
tcf(c_5892,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_5274]) ).
tcf(c_5893,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_5274]) ).
tcf(c_5894,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_5274]) ).
tcf(c_5897,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_5274]) ).
tcf(c_5949,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5275]) ).
tcf(c_5951,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_5275]) ).
tcf(c_5952,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_5275]) ).
tcf(c_5953,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_5275]) ).
tcf(c_5954,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_5275]) ).
tcf(c_5957,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_5275]) ).
tcf(c_5982,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5334]) ).
tcf(c_5984,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_5334]) ).
tcf(c_5985,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_5334]) ).
tcf(c_5986,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_5334]) ).
tcf(c_5987,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_5334]) ).
tcf(c_5990,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_5334]) ).
tcf(c_6058,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5335]) ).
tcf(c_6060,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_5335]) ).
tcf(c_6061,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_756,c_5335]) ).
tcf(c_6062,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_5335]) ).
tcf(c_6063,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_758,c_5335]) ).
tcf(c_6066,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_5335]) ).
tcf(c_6111,plain,
( element(apply(x,subtract(any1,zero(any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_5384,c_66]) ).
tcf(c_6112,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_5384,c_5192]) ).
tcf(c_6113,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5384,c_4937]) ).
tcf(c_6126,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(apply(x,sK2(x,any1,any2)),any2) ),
inference(superposition,[status(thm)],[c_2252,c_66]) ).
tcf(c_6138,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3852]) ).
tcf(c_6139,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3852]) ).
tcf(c_6140,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_4899,c_3852]) ).
tcf(c_6142,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_5372,c_3852]) ).
tcf(c_6144,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_3156,c_3852]) ).
tcf(c_6145,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2710,c_3852]) ).
tcf(c_6146,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_2417,c_3852]) ).
tcf(c_6167,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_4285]) ).
tcf(c_6168,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_4285]) ).
tcf(c_6169,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_4285]) ).
tcf(c_6170,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_4285]) ).
tcf(c_6171,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4230,c_4285]) ).
tcf(c_6172,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_3683,c_4285]) ).
tcf(c_6173,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_3677,c_4285]) ).
tcf(c_6174,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_3634,c_4285]) ).
tcf(c_6175,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_3628,c_4285]) ).
tcf(c_6176,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2999,c_4285]) ).
tcf(c_6177,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2998,c_4285]) ).
tcf(c_6178,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2670,c_4285]) ).
tcf(c_6179,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2669,c_4285]) ).
tcf(c_6180,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2177,c_4285]) ).
tcf(c_6181,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2176,c_4285]) ).
tcf(c_6182,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2156,c_4285]) ).
tcf(c_6183,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2155,c_4285]) ).
tcf(c_6184,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2094,c_4285]) ).
tcf(c_6185,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2005,c_4285]) ).
tcf(c_6186,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_2004,c_4285]) ).
tcf(c_6280,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_6126,c_531,c_2166,c_2176,c_6126]) ).
tcf(c_6286,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6280,c_2036]) ).
tcf(c_6287,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6280,c_2025]) ).
tcf(c_6288,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6280,c_65]) ).
tcf(c_6290,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_6280,c_3519]) ).
tcf(c_6294,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6280,c_3182]) ).
tcf(c_6295,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6280,c_2737]) ).
tcf(c_6296,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_6280,c_2348]) ).
tcf(c_6297,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6280,c_2447]) ).
tcf(c_6356,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5632,c_4285]) ).
tcf(c_6357,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5632,c_3801]) ).
tcf(c_6358,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5632,c_2518]) ).
tcf(c_6359,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5632,c_2092]) ).
tcf(c_6360,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5632,c_2003]) ).
tcf(c_6361,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5632,c_747]) ).
tcf(c_6378,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5634,c_4285]) ).
tcf(c_6379,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5634,c_3801]) ).
tcf(c_6380,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5634,c_2518]) ).
tcf(c_6381,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5634,c_2092]) ).
tcf(c_6382,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5634,c_2003]) ).
tcf(c_6383,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5634,c_747]) ).
tcf(c_6400,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5679,c_4285]) ).
tcf(c_6401,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5679,c_3801]) ).
tcf(c_6402,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5679,c_2518]) ).
tcf(c_6403,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5679,c_2092]) ).
tcf(c_6404,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5679,c_2003]) ).
tcf(c_6405,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5679,c_747]) ).
tcf(c_6446,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5681,c_4285]) ).
tcf(c_6447,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5681,c_3801]) ).
tcf(c_6448,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5681,c_2518]) ).
tcf(c_6449,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5681,c_2092]) ).
tcf(c_6450,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5681,c_2003]) ).
tcf(c_6451,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5681,c_747]) ).
tcf(c_6468,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5757,c_4285]) ).
tcf(c_6469,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5757,c_3801]) ).
tcf(c_6470,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5757,c_2518]) ).
tcf(c_6471,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5757,c_2092]) ).
tcf(c_6472,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5757,c_2003]) ).
tcf(c_6473,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5757,c_747]) ).
tcf(c_6506,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5759,c_4285]) ).
tcf(c_6507,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5759,c_3801]) ).
tcf(c_6508,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5759,c_2518]) ).
tcf(c_6509,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5759,c_2092]) ).
tcf(c_6510,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5759,c_2003]) ).
tcf(c_6511,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5759,c_747]) ).
tcf(c_6547,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5815,c_4285]) ).
tcf(c_6548,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5815,c_3801]) ).
tcf(c_6549,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5815,c_2518]) ).
tcf(c_6550,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5815,c_2092]) ).
tcf(c_6551,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5815,c_2003]) ).
tcf(c_6552,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5815,c_747]) ).
tcf(c_6585,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5817,c_4285]) ).
tcf(c_6586,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5817,c_3801]) ).
tcf(c_6587,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5817,c_2518]) ).
tcf(c_6588,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5817,c_2092]) ).
tcf(c_6589,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5817,c_2003]) ).
tcf(c_6590,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_5817,c_747]) ).
tcf(c_6650,plain,
( element(apply(x,sK0(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,subtract(any1,zero(any1),sK1(x,any1))),any2) ),
inference(superposition,[status(thm)],[c_5866,c_66]) ).
tcf(c_6659,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_4285]) ).
tcf(c_6660,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_3801]) ).
tcf(c_6661,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_2518]) ).
tcf(c_6662,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_2092]) ).
tcf(c_6663,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_2003]) ).
tcf(c_6664,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_747]) ).
tcf(c_6681,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_4285]) ).
tcf(c_6682,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_3801]) ).
tcf(c_6683,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_2518]) ).
tcf(c_6684,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_2092]) ).
tcf(c_6685,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_2003]) ).
tcf(c_6686,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_747]) ).
tcf(c_6732,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(apply(x,sK2(x,any1,any2)),any2) ),
inference(superposition,[status(thm)],[c_2253,c_66]) ).
tcf(c_6736,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_6732,c_531,c_2156,c_2166,c_6732]) ).
tcf(c_6742,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6736,c_2036]) ).
tcf(c_6743,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6736,c_2025]) ).
tcf(c_6744,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6736,c_65]) ).
tcf(c_6746,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_6736,c_3519]) ).
tcf(c_6750,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_3182]) ).
tcf(c_6751,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_2737]) ).
tcf(c_6752,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_6736,c_2348]) ).
tcf(c_6753,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_2447]) ).
tcf(c_6874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( subtract(X1,subtract(X1,subtract(X1,X3,X4),subtract(X1,X0,X2)),subtract(X1,subtract(X1,X3,X4),subtract(X1,X0,X2))) = zero(X1) )
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_2294]) ).
tcf(c_6875,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any2,subtract(any2,subtract(any2,X1,X2),apply(x,X0)),subtract(any2,subtract(any2,X1,X2),apply(x,X0))) = zero(any2) )
| ~ element(X2,any2)
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2294]) ).
tcf(c_6876,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2)),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2294]) ).
tcf(c_6877,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK1(x,any1)),subtract(any1,subtract(any1,X0,X1),sK1(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2294]) ).
tcf(c_6878,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK1(x,any1)),subtract(any1,subtract(any1,X0,X1),sK1(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2294]) ).
tcf(c_6879,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK0(x,any1)),subtract(any1,subtract(any1,X0,X1),sK0(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2294]) ).
tcf(c_6880,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK0(x,any1)),subtract(any1,subtract(any1,X0,X1),sK0(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2294]) ).
tcf(c_6881,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6736,c_2294]) ).
tcf(c_6882,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_6280,c_2294]) ).
tcf(c_6883,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_2294]) ).
tcf(c_6884,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3173,c_2294]) ).
tcf(c_6885,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2726,c_2294]) ).
tcf(c_6886,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2430,c_2294]) ).
tcf(c_6887,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),zero(any1)),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2294]) ).
tcf(c_6888,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),zero(any1)),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2294]) ).
tcf(c_6889,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),zero(any1)),subtract(any1,subtract(any1,X0,X1),zero(any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2294]) ).
tcf(c_6890,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1))),subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2294]) ).
tcf(c_7035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(any2,apply(x,subtract(any1,subtract(any1,X0,X1),X2)),subtract(any2,apply(x,subtract(any1,subtract(any1,X0,X1),X2)),X3)) = X3 )
| ~ element(X3,any2)
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2347]) ).
tcf(c_7036,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),X1)) = X1 )
| ~ injection(x)
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2347]) ).
tcf(c_7037,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2347]) ).
tcf(c_7038,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2347]) ).
tcf(c_7039,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2347]) ).
tcf(c_7040,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2347]) ).
tcf(c_7041,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),subtract(any2,apply(x,subtract(any1,zero(any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2347]) ).
tcf(c_7042,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),subtract(any2,apply(x,subtract(any1,zero(any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2347]) ).
tcf(c_7043,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),subtract(any2,apply(x,subtract(any1,zero(any1),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2347]) ).
tcf(c_7128,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_4285]) ).
tcf(c_7129,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_3801]) ).
tcf(c_7130,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_2518]) ).
tcf(c_7131,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_2092]) ).
tcf(c_7132,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_2003]) ).
tcf(c_7133,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_747]) ).
tcf(c_7182,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_4285]) ).
tcf(c_7183,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_3801]) ).
tcf(c_7184,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_2518]) ).
tcf(c_7185,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_2092]) ).
tcf(c_7186,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_2003]) ).
tcf(c_7187,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_747]) ).
tcf(c_7214,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_4285]) ).
tcf(c_7215,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_3801]) ).
tcf(c_7216,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_2518]) ).
tcf(c_7217,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_2092]) ).
tcf(c_7218,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_2003]) ).
tcf(c_7219,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_747]) ).
tcf(c_7267,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_4285]) ).
tcf(c_7268,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_3801]) ).
tcf(c_7269,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_2518]) ).
tcf(c_7270,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_2092]) ).
tcf(c_7271,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_2003]) ).
tcf(c_7272,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_747]) ).
tcf(c_7294,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_4285]) ).
tcf(c_7295,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_3801]) ).
tcf(c_7296,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_2518]) ).
tcf(c_7297,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_2092]) ).
tcf(c_7298,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_2003]) ).
tcf(c_7299,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_747]) ).
tcf(c_7326,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_4285]) ).
tcf(c_7327,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_3801]) ).
tcf(c_7328,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_2518]) ).
tcf(c_7329,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_2092]) ).
tcf(c_7330,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_2003]) ).
tcf(c_7331,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_747]) ).
tcf(c_7348,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_6112,c_3436]) ).
tcf(c_7349,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),sK1(x,any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_6112,c_3391]) ).
tcf(c_7351,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),sK1(x,any1)) = zero(any1) )
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_6112,c_810]) ).
tcf(c_7352,plain,
( element(apply(x,subtract(any1,zero(any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_6112,c_765]) ).
tcf(c_7353,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,zero(any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,zero(any1),sK0(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_6112,c_435]) ).
tcf(c_7421,plain,
( element(apply(x,sK0(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,subtract(any1,zero(any1),sK0(x,any1))),any2) ),
inference(superposition,[status(thm)],[c_6113,c_66]) ).
tcf(c_7428,plain,
( element(apply(x,subtract(any1,zero(any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_7352,c_1083,c_2430,c_5315,c_6111]) ).
tcf(c_7434,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_2294]) ).
tcf(c_7435,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_2036]) ).
tcf(c_7436,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,zero(any1),sK0(x,any1))),X0),subtract(any2,apply(x,subtract(any1,zero(any1),sK0(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_2025]) ).
tcf(c_7437,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),sK0(x,any1))),subtract(any2,apply(x,subtract(any1,zero(any1),sK0(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_65]) ).
tcf(c_7438,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),sK0(x,any1))),apply(x,subtract(any1,zero(any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7428,c_61]) ).
tcf(c_7439,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7428,c_3519]) ).
tcf(c_7440,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7428,c_2479]) ).
tcf(c_7441,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_7428,c_4058]) ).
tcf(c_7442,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7428,c_3521]) ).
tcf(c_7445,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7428,c_2348]) ).
tcf(c_7446,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_7428,c_2447]) ).
tcf(c_7447,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_7428,c_2350]) ).
tcf(c_7507,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(apply(x,sK2(x,any1,any2)),any2) ),
inference(superposition,[status(thm)],[c_2254,c_66]) ).
tcf(c_7511,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_7507,c_531,c_2155,c_2166,c_7507]) ).
tcf(c_7517,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7511,c_2294]) ).
tcf(c_7518,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7511,c_2036]) ).
tcf(c_7519,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7511,c_2025]) ).
tcf(c_7520,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7511,c_65]) ).
tcf(c_7522,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7511,c_3519]) ).
tcf(c_7526,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_3182]) ).
tcf(c_7527,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_2737]) ).
tcf(c_7528,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7511,c_2348]) ).
tcf(c_7529,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_2447]) ).
tcf(c_7617,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_2671,c_552,c_2671]) ).
tcf(c_7618,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),subtract(any1,sK1(x,any1),zero(any1))) = zero(any1) ) ),
inference(renaming,[status(thm)],[c_7617]) ).
tcf(c_7632,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),subtract(any1,X0,X1)),subtract(any1,zero(any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2716]) ).
tcf(c_7633,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),sK2(x,any1,any2)),subtract(any1,zero(any1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2716]) ).
tcf(c_7638,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),zero(any1)),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3156,c_2716]) ).
tcf(c_7639,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),zero(any1)),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2710,c_2716]) ).
tcf(c_7657,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2747]) ).
tcf(c_7658,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))) = subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_2747]) ).
tcf(c_7663,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),zero(any1))) = subtract(any2,zero(any2),apply(x,zero(any1))) ) ),
inference(superposition,[status(thm)],[c_3156,c_2747]) ).
tcf(c_7664,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),zero(any1))) = subtract(any2,zero(any2),apply(x,zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2710,c_2747]) ).
tcf(c_7682,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),subtract(any2,X0,X1)),subtract(any2,zero(any2),subtract(any2,X0,X1))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_2891]) ).
tcf(c_7683,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,X0)),subtract(any2,zero(any2),apply(x,X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_2891]) ).
tcf(c_7684,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7511,c_2891]) ).
tcf(c_7685,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6736,c_2891]) ).
tcf(c_7686,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6280,c_2891]) ).
tcf(c_7688,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3173,c_2891]) ).
tcf(c_7689,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2726,c_2891]) ).
tcf(c_7691,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_2891]) ).
tcf(c_7712,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3001,c_552,c_3001]) ).
tcf(c_7713,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),subtract(any1,sK0(x,any1),zero(any1))) = zero(any1) ) ),
inference(renaming,[status(thm)],[c_7712]) ).
tcf(c_7721,plain,
( ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),zero(any2))) = zero(any2) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3024,c_552,c_3024]) ).
tcf(c_7722,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK1(x,any1)),subtract(any2,apply(x,sK1(x,any1)),zero(any2))) = zero(any2) ) ),
inference(renaming,[status(thm)],[c_7721]) ).
tcf(c_7723,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(light_normalisation,[status(thm)],[c_7722,c_3425]) ).
tcf(c_7737,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),subtract(any1,X0,X1)),subtract(any1,zero(any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3162]) ).
tcf(c_7738,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),sK2(x,any1,any2)),subtract(any1,zero(any1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3162]) ).
tcf(c_7743,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),zero(any1)),subtract(any1,zero(any1),zero(any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_3156,c_3162]) ).
tcf(c_7761,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),subtract(any1,X0,X1))) = subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3192]) ).
tcf(c_7762,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))) = subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3192]) ).
tcf(c_7767,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),zero(any1))) = subtract(any2,zero(any2),apply(x,zero(any1))) ) ),
inference(superposition,[status(thm)],[c_3156,c_3192]) ).
tcf(c_7785,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),subtract(any2,X0,X1)),subtract(any2,zero(any2),subtract(any2,X0,X1))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_3299]) ).
tcf(c_7786,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,X0)),subtract(any2,zero(any2),apply(x,X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_3299]) ).
tcf(c_7787,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7511,c_3299]) ).
tcf(c_7788,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6736,c_3299]) ).
tcf(c_7789,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6280,c_3299]) ).
tcf(c_7791,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3173,c_3299]) ).
tcf(c_7794,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_3299]) ).
tcf(c_7819,plain,
( element(zero(any2),any2)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ~ element(apply(x,sK2(x,any1,any2)),any2) ),
inference(superposition,[status(thm)],[c_2255,c_66]) ).
tcf(c_7835,plain,
( element(zero(any2),any2)
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_7819,c_531,c_2094,c_2166,c_7819]) ).
tcf(c_7841,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7835,c_2294]) ).
tcf(c_7842,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7835,c_2036]) ).
tcf(c_7843,plain,
! [X0: $i] :
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7835,c_2025]) ).
tcf(c_7844,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7835,c_65]) ).
tcf(c_7846,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_3299]) ).
tcf(c_7847,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_2891]) ).
tcf(c_7848,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7835,c_3519]) ).
tcf(c_7852,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_3182]) ).
tcf(c_7853,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_2737]) ).
tcf(c_7854,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_7835,c_2348]) ).
tcf(c_7855,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_2447]) ).
tcf(c_7920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(any2,subtract(any2,X2,X3),subtract(any2,subtract(any2,X2,X3),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X3,any2)
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3901]) ).
tcf(c_7921,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x)
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_749,c_3901]) ).
tcf(c_7922,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4899,c_3901]) ).
tcf(c_7923,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_756,c_3901]) ).
tcf(c_7924,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_5372,c_3901]) ).
tcf(c_7925,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_758,c_3901]) ).
tcf(c_7926,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_3156,c_3901]) ).
tcf(c_7927,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2710,c_3901]) ).
tcf(c_7928,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,zero(any1)))) = apply(x,zero(any1)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2417,c_3901]) ).
tcf(c_7999,plain,
( ( apply(x,subtract(any1,sK1(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3637,c_552,c_3637]) ).
tcf(c_8000,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) ) ),
inference(renaming,[status(thm)],[c_7999]) ).
tcf(c_8005,plain,
( element(apply(x,subtract(any1,sK1(x,any1),zero(any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_8000,c_66]) ).
tcf(c_8006,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8000,c_7723]) ).
tcf(c_8017,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4029,c_8006]) ).
tcf(c_8020,plain,
( ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) )
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3686,c_552,c_3686]) ).
tcf(c_8021,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)) ) ),
inference(renaming,[status(thm)],[c_8020]) ).
tcf(c_8027,plain,
( element(apply(x,subtract(any1,sK0(x,any1),zero(any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(zero(any2),any2)
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_8021,c_66]) ).
tcf(c_8028,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_8021,c_8000]) ).
tcf(c_8029,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8021,c_7723]) ).
tcf(c_8042,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4029,c_8028]) ).
tcf(c_8044,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),zero(any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,sK1(x,any1),zero(any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_8028,c_3391]) ).
tcf(c_8046,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),zero(any1)) = zero(any1) )
| ~ element(subtract(any1,sK1(x,any1),zero(any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_8028,c_810]) ).
tcf(c_8047,plain,
( element(apply(x,subtract(any1,sK0(x,any1),zero(any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(subtract(any1,sK1(x,any1),zero(any1)),any1) ),
inference(superposition,[status(thm)],[c_8028,c_765]) ).
tcf(c_8048,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),zero(any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),zero(any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_8028,c_435]) ).
tcf(c_8050,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),zero(any1))) = apply(x,sK0(x,any1)) ) ),
inference(light_normalisation,[status(thm)],[c_8042,c_3425]) ).
tcf(c_8104,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),zero(any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),zero(any1)),any1) ),
inference(superposition,[status(thm)],[c_8050,c_3436]) ).
tcf(c_8105,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),zero(any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,sK0(x,any1),zero(any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_8050,c_3391]) ).
tcf(c_8107,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),zero(any1)) = zero(any1) )
| ~ element(subtract(any1,sK0(x,any1),zero(any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_8050,c_810]) ).
tcf(c_8108,plain,
( element(apply(x,sK0(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(subtract(any1,sK0(x,any1),zero(any1)),any1) ),
inference(superposition,[status(thm)],[c_8050,c_765]) ).
tcf(c_8109,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),zero(any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK0(x,any1),zero(any1)),any1)
| ( apply(x,sK0(x,any1)) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_8050,c_435]) ).
tcf(c_8135,plain,
( element(apply(x,sK0(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_8108,c_1083,c_5315]) ).
tcf(c_8141,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1))),subtract(any2,subtract(any2,X0,X1),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8135,c_2294]) ).
tcf(c_8148,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_8135,c_3519]) ).
tcf(c_8149,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8135,c_2479]) ).
tcf(c_8150,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_8135,c_4058]) ).
tcf(c_8151,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8135,c_3521]) ).
tcf(c_8212,plain,
( element(apply(x,subtract(any1,sK0(x,any1),zero(any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_8047,c_2430,c_8027,c_8135]) ).
tcf(c_8220,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_2294]) ).
tcf(c_8221,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_2036]) ).
tcf(c_8222,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),X0),subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_2025]) ).
tcf(c_8223,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_65]) ).
tcf(c_8224,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),zero(any1))),apply(x,subtract(any1,sK0(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8212,c_61]) ).
tcf(c_8227,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_8212,c_3519]) ).
tcf(c_8228,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8212,c_2479]) ).
tcf(c_8229,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_8212,c_4058]) ).
tcf(c_8230,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8212,c_3521]) ).
tcf(c_8233,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_8212,c_2348]) ).
tcf(c_8234,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_8212,c_2447]) ).
tcf(c_8235,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_8212,c_2350]) ).
tcf(c_8322,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4191]) ).
tcf(c_8323,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4191]) ).
tcf(c_8328,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_3156,c_4191]) ).
tcf(c_8329,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2710,c_4191]) ).
tcf(c_8347,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4468]) ).
tcf(c_8348,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4468]) ).
tcf(c_8353,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_3156,c_4468]) ).
tcf(c_8372,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1)))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4579]) ).
tcf(c_8374,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4899,c_4579]) ).
tcf(c_8375,plain,
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_756,c_4579]) ).
tcf(c_8377,plain,
( injection(x)
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_758,c_4579]) ).
tcf(c_8380,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_4579]) ).
tcf(c_8423,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_7844]) ).
tcf(c_8424,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_7844]) ).
tcf(c_8425,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7835,c_7844]) ).
tcf(c_8426,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_7844]) ).
tcf(c_8427,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_7844]) ).
tcf(c_8428,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6280,c_7844]) ).
tcf(c_8434,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_7844]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,subtract(any1,X0,X1),X2))) = subtract(any1,subtract(any1,X0,X1),X2) )
| ~ injection(x)
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2517]) ).
tcf(c_8462,plain,
! [X0: $i] :
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),X0))) = subtract(any1,sK2(x,any1,any2),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2517]) ).
tcf(c_8463,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,sK1(x,any1),X0))) = subtract(any1,sK1(x,any1),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2517]) ).
tcf(c_8465,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,sK0(x,any1),X0))) = subtract(any1,sK0(x,any1),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2517]) ).
tcf(c_8467,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,zero(any1),X0))) = subtract(any1,zero(any1),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2517]) ).
tcf(c_8468,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,zero(any1),X0))) = subtract(any1,zero(any1),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2517]) ).
tcf(c_8469,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,zero(any1),X0))) = subtract(any1,zero(any1),X0) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2517]) ).
tcf(c_8513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3902]) ).
tcf(c_8514,plain,
! [X0: $i] :
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),X0),subtract(any1,subtract(any1,sK2(x,any1,any2),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_3902]) ).
tcf(c_8515,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),X0),subtract(any1,subtract(any1,sK1(x,any1),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_3902]) ).
tcf(c_8517,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),X0),subtract(any1,subtract(any1,sK0(x,any1),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_3902]) ).
tcf(c_8519,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,subtract(any1,zero(any1),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_3902]) ).
tcf(c_8520,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,subtract(any1,zero(any1),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_3902]) ).
tcf(c_8521,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,zero(any1),X0),subtract(any1,subtract(any1,zero(any1),X0),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ injection(x)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_3902]) ).
tcf(c_8589,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4906]) ).
tcf(c_8590,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK2(x,any1,any2)),subtract(any1,sK1(x,any1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4906]) ).
tcf(c_8612,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_4932]) ).
tcf(c_8613,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,X0))) = apply(x,X0) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_4932]) ).
tcf(c_8618,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4050,c_4932]) ).
tcf(c_8624,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = apply(x,subtract(any1,zero(any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_7428,c_4932]) ).
tcf(c_8625,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_8212,c_4932]) ).
tcf(c_8648,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5379]) ).
tcf(c_8649,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK2(x,any1,any2)),subtract(any1,sK0(x,any1),sK2(x,any1,any2))) = zero(any1) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_5379]) ).
tcf(c_8669,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_4285]) ).
tcf(c_8670,plain,
( ( subtract(any1,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_3801]) ).
tcf(c_8671,plain,
( ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_2518]) ).
tcf(c_8672,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2))) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_2092]) ).
tcf(c_8673,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_2003]) ).
tcf(c_8674,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_747]) ).
tcf(c_8703,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_2721,c_2005,c_2721]) ).
tcf(c_8710,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),zero(any1))) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_3168,c_2004,c_3168]) ).
tcf(c_8743,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_4168,c_2005,c_4168]) ).
tcf(c_8749,plain,
( element(sK2(x,any1,any2),any1)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK2(x,any1,any2)),any1) ),
inference(superposition,[status(thm)],[c_8743,c_66]) ).
tcf(c_8754,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) = sK2(x,any1,any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_4250,c_2004,c_4250]) ).
tcf(c_8760,plain,
( element(sK2(x,any1,any2),any1)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,zero(any1),sK2(x,any1,any2)),any1) ),
inference(superposition,[status(thm)],[c_8754,c_66]) ).
tcf(c_8771,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(apply(x,sK2(x,any1,any2)),any2) ),
inference(superposition,[status(thm)],[c_2408,c_66]) ).
tcf(c_8775,plain,
( element(zero(any2),any2)
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_8771,c_531,c_2166,c_2177,c_8771]) ).
tcf(c_8781,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),zero(any2)),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8775,c_2294]) ).
tcf(c_8782,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),zero(any2))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8775,c_2036]) ).
tcf(c_8783,plain,
! [X0: $i] :
( ( subtract(any2,subtract(any2,zero(any2),X0),subtract(any2,zero(any2),X0)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8775,c_2025]) ).
tcf(c_8784,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),X0)) = X0 )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8775,c_65]) ).
tcf(c_8787,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_7844]) ).
tcf(c_8788,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8775,c_3299]) ).
tcf(c_8789,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8775,c_2891]) ).
tcf(c_8790,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_8775,c_3519]) ).
tcf(c_8794,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_3182]) ).
tcf(c_8795,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_2737]) ).
tcf(c_8796,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),zero(any2))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_8775,c_2348]) ).
tcf(c_8797,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_2447]) ).
tcf(c_8837,plain,
( ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_5532]) ).
tcf(c_8838,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6063,c_5532]) ).
tcf(c_8839,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_6061,c_5532]) ).
tcf(c_8840,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5987,c_5532]) ).
tcf(c_8841,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5985,c_5532]) ).
tcf(c_8842,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5954,c_5532]) ).
tcf(c_8843,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5952,c_5532]) ).
tcf(c_8844,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5894,c_5532]) ).
tcf(c_8845,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5892,c_5532]) ).
tcf(c_8846,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5817,c_5532]) ).
tcf(c_8847,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5815,c_5532]) ).
tcf(c_8848,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5759,c_5532]) ).
tcf(c_8849,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5757,c_5532]) ).
tcf(c_8850,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5681,c_5532]) ).
tcf(c_8851,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5679,c_5532]) ).
tcf(c_8852,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5634,c_5532]) ).
tcf(c_8853,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_5632,c_5532]) ).
tcf(c_8854,plain,
( ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_5532]) ).
tcf(c_8855,plain,
( ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_5532]) ).
tcf(c_8856,plain,
( ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_5532]) ).
tcf(c_8857,plain,
( ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_5532]) ).
tcf(c_8858,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4230,c_5532]) ).
tcf(c_8859,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3683,c_5532]) ).
tcf(c_8860,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3677,c_5532]) ).
tcf(c_8861,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3634,c_5532]) ).
tcf(c_8862,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3628,c_5532]) ).
tcf(c_8863,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2999,c_5532]) ).
tcf(c_8864,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2998,c_5532]) ).
tcf(c_8865,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2670,c_5532]) ).
tcf(c_8866,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2669,c_5532]) ).
tcf(c_8867,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2177,c_5532]) ).
tcf(c_8868,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2176,c_5532]) ).
tcf(c_8869,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2156,c_5532]) ).
tcf(c_8870,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2155,c_5532]) ).
tcf(c_8871,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2094,c_5532]) ).
tcf(c_8872,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2005,c_5532]) ).
tcf(c_8873,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))),apply(x,subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2004,c_5532]) ).
tcf(c_10045,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8377,c_6139]) ).
tcf(c_10046,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6063,c_6139]) ).
tcf(c_10047,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6061,c_6139]) ).
tcf(c_10048,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5987,c_6139]) ).
tcf(c_10049,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_5985,c_6139]) ).
tcf(c_10050,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5954,c_6139]) ).
tcf(c_10051,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5952,c_6139]) ).
tcf(c_10052,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5894,c_6139]) ).
tcf(c_10053,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_5892,c_6139]) ).
tcf(c_10054,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5817,c_6139]) ).
tcf(c_10055,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5815,c_6139]) ).
tcf(c_10056,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5759,c_6139]) ).
tcf(c_10057,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5757,c_6139]) ).
tcf(c_10058,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = subtract(any1,sK0(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5681,c_6139]) ).
tcf(c_10059,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5679,c_6139]) ).
tcf(c_10060,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = subtract(any1,sK1(x,any1),sK0(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5634,c_6139]) ).
tcf(c_10061,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = subtract(any1,sK1(x,any1),sK1(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_5632,c_6139]) ).
tcf(c_10062,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4522,c_6139]) ).
tcf(c_10063,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4521,c_6139]) ).
tcf(c_10064,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4497,c_6139]) ).
tcf(c_10065,plain,
( ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4496,c_6139]) ).
tcf(c_10066,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_4230,c_6139]) ).
tcf(c_10067,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_3683,c_6139]) ).
tcf(c_10068,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_3677,c_6139]) ).
tcf(c_10069,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_3634,c_6139]) ).
tcf(c_10070,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_3628,c_6139]) ).
tcf(c_10071,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2999,c_6139]) ).
tcf(c_10072,plain,
( ( subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2998,c_6139]) ).
tcf(c_10073,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2670,c_6139]) ).
tcf(c_10074,plain,
( ( subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2669,c_6139]) ).
tcf(c_10075,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2177,c_6139]) ).
tcf(c_10076,plain,
( ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2176,c_6139]) ).
tcf(c_10077,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2156,c_6139]) ).
tcf(c_10078,plain,
( ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2155,c_6139]) ).
tcf(c_10079,plain,
( ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2094,c_6139]) ).
tcf(c_10080,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2005,c_6139]) ).
tcf(c_10081,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_2004,c_6139]) ).
tcf(c_10291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subtract(any2,apply(x,subtract(any1,subtract(any1,X0,X1),X2)),apply(x,X3)) = apply(x,subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),X3)) )
| ~ element(X3,any1)
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2603]) ).
tcf(c_10292,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK2(x,any1,any2),X0),X1)) )
| ~ injection(x)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_749,c_2603]) ).
tcf(c_10293,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK1(x,any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2603]) ).
tcf(c_10294,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK1(x,any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2603]) ).
tcf(c_10295,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK0(x,any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2603]) ).
tcf(c_10296,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK0(x,any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2603]) ).
tcf(c_10297,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,zero(any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_3156,c_2603]) ).
tcf(c_10298,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,zero(any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2710,c_2603]) ).
tcf(c_10299,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,zero(any1),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2603]) ).
tcf(c_10386,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,subtract(any1,X0,X1),X2)),subtract(any1,sK1(x,any1),subtract(any1,subtract(any1,X0,X1),X2))) = zero(any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2667]) ).
tcf(c_10388,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0)),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2667]) ).
tcf(c_10389,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0)),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2667]) ).
tcf(c_10390,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0)),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2667]) ).
tcf(c_10391,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0)),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2667]) ).
tcf(c_10394,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,zero(any1),X0)),subtract(any1,sK1(x,any1),subtract(any1,zero(any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2667]) ).
tcf(c_10476,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),zero(any1)) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2109,c_2819]) ).
tcf(c_10491,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),zero(any1)) = sK2(x,any1,any2) ) ),
inference(superposition,[status(thm)],[c_2110,c_2820]) ).
tcf(c_10513,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,subtract(any1,X0,X1),X2)),subtract(any1,sK0(x,any1),subtract(any1,subtract(any1,X0,X1),X2))) = zero(any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_2996]) ).
tcf(c_10515,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0)),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_2996]) ).
tcf(c_10516,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0)),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_2996]) ).
tcf(c_10517,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0)),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_2996]) ).
tcf(c_10518,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0)),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_2996]) ).
tcf(c_10521,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,zero(any1),X0)),subtract(any1,sK0(x,any1),subtract(any1,zero(any1),X0))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_2996]) ).
tcf(c_10600,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X2,subtract(any2,X0,X1)))) = subtract(any2,X2,subtract(any2,X0,X1)) )
| ~ element(X2,any2)
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_3043]) ).
tcf(c_10601,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X1,apply(x,X0)))) = subtract(any2,X1,apply(x,X0)) )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_3043]) ).
tcf(c_10607,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,zero(any2)))) = subtract(any2,X0,zero(any2)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_3043]) ).
tcf(c_10610,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,zero(any2)))) = subtract(any2,X0,zero(any2)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2430,c_3043]) ).
tcf(c_10611,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,sK0(x,any1))))) = subtract(any2,X0,apply(x,sK0(x,any1))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8135,c_3043]) ).
tcf(c_10612,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,sK0(x,any1))))) = subtract(any2,X0,apply(x,sK0(x,any1))) )
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_3043]) ).
tcf(c_10613,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK0(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK0(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_3043]) ).
tcf(c_10614,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),zero(any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),zero(any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_3043]) ).
tcf(c_10701,plain,
( element(apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_3702,c_66]) ).
tcf(c_10702,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3702,c_2132]) ).
tcf(c_10703,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3702,c_2133]) ).
tcf(c_10712,plain,
( element(apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_10701,c_8135,c_10701]) ).
tcf(c_10718,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_2294]) ).
tcf(c_10719,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_2036]) ).
tcf(c_10720,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),X0),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_2025]) ).
tcf(c_10721,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_65]) ).
tcf(c_10723,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_3043]) ).
tcf(c_10724,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10712,c_4932]) ).
tcf(c_10728,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_10712,c_3519]) ).
tcf(c_10729,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10712,c_2479]) ).
tcf(c_10730,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10712,c_4058]) ).
tcf(c_10731,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10712,c_3521]) ).
tcf(c_10734,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_10712,c_2348]) ).
tcf(c_10735,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10712,c_2447]) ).
tcf(c_10819,plain,
( element(apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_3728,c_66]) ).
tcf(c_10820,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3728,c_3702]) ).
tcf(c_10821,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3728,c_2132]) ).
tcf(c_10822,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3728,c_2133]) ).
tcf(c_10833,plain,
( element(apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_10819,c_8135,c_10819]) ).
tcf(c_10839,plain,
( element(apply(x,zero(any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2077,c_10833]) ).
tcf(c_10840,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_2294]) ).
tcf(c_10841,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_2036]) ).
tcf(c_10842,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),X0),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_2025]) ).
tcf(c_10843,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_65]) ).
tcf(c_10845,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_3043]) ).
tcf(c_10846,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10833,c_4932]) ).
tcf(c_10850,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_10833,c_3519]) ).
tcf(c_10851,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10833,c_2479]) ).
tcf(c_10852,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10833,c_4058]) ).
tcf(c_10853,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10833,c_3521]) ).
tcf(c_10856,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_10833,c_2348]) ).
tcf(c_10857,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_10833,c_2447]) ).
tcf(c_10929,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_10703,c_3436]) ).
tcf(c_10930,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_10703,c_3391]) ).
tcf(c_10932,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = zero(any1) )
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_10703,c_810]) ).
tcf(c_10934,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_10703,c_435]) ).
tcf(c_10999,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_10822,c_3436]) ).
tcf(c_11004,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_10822,c_435]) ).
tcf(c_11024,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2077,c_10820]) ).
tcf(c_11025,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_10820,c_3436]) ).
tcf(c_11030,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_10820,c_435]) ).
tcf(c_11063,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),subtract(any1,X0,X1))),apply(x,subtract(any1,zero(any1),subtract(any1,X0,X1)))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_3233]) ).
tcf(c_11064,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))),apply(x,subtract(any1,zero(any1),sK2(x,any1,any2)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_3233]) ).
tcf(c_11065,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),sK1(x,any1))),apply(x,subtract(any1,zero(any1),sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4899,c_3233]) ).
tcf(c_11071,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),zero(any1))),apply(x,subtract(any1,zero(any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_3233]) ).
tcf(c_11093,plain,
( element(apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_3747,c_66]) ).
tcf(c_11094,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3747,c_3728]) ).
tcf(c_11095,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3747,c_3702]) ).
tcf(c_11096,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3747,c_2132]) ).
tcf(c_11097,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3747,c_2133]) ).
tcf(c_11115,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK0(x,any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_11097,c_3436]) ).
tcf(c_11120,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK0(x,any1),sK0(x,any1)),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_11097,c_435]) ).
tcf(c_11160,plain,
( element(apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_11093,c_8135,c_11093]) ).
tcf(c_11168,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_2294]) ).
tcf(c_11169,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_2036]) ).
tcf(c_11170,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),X0),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_2025]) ).
tcf(c_11171,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_65]) ).
tcf(c_11173,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_3043]) ).
tcf(c_11174,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11160,c_4932]) ).
tcf(c_11178,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11160,c_3519]) ).
tcf(c_11179,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11160,c_2479]) ).
tcf(c_11180,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11160,c_4058]) ).
tcf(c_11181,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11160,c_3521]) ).
tcf(c_11184,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11160,c_2348]) ).
tcf(c_11185,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11160,c_2447]) ).
tcf(c_11260,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2077,c_11094]) ).
tcf(c_11261,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_11094,c_3436]) ).
tcf(c_11266,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_11094,c_435]) ).
tcf(c_11289,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_11095,c_3436]) ).
tcf(c_11294,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_11095,c_435]) ).
tcf(c_11319,plain,
( element(apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ~ element(apply(x,sK0(x,any1)),any2) ),
inference(superposition,[status(thm)],[c_3775,c_66]) ).
tcf(c_11320,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3775,c_3747]) ).
tcf(c_11321,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3775,c_3728]) ).
tcf(c_11322,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))) ) ),
inference(superposition,[status(thm)],[c_3775,c_3702]) ).
tcf(c_11323,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3775,c_2132]) ).
tcf(c_11324,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_3775,c_2133]) ).
tcf(c_11359,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| ( apply(x,sK0(x,any1)) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_11324,c_3436]) ).
tcf(c_11360,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(any1) )
| ~ element(zero(any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_11324,c_3391]) ).
tcf(c_11362,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(any1) )
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_11324,c_810]) ).
tcf(c_11364,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| ( apply(x,X0) != zero(any2) ) ),
inference(superposition,[status(thm)],[c_11324,c_435]) ).
tcf(c_11393,plain,
( element(apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_11319,c_8135,c_11319]) ).
tcf(c_11400,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_2294]) ).
tcf(c_11401,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_2036]) ).
tcf(c_11402,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),X0),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_2025]) ).
tcf(c_11403,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_65]) ).
tcf(c_11405,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_3043]) ).
tcf(c_11406,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11393,c_4932]) ).
tcf(c_11410,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11393,c_3519]) ).
tcf(c_11411,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11393,c_2479]) ).
tcf(c_11412,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11393,c_4058]) ).
tcf(c_11413,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11393,c_3521]) ).
tcf(c_11416,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11393,c_2348]) ).
tcf(c_11417,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11393,c_2447]) ).
tcf(c_11492,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1)))) = apply(x,subtract(any1,X0,X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4877]) ).
tcf(c_11493,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4877]) ).
tcf(c_11494,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_4899,c_4877]) ).
tcf(c_11495,plain,
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = apply(x,sK1(x,any1)) ) ),
inference(superposition,[status(thm)],[c_756,c_4877]) ).
tcf(c_11497,plain,
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_758,c_4877]) ).
tcf(c_11500,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,zero(any1)))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2417,c_4877]) ).
tcf(c_11521,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1))),subtract(any2,zero(any2),apply(x,subtract(any1,X0,X1)))) = zero(any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5157]) ).
tcf(c_11522,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_5157]) ).
tcf(c_11523,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK1(x,any1))),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4899,c_5157]) ).
tcf(c_11524,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK1(x,any1))),subtract(any2,zero(any2),apply(x,sK1(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_756,c_5157]) ).
tcf(c_11529,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,zero(any1))),subtract(any2,zero(any2),apply(x,zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_2417,c_5157]) ).
tcf(c_11564,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_11320,c_3436]) ).
tcf(c_11569,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK0(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_11320,c_435]) ).
tcf(c_11592,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = apply(x,zero(any1)) ) ),
inference(superposition,[status(thm)],[c_2077,c_11321]) ).
tcf(c_11593,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_11321,c_3436]) ).
tcf(c_11598,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_11321,c_435]) ).
tcf(c_11623,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = sK1(x,any1) )
| ~ injection(x)
| ~ element(sK1(x,any1),any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) != apply(x,sK0(x,any1)) ) ),
inference(superposition,[status(thm)],[c_11322,c_3436]) ).
tcf(c_11628,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK1(x,any1),sK0(x,any1)) = X0 )
| ~ injection(x)
| ~ element(X0,any1)
| ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ( apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) != apply(x,X0) ) ),
inference(superposition,[status(thm)],[c_11322,c_435]) ).
tcf(c_11651,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),subtract(any2,X0,X1)),subtract(any2,zero(any2),subtract(any2,X0,X1))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_4057]) ).
tcf(c_11652,plain,
! [X0: $i] :
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,X0)),subtract(any2,zero(any2),apply(x,X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_4057]) ).
tcf(c_11658,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),zero(any2)),subtract(any2,zero(any2),zero(any2))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4050,c_4057]) ).
tcf(c_11662,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8135,c_4057]) ).
tcf(c_11663,plain,
( ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,sK0(x,any1))),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = zero(any2) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_4057]) ).
tcf(c_11664,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_7428,c_4057]) ).
tcf(c_11665,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10833,c_4057]) ).
tcf(c_11666,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_8212,c_4057]) ).
tcf(c_11667,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_10712,c_4057]) ).
tcf(c_11668,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11160,c_4057]) ).
tcf(c_11669,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11393,c_4057]) ).
tcf(c_11726,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1))) = apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_4950]) ).
tcf(c_11727,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK1(x,any1),sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_4950]) ).
tcf(c_11728,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_4899,c_4950]) ).
tcf(c_11734,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2417,c_4950]) ).
tcf(c_11761,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,X0,X1))) = apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1))) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_5404]) ).
tcf(c_11762,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK2(x,any1,any2))) = apply(x,subtract(any1,sK0(x,any1),sK2(x,any1,any2))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_749,c_5404]) ).
tcf(c_11763,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_4899,c_5404]) ).
tcf(c_11769,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_2417,c_5404]) ).
tcf(c_11780,plain,
( element(apply(x,subtract(any1,zero(any1),sK1(x,any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_5865,c_2430,c_5865,c_8135]) ).
tcf(c_11787,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_2294]) ).
tcf(c_11788,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_2036]) ).
tcf(c_11789,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,zero(any1),sK1(x,any1))),X0),subtract(any2,apply(x,subtract(any1,zero(any1),sK1(x,any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_2025]) ).
tcf(c_11790,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,zero(any1),sK1(x,any1))),subtract(any2,apply(x,subtract(any1,zero(any1),sK1(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_65]) ).
tcf(c_11792,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK1(x,any1)))))) = subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK1(x,any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_3043]) ).
tcf(c_11793,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11780,c_4057]) ).
tcf(c_11794,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11780,c_4932]) ).
tcf(c_11798,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11780,c_3519]) ).
tcf(c_11799,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11780,c_2479]) ).
tcf(c_11800,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11780,c_4058]) ).
tcf(c_11801,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_11780,c_3521]) ).
tcf(c_11804,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_11780,c_2348]) ).
tcf(c_11805,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK1(x,any1))))) = apply(x,subtract(any1,zero(any1),sK1(x,any1))) ) ),
inference(superposition,[status(thm)],[c_11780,c_2447]) ).
tcf(c_11885,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_6288]) ).
tcf(c_11886,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_6288]) ).
tcf(c_11887,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_6288]) ).
tcf(c_11889,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_6288]) ).
tcf(c_11890,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_6288]) ).
tcf(c_11891,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_6280,c_6288]) ).
tcf(c_11897,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_6288]) ).
tcf(c_11940,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_6744]) ).
tcf(c_11941,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_6744]) ).
tcf(c_11942,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_6744]) ).
tcf(c_11944,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_6744]) ).
tcf(c_11945,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_6736,c_6744]) ).
tcf(c_11952,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_6744]) ).
tcf(c_11993,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK1(x,any1)),subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK1(x,any1))) = zero(any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_6878]) ).
tcf(c_11995,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_6878]) ).
tcf(c_11996,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),X0),sK1(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_6878]) ).
tcf(c_11997,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_6878]) ).
tcf(c_11998,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),X0),sK1(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_6878]) ).
tcf(c_12001,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,zero(any1),X0),sK1(x,any1)),subtract(any1,subtract(any1,zero(any1),X0),sK1(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_6878]) ).
tcf(c_12072,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_7520]) ).
tcf(c_12073,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_7520]) ).
tcf(c_12074,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_7520]) ).
tcf(c_12076,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) ) ),
inference(superposition,[status(thm)],[c_7511,c_7520]) ).
tcf(c_12084,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_7520]) ).
tcf(c_12124,plain,
( element(apply(x,subtract(any1,sK1(x,any1),zero(any1))),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(global_subsumption_just,[status(thm)],[c_8005,c_2430,c_8005,c_8135]) ).
tcf(c_12131,plain,
( element(apply(x,sK1(x,any1)),any2)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_4029,c_12124]) ).
tcf(c_12132,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = zero(any2) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_2294]) ).
tcf(c_12133,plain,
! [X0: $i,X1: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_2036]) ).
tcf(c_12134,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),X0),subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_2025]) ).
tcf(c_12135,plain,
! [X0: $i] :
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_65]) ).
tcf(c_12136,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),zero(any1))),apply(x,subtract(any1,sK1(x,any1),zero(any1)))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_12124,c_61]) ).
tcf(c_12137,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),zero(any1)))))) = subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),zero(any1)))) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_3043]) ).
tcf(c_12141,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_12124,c_4057]) ).
tcf(c_12142,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_12124,c_4932]) ).
tcf(c_12146,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = zero(any2) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_12124,c_3519]) ).
tcf(c_12147,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_12124,c_2479]) ).
tcf(c_12148,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_12124,c_4058]) ).
tcf(c_12149,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = zero(any2) ) ),
inference(superposition,[status(thm)],[c_12124,c_3521]) ).
tcf(c_12152,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) )
| ~ injection(x) ),
inference(superposition,[status(thm)],[c_12124,c_2348]) ).
tcf(c_12153,plain,
( ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,subtract(any1,sK1(x,any1),zero(any1))))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))) ) ),
inference(superposition,[status(thm)],[c_12124,c_2447]) ).
tcf(c_12249,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK0(x,any1)),subtract(any1,subtract(any1,subtract(any1,X0,X1),X2),sK0(x,any1))) = zero(any1) )
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_6880]) ).
tcf(c_12251,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_4899,c_6880]) ).
tcf(c_12252,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),X0),sK0(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_756,c_6880]) ).
tcf(c_12253,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_5372,c_6880]) ).
tcf(c_12254,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),X0),sK0(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_758,c_6880]) ).
tcf(c_12257,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,zero(any1),X0),sK0(x,any1)),subtract(any1,subtract(any1,zero(any1),X0),sK0(x,any1))) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_2417,c_6880]) ).
tcf(c_12295,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),subtract(any1,X0,X1))),X2)) = X2 )
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_7038]) ).
tcf(c_12298,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_756,c_7038]) ).
tcf(c_12300,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any2,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_758,c_7038]) ).
tcf(c_12352,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),subtract(any1,X0,X1))),X2)) = X2 )
| ~ element(X2,any2)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_7040]) ).
tcf(c_12355,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_756,c_7040]) ).
tcf(c_12357,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any2,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_758,c_7040]) ).
tcf(c_12383,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,X2,subtract(any2,X0,X1)),subtract(any2,subtract(any2,X2,subtract(any2,X0,X1)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X2,any2)
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_7925]) ).
tcf(c_12384,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,X1,apply(x,X0)),subtract(any2,subtract(any2,X1,apply(x,X0)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_7925]) ).
tcf(c_12390,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,zero(any2)),subtract(any2,subtract(any2,X0,zero(any2)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_4050,c_7925]) ).
tcf(c_12393,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,zero(any2)),subtract(any2,subtract(any2,X0,zero(any2)),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_2430,c_7925]) ).
tcf(c_12394,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,sK0(x,any1))),subtract(any2,subtract(any2,X0,apply(x,sK0(x,any1))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8135,c_7925]) ).
tcf(c_12395,plain,
! [X0: $i] :
( injection(x)
| ( subtract(any2,subtract(any2,X0,apply(x,sK0(x,any1))),subtract(any2,subtract(any2,X0,apply(x,sK0(x,any1))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2)
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_7925]) ).
tcf(c_12396,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK1(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11780,c_7925]) ).
tcf(c_12397,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK0(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_7428,c_7925]) ).
tcf(c_12398,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK1(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10833,c_7925]) ).
tcf(c_12399,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),zero(any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),zero(any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12124,c_7925]) ).
tcf(c_12400,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),zero(any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),zero(any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_8212,c_7925]) ).
tcf(c_12401,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK1(x,any1),sK0(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_10712,c_7925]) ).
tcf(c_12402,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11160,c_7925]) ).
tcf(c_12403,plain,
! [X0: $i] :
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),subtract(any2,subtract(any2,X0,apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_11393,c_7925]) ).
tcf(c_12526,plain,
( element(sK2(x,any1,any2),any1)
| ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_8749,c_531,c_2005]) ).
tcf(c_12532,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2)),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2294]) ).
tcf(c_12533,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2036]) ).
tcf(c_12534,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),X0),subtract(any1,sK2(x,any1,any2),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2025]) ).
tcf(c_12535,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_65]) ).
tcf(c_12548,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK2(x,any1,any2),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2603]) ).
tcf(c_12555,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_12526,c_4191]) ).
tcf(c_12556,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12526,c_3901]) ).
tcf(c_12559,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))) = subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_12526,c_2747]) ).
tcf(c_12560,plain,
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),sK2(x,any1,any2)),subtract(any1,zero(any1),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_12526,c_2716]) ).
tcf(c_12561,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2347]) ).
tcf(c_12591,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),X0),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12526,c_2295]) ).
tcf(c_12592,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,subtract(any1,sK2(x,any1,any2),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_2091]) ).
tcf(c_12595,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0)) = apply(x,subtract(any1,sK2(x,any1,any2),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12526,c_353]) ).
tcf(c_12597,plain,
! [X0: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12526,c_2037]) ).
tcf(c_12711,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_12535]) ).
tcf(c_12752,plain,
( element(sK2(x,any1,any2),any1)
| ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ) ),
inference(global_subsumption_just,[status(thm)],[c_8760,c_531,c_2004]) ).
tcf(c_12758,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2)),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2294]) ).
tcf(c_12759,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK2(x,any1,any2))) = sK2(x,any1,any2) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2036]) ).
tcf(c_12760,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,sK2(x,any1,any2),X0),subtract(any1,sK2(x,any1,any2),X0)) = zero(any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2025]) ).
tcf(c_12761,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),X0)) = X0 )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_65]) ).
tcf(c_12775,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,X1)) = apply(x,subtract(any1,subtract(any1,sK2(x,any1,any2),X0),X1)) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2603]) ).
tcf(c_12781,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) ) ),
inference(superposition,[status(thm)],[c_12752,c_4468]) ).
tcf(c_12783,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,X0,X1),subtract(any2,subtract(any2,X0,X1),apply(x,sK2(x,any1,any2)))) = apply(x,sK2(x,any1,any2)) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12752,c_3901]) ).
tcf(c_12784,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( apply(x,subtract(any1,zero(any1),sK2(x,any1,any2))) = subtract(any2,zero(any2),apply(x,sK2(x,any1,any2))) ) ),
inference(superposition,[status(thm)],[c_12752,c_3192]) ).
tcf(c_12785,plain,
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,subtract(any1,zero(any1),sK2(x,any1,any2)),subtract(any1,zero(any1),sK2(x,any1,any2))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_12752,c_3162]) ).
tcf(c_12788,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),X1)) = X1 )
| ~ element(X1,any2)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2347]) ).
tcf(c_12818,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,subtract(any2,apply(x,sK2(x,any1,any2)),X0),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = zero(any2) )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12752,c_2295]) ).
tcf(c_12819,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,subtract(any1,sK2(x,any1,any2),X0)),apply(x,subtract(any1,sK2(x,any1,any2),X0))) = zero(any2) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_2091]) ).
tcf(c_12822,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,X0)) = apply(x,subtract(any1,sK2(x,any1,any2),X0)) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_12752,c_353]) ).
tcf(c_12824,plain,
! [X0: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any2,apply(x,sK2(x,any1,any2)),subtract(any2,apply(x,sK2(x,any1,any2)),X0)) = X0 )
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_12752,c_2037]) ).
tcf(c_12889,plain,
! [X0: $i,X1: $i] :
( ( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) )
| ( subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),subtract(any1,X0,X1))) = subtract(any1,X0,X1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_12761]) ).
tcf(c_12911,plain,
! [X0: $i,X1: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),subtract(any2,X0,X1))) = subtract(any2,X0,X1) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X1,any2)
| ~ element(X0,any2) ),
inference(superposition,[status(thm)],[c_66,c_8784]) ).
tcf(c_12912,plain,
! [X0: $i] :
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,X0))) = apply(x,X0) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_765,c_8784]) ).
tcf(c_12913,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),zero(any2))) = zero(any2) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) ) ),
inference(superposition,[status(thm)],[c_8775,c_8784]) ).
tcf(c_12923,plain,
( ( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK0(x,any1)))) = apply(x,sK0(x,any1)) )
| ( subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1) )
| ~ element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_3435,c_8784]) ).
tcf(c_12973,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1)))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_10389]) ).
tcf(c_12977,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_10389]) ).
tcf(c_12978,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_10389]) ).
tcf(c_12979,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_10389]) ).
tcf(c_12980,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_10389]) ).
tcf(c_12983,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1))),subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),zero(any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_10389]) ).
tcf(c_13008,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1)))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_10391]) ).
tcf(c_13012,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_10391]) ).
tcf(c_13013,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_10391]) ).
tcf(c_13014,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_10391]) ).
tcf(c_13015,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_10391]) ).
tcf(c_13018,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),zero(any1))),subtract(any1,sK1(x,any1),subtract(any1,sK0(x,any1),zero(any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_10391]) ).
tcf(c_13069,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),subtract(any1,X0,X1)))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_10516]) ).
tcf(c_13073,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_10516]) ).
tcf(c_13074,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_10516]) ).
tcf(c_13075,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_10516]) ).
tcf(c_13076,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_10516]) ).
tcf(c_13079,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),zero(any1))),subtract(any1,sK0(x,any1),subtract(any1,sK1(x,any1),zero(any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_10516]) ).
tcf(c_13104,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),subtract(any1,X0,X1)))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_10518]) ).
tcf(c_13108,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_10518]) ).
tcf(c_13109,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_10518]) ).
tcf(c_13110,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_10518]) ).
tcf(c_13111,plain,
( injection(x)
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_10518]) ).
tcf(c_13114,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1))),subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),zero(any1)))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_10518]) ).
tcf(c_13146,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK1(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_11996]) ).
tcf(c_13150,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_11996]) ).
tcf(c_13151,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_11996]) ).
tcf(c_13152,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_11996]) ).
tcf(c_13153,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_11996]) ).
tcf(c_13156,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_11996]) ).
tcf(c_13181,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),subtract(any1,X0,X1)),sK1(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_11998]) ).
tcf(c_13185,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_11998]) ).
tcf(c_13186,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK1(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_11998]) ).
tcf(c_13187,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_11998]) ).
tcf(c_13188,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_11998]) ).
tcf(c_13191,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),sK1(x,any1)),subtract(any1,subtract(any1,sK0(x,any1),zero(any1)),sK1(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_11998]) ).
tcf(c_13246,plain,
! [X0: $i,X1: $i] :
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),subtract(any1,X0,X1)),sK0(x,any1))) = zero(any1) )
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(superposition,[status(thm)],[c_66,c_12252]) ).
tcf(c_13250,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_4899,c_12252]) ).
tcf(c_13251,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK1(x,any1)),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_756,c_12252]) ).
tcf(c_13252,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_5372,c_12252]) ).
tcf(c_13253,plain,
( injection(x)
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),sK0(x,any1)),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_758,c_12252]) ).
tcf(c_13256,plain,
( injection(x)
| ( apply(x,sK2(x,any1,any2)) = zero(any2) )
| ( subtract(any1,subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK0(x,any1)),subtract(any1,subtract(any1,sK1(x,any1),zero(any1)),sK0(x,any1))) = zero(any1) ) ),
inference(superposition,[status(thm)],[c_2417,c_12252]) ).
tcf(c_13304,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_13256,c_13253,c_13252,c_13251,c_13250,c_13246,c_13191,c_13188,c_13187,c_13186,c_13185,c_13181,c_13156,c_13153,c_13152,c_13151,c_13150,c_13146,c_13114,c_13111,c_13110,c_13109,c_13108,c_13104,c_13079,c_13076,c_13075,c_13074,c_13073,c_13069,c_13018,c_13015,c_13014,c_13013,c_13012,c_13008,c_12983,c_12980,c_12979,c_12978,c_12977,c_12973,c_12923,c_12913,c_12912,c_12911,c_12889,c_12824,c_12822,c_12819,c_12818,c_12788,c_12785,c_12784,c_12783,c_12781,c_12775,c_12761,c_12760,c_12759,c_12758,c_12752,c_12711,c_12597,c_12595,c_12592,c_12591,c_12561,c_12560,c_12559,c_12556,c_12555,c_12548,c_12535,c_12534,c_12533,c_12532,c_12526,c_12403,c_12402,c_12401,c_12400,c_12399,c_12398,c_12397,c_12396,c_12395,c_12394,c_12393,c_12390,c_12384,c_12383,c_12357,c_12355,c_12352,c_12300,c_12298,c_12295,c_12257,c_12254,c_12253,c_12252,c_12251,c_12249,c_12153,c_12152,c_12149,c_12148,c_12147,c_12146,c_12142,c_12141,c_12137,c_12136,c_12135,c_12134,c_12133,c_12132,c_12131,c_12124,c_12084,c_12076,c_12074,c_12073,c_12072,c_12001,c_11998,c_11997,c_11996,c_11995,c_11993,c_11952,c_11945,c_11944,c_11942,c_11941,c_11940,c_11897,c_11891,c_11890,c_11889,c_11887,c_11886,c_11885,c_11805,c_11804,c_11801,c_11800,c_11799,c_11798,c_11794,c_11793,c_11792,c_11790,c_11789,c_11788,c_11787,c_11780,c_11769,c_11763,c_11762,c_11761,c_11734,c_11728,c_11727,c_11726,c_11669,c_11668,c_11667,c_11666,c_11665,c_11664,c_11663,c_11662,c_11658,c_11652,c_11651,c_11628,c_11623,c_11598,c_11593,c_11592,c_11569,c_11564,c_11529,c_11524,c_11523,c_11522,c_11521,c_11500,c_11497,c_11495,c_11494,c_11493,c_11492,c_11417,c_11416,c_11413,c_11412,c_11411,c_11410,c_11406,c_11405,c_11403,c_11402,c_11401,c_11400,c_11393,c_11362,c_11364,c_11360,c_11359,c_11319,c_11324,c_11323,c_11322,c_11321,c_11320,c_11294,c_11289,c_11266,c_11261,c_11260,c_11185,c_11184,c_11181,c_11180,c_11179,c_11178,c_11174,c_11173,c_11171,c_11170,c_11169,c_11168,c_11160,c_11120,c_11115,c_11093,c_11097,c_11096,c_11095,c_11094,c_11071,c_11065,c_11064,c_11063,c_11030,c_11025,c_11024,c_11004,c_10999,c_10932,c_10934,c_10930,c_10929,c_10857,c_10856,c_10853,c_10852,c_10851,c_10850,c_10846,c_10845,c_10843,c_10842,c_10841,c_10840,c_10839,c_10833,c_10819,c_10822,c_10821,c_10820,c_10735,c_10734,c_10731,c_10730,c_10729,c_10728,c_10724,c_10723,c_10721,c_10720,c_10719,c_10718,c_10712,c_10701,c_10703,c_10702,c_10614,c_10613,c_10612,c_10611,c_10610,c_10607,c_10601,c_10600,c_10521,c_10518,c_10517,c_10516,c_10515,c_10513,c_10491,c_10476,c_10394,c_10391,c_10390,c_10389,c_10388,c_10386,c_10299,c_10298,c_10297,c_10296,c_10295,c_10294,c_10293,c_10292,c_10291,c_10081,c_10080,c_10079,c_10078,c_10077,c_10076,c_10075,c_10074,c_10073,c_10072,c_10071,c_10070,c_10069,c_10068,c_10067,c_10066,c_10065,c_10064,c_10063,c_10062,c_10061,c_10060,c_10059,c_10058,c_10057,c_10056,c_10055,c_10054,c_10053,c_10052,c_10051,c_10050,c_10049,c_10048,c_10047,c_10046,c_10045,c_8873,c_8872,c_8871,c_8870,c_8869,c_8868,c_8867,c_8866,c_8865,c_8864,c_8863,c_8862,c_8861,c_8860,c_8859,c_8858,c_8857,c_8856,c_8855,c_8854,c_8853,c_8852,c_8851,c_8850,c_8849,c_8848,c_8847,c_8846,c_8845,c_8844,c_8843,c_8842,c_8841,c_8840,c_8839,c_8838,c_8837,c_8797,c_8796,c_8795,c_8794,c_8790,c_8789,c_8788,c_8787,c_8784,c_8783,c_8782,c_8781,c_8775,c_8771,c_8760,c_8754,c_8749,c_8743,c_8710,c_8703,c_8674,c_8673,c_8672,c_8671,c_8670,c_8669,c_8649,c_8648,c_8625,c_8624,c_8618,c_8613,c_8612,c_8590,c_8589,c_8521,c_8520,c_8519,c_8517,c_8515,c_8514,c_8513,c_8469,c_8468,c_8467,c_8465,c_8463,c_8462,c_8461,c_8434,c_8428,c_8427,c_8426,c_8425,c_8424,c_8423,c_8380,c_8377,c_8375,c_8374,c_8372,c_8353,c_8348,c_8347,c_8329,c_8328,c_8323,c_8322,c_8235,c_8234,c_8233,c_8230,c_8229,c_8228,c_8227,c_8224,c_8223,c_8222,c_8221,c_8220,c_8212,c_8151,c_8150,c_8149,c_8148,c_8141,c_8135,c_8108,c_8107,c_8109,c_8105,c_8104,c_8050,c_8047,c_8046,c_8048,c_8044,c_8042,c_8029,c_8027,c_8028,c_8021,c_8017,c_8006,c_8005,c_8000,c_7928,c_7927,c_7926,c_7925,c_7924,c_7923,c_7922,c_7921,c_7920,c_7855,c_7854,c_7853,c_7852,c_7848,c_7847,c_7846,c_7844,c_7843,c_7842,c_7841,c_7835,c_7819,c_7794,c_7791,c_7789,c_7788,c_7787,c_7786,c_7785,c_7767,c_7762,c_7761,c_7743,c_7738,c_7737,c_7723,c_7722,c_7713,c_7691,c_7689,c_7688,c_7686,c_7685,c_7684,c_7683,c_7682,c_7664,c_7663,c_7658,c_7657,c_7639,c_7638,c_7633,c_7632,c_7618,c_7529,c_7528,c_7527,c_7526,c_7522,c_7520,c_7519,c_7518,c_7517,c_7511,c_7507,c_7447,c_7446,c_7445,c_7442,c_7441,c_7440,c_7439,c_7438,c_7437,c_7436,c_7435,c_7434,c_7428,c_7421,c_7352,c_7351,c_7353,c_7349,c_7348,c_7331,c_7330,c_7329,c_7328,c_7327,c_7326,c_7299,c_7298,c_7297,c_7296,c_7295,c_7294,c_7272,c_7271,c_7270,c_7269,c_7268,c_7267,c_7219,c_7218,c_7217,c_7216,c_7215,c_7214,c_7187,c_7186,c_7185,c_7184,c_7183,c_7182,c_7133,c_7132,c_7131,c_7130,c_7129,c_7128,c_7043,c_7042,c_7041,c_7040,c_7039,c_7038,c_7037,c_7036,c_7035,c_6890,c_6889,c_6888,c_6887,c_6886,c_6885,c_6884,c_6883,c_6882,c_6881,c_6880,c_6879,c_6878,c_6877,c_6876,c_6875,c_6874,c_6753,c_6752,c_6751,c_6750,c_6746,c_6744,c_6743,c_6742,c_6736,c_6732,c_6686,c_6685,c_6684,c_6683,c_6682,c_6681,c_6664,c_6663,c_6662,c_6661,c_6660,c_6659,c_6650,c_6590,c_6589,c_6588,c_6587,c_6586,c_6585,c_6552,c_6551,c_6550,c_6549,c_6548,c_6547,c_6511,c_6510,c_6509,c_6508,c_6507,c_6506,c_6473,c_6472,c_6471,c_6470,c_6469,c_6468,c_6451,c_6450,c_6449,c_6448,c_6447,c_6446,c_6405,c_6404,c_6403,c_6402,c_6401,c_6400,c_6383,c_6382,c_6381,c_6380,c_6379,c_6378,c_6361,c_6360,c_6359,c_6358,c_6357,c_6356,c_6297,c_6296,c_6295,c_6294,c_6290,c_6288,c_6287,c_6286,c_6280,c_6186,c_6185,c_6184,c_6183,c_6182,c_6181,c_6180,c_6179,c_6178,c_6177,c_6176,c_6175,c_6174,c_6173,c_6172,c_6171,c_6170,c_6169,c_6168,c_6167,c_6146,c_6145,c_6144,c_6142,c_6140,c_6139,c_6138,c_6126,c_6113,c_6111,c_6112,c_6066,c_6063,c_6062,c_6061,c_6060,c_6058,c_5990,c_5987,c_5986,c_5985,c_5984,c_5982,c_5957,c_5954,c_5953,c_5952,c_5951,c_5949,c_5897,c_5894,c_5893,c_5892,c_5891,c_5889,c_5866,c_5865,c_5843,c_5820,c_5817,c_5816,c_5815,c_5814,c_5812,c_5762,c_5759,c_5758,c_5757,c_5756,c_5754,c_5684,c_5681,c_5680,c_5679,c_5678,c_5676,c_5637,c_5634,c_5633,c_5632,c_5631,c_5629,c_5596,c_5595,c_5594,c_5593,c_5592,c_5591,c_5590,c_5539,c_5538,c_5537,c_5535,c_5533,c_5532,c_5531,c_5499,c_5498,c_5405,c_5404,c_5401,c_5396,c_5392,c_5391,c_5388,c_5385,c_5384,c_5383,c_5382,c_5380,c_5379,c_5378,c_5367,c_5338,c_5335,c_5334,c_5333,c_5331,c_5278,c_5275,c_5274,c_5273,c_5271,c_5248,c_5192,c_5190,c_5187,c_5186,c_5185,c_5184,c_5183,c_5162,c_5161,c_5158,c_5157,c_5156,c_5104,c_5101,c_5099,c_5098,c_5097,c_5029,c_5028,c_4971,c_4957,c_4950,c_4937,c_4932,c_4928,c_4927,c_4926,c_4923,c_4922,c_4920,c_4919,c_4918,c_4916,c_4914,c_4913,c_4910,c_4909,c_4907,c_4906,c_4905,c_4882,c_4878,c_4877,c_4876,c_4853,c_4850,c_4849,c_4848,c_4847,c_4821,c_4818,c_4817,c_4815,c_4802,c_4787,c_4786,c_4785,c_4784,c_4783,c_4768,c_4767,c_4766,c_4765,c_4764,c_4729,c_4728,c_4727,c_4726,c_4725,c_4673,c_4672,c_4671,c_4670,c_4669,c_4646,c_4645,c_4644,c_4643,c_4642,c_4633,c_4628,c_4609,c_4604,c_4584,c_4583,c_4580,c_4579,c_4578,c_4525,c_4522,c_4521,c_4519,c_4500,c_4497,c_4496,c_4494,c_4473,c_4470,c_4469,c_4468,c_4467,c_4432,c_4429,c_4428,c_4426,c_4359,c_4358,c_4357,c_4356,c_4355,c_4354,c_4353,c_4352,c_4351,c_4350,c_4349,c_4348,c_4347,c_4346,c_4345,c_4301,c_4297,c_4293,c_4290,c_4289,c_4288,c_4285,c_4284,c_4253,c_4250,c_4249,c_4233,c_4230,c_4229,c_4227,c_4196,c_4194,c_4193,c_4192,c_4191,c_4190,c_4172,c_4171,c_4168,c_4167,c_4152,c_4144,c_4129,c_4096,c_4087,c_4062,c_4061,c_4060,c_4058,c_4057,c_4056,c_4050,c_4046,c_4029,c_3911,c_3910,c_3909,c_3908,c_3907,c_3906,c_3905,c_3904,c_3903,c_3902,c_3901,c_3900,c_3856,c_3855,c_3854,c_3853,c_3852,c_3851,c_3806,c_3805,c_3804,c_3801,c_3800,c_3775,c_3774,c_3773,c_3772,c_3747,c_3746,c_3745,c_3744,c_3728,c_3727,c_3726,c_3725,c_3702,c_3701,c_3700,c_3699,c_3686,c_3683,c_3680,c_3677,c_3676,c_3674,c_3637,c_3634,c_3631,c_3628,c_3627,c_3625,c_3615,c_3599,c_3598,c_3595,c_3594,c_3580,c_3554,c_3551,c_3550,c_3549,c_3548,c_3524,c_3523,c_3522,c_3521,c_3520,c_3519,c_3518,c_3465,c_3464,c_3463,c_3462,c_3435,c_3434,c_3436,c_3432,c_3425,c_3411,c_3402,c_3391,c_3381,c_3380,c_3379,c_3378,c_3365,c_3364,c_3363,c_3362,c_3356,c_3352,c_3335,c_3327,c_3312,c_3299,c_3233,c_3232,c_3231,c_3230,c_3229,c_3228,c_3227,c_3192,c_3182,c_3176,c_3173,c_3172,c_3169,c_3168,c_3167,c_3163,c_3162,c_3156,c_3150,c_3146,c_3142,c_3124,c_3111,c_3110,c_3109,c_3108,c_3085,c_3084,c_3083,c_3082,c_3047,c_3044,c_3043,c_3024,c_3021,c_3020,c_3001,c_2999,c_2998,c_2996,c_2960,c_2959,c_2958,c_2949,c_2941,c_2920,c_2908,c_2891,c_2879,c_2878,c_2877,c_2821,c_2820,c_2819,c_2818,c_2817,c_2816,c_2815,c_2814,c_2813,c_2805,c_2798,c_2791,c_2747,c_2737,c_2731,c_2726,c_2725,c_2722,c_2721,c_2720,c_2718,c_2717,c_2716,c_2710,c_2702,c_2671,c_2670,c_2669,c_2667,c_2645,c_2644,c_2617,c_2607,c_2606,c_2605,c_2604,c_2603,c_2567,c_2566,c_2565,c_2559,c_2521,c_2518,c_2517,c_2479,c_2447,c_2435,c_2430,c_2429,c_2428,c_2427,c_2426,c_2425,c_2424,c_2423,c_2417,c_2410,c_2409,c_2408,c_2400,c_2350,c_2349,c_2348,c_2347,c_2298,c_2297,c_2296,c_2295,c_2294,c_2259,c_2258,c_2257,c_2256,c_2255,c_2254,c_2253,c_2252,c_2233,c_2232,c_2219,c_2218,c_2205,c_2204,c_2194,c_2193,c_2177,c_2176,c_2174,c_2156,c_2155,c_2153,c_2133,c_2132,c_2123,c_2122,c_2111,c_2110,c_2109,c_2094,c_2093,c_2092,c_2091,c_2084,c_2077,c_2040,c_2039,c_2038,c_2037,c_2036,c_2025,c_2005,c_2004,c_2003,c_2002,c_1987,c_2070,c_4899,c_5372,c_810,c_747,c_749,c_752,c_435,c_760,c_758,c_756,c_754,c_765,c_365,c_353,c_66,c_65,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Wed Sep 23 16:06:58 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 5.98/2.33 % SZS status Started for theBenchmark.p
% 5.98/2.33 % SZS status Theorem for theBenchmark.p
% 5.98/2.33
% 5.98/2.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.98/2.33
% 5.98/2.33 % ------ iProver source info
% 5.98/2.33
% 5.98/2.33 % git: date: 2026-07-19 20:42:38 +0200
% 5.98/2.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.98/2.33 % git: non_committed_changes: false
% 5.98/2.33
% 5.98/2.33 % ------ Parsing...
% 5.98/2.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.98/2.33
% 5.98/2.33 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 5.98/2.33
% 5.98/2.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.98/2.33
% 5.98/2.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.98/2.33 % ------ Proving...
% 5.98/2.33 % ------ Problem Properties
% 5.98/2.33
% 5.98/2.33 %
% 5.98/2.33 % clauses 15
% 5.98/2.33 % conjectures 0
% 5.98/2.33 % EPR 0
% 5.98/2.33 % Horn 11
% 5.98/2.33 % unary 1
% 5.98/2.33 % binary 9
% 5.98/2.33 % lits 37
% 5.98/2.33 % lits eq 12
% 5.98/2.33 % fd_pure 0
% 5.98/2.33 % fd_pseudo 0
% 5.98/2.33 % fd_cond 1
% 5.98/2.33 % fd_pseudo_cond 1
% 5.98/2.33 % AC symbols 0
% 5.98/2.33
% 5.98/2.33 % ------ Schedule dynamic 5 is on
% 5.98/2.33
% 5.98/2.33 % ------ no conjectures: strip conj schedule
% 5.98/2.33
% 5.98/2.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 5.98/2.33
% 5.98/2.33
% 5.98/2.33 % ------
% 5.98/2.33 % Current options:
% 5.98/2.33 % ------
% 5.98/2.33
% 5.98/2.33
% 5.98/2.33 %
% 5.98/2.33
% 5.98/2.33 % ------ Proving...
% 5.98/2.33 %
% 5.98/2.33
% 5.98/2.33 % SZS status Theorem for theBenchmark.p
% 5.98/2.33
% 5.98/2.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.98/2.39
% 5.98/2.39
%------------------------------------------------------------------------------