%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HAL001+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 10:18:52 AM UTC 2026
% Result : Theorem 10.06s 2.23s
% Output : Refutation 10.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 38
% Syntax : Number of formulae : 272 ( 83 unt; 14 def)
% Number of atoms : 789 ( 191 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 961 ( 444 ~; 442 |; 44 &)
% ( 17 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 15 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-3 aty)
% Number of variables : 323 ( 0 sgn 313 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) )
& apply(X0,zero(X1)) = zero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( injection(X0)
& morphism(X0,X1,X2) )
=> ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) )
=> X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) )
=> X3 = X4 ) )
=> injection(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] :
( ( exact(X0,X1)
& morphism(X0,X2,X3)
& morphism(X1,X3,X4) )
=> ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exact_properties) ).
fof(f8,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( commute(X0,X1,X2,X3)
& morphism(X0,X4,X5)
& morphism(X1,X5,X7)
& morphism(X2,X4,X6)
& morphism(X3,X6,X7) )
=> ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commute_properties) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X1,X0)
& element(X2,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_in_domain) ).
fof(f11,axiom,
! [X0,X1] :
( element(X1,X0)
=> subtract(X0,X1,X1) = zero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_to_0) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( element(X1,X0)
& element(X2,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
fof(f14,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
fof(f15,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_morphism) ).
fof(f16,axiom,
morphism(gamma,d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_morphism) ).
fof(f17,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_morphism) ).
fof(f18,axiom,
morphism(f,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_morphism) ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(f20,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_morphism) ).
fof(f21,axiom,
injection(alpha),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_injection) ).
fof(f22,axiom,
injection(gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_injection) ).
fof(f25,axiom,
exact(alpha,beta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_beta_exact) ).
fof(f27,axiom,
commute(alpha,g,f,gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
fof(f28,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(f29,axiom,
injection(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_injection) ).
fof(f30,axiom,
injection(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_injection) ).
fof(f31,conjecture,
injection(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_injection) ).
fof(f32,negated_conjecture,
~ injection(g),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
~ injection(g),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3,X4] :
( X3 != X4
& element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3,X4] :
( X3 != X4
& element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f36]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(ennf_transformation,[],[f6]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(flattening,[],[f44]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ commute(X0,X1,X2,X3)
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(ennf_transformation,[],[f8]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ commute(X0,X1,X2,X3)
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X3,X1)
| ~ element(X4,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X3,X1)
| ~ element(X4,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) )
& apply(X0,zero(X1)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f53,plain,
! [X0,X1] :
( subtract(X0,X1,X1) = zero(X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f54,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f55,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ( sK0(X0,X1) != sK1(X0,X1)
& element(sK0(X0,X1),X1)
& element(sK1(X0,X1),X1)
& apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1)),skolemize(X4,sK1(X0,X1))],[f35]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(nnf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( element(X7,X2)
& apply(X0,X7) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ( element(sK6(X0,X2,X5),X2)
& apply(X0,sK6(X0,X2,X5)) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X7,sK6(X0,X2,X5))],[f67]) ).
fof(f70,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[],[f14]) ).
fof(f71,plain,
morphism(beta,b,c),
inference(cnf_transformation,[],[f15]) ).
fof(f72,plain,
morphism(gamma,d,e),
inference(cnf_transformation,[],[f16]) ).
fof(f73,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f17]) ).
fof(f74,plain,
morphism(f,a,d),
inference(cnf_transformation,[],[f18]) ).
fof(f75,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f76,plain,
morphism(h,c,r),
inference(cnf_transformation,[],[f20]) ).
fof(f77,plain,
injection(alpha),
inference(cnf_transformation,[],[f21]) ).
fof(f78,plain,
injection(gamma),
inference(cnf_transformation,[],[f22]) ).
fof(f81,plain,
exact(alpha,beta),
inference(cnf_transformation,[],[f25]) ).
fof(f83,plain,
commute(alpha,g,f,gamma),
inference(cnf_transformation,[],[f27]) ).
fof(f84,plain,
commute(beta,h,g,delta),
inference(cnf_transformation,[],[f28]) ).
fof(f85,plain,
injection(f),
inference(cnf_transformation,[],[f29]) ).
fof(f86,plain,
injection(h),
inference(cnf_transformation,[],[f30]) ).
fof(f87,plain,
~ injection(g),
inference(cnf_transformation,[],[f33]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| element(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| element(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f91,plain,
! [X2,X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ injection(X0)
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4)
| X3 = X4
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ exact(X0,X1)
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4)
| apply(X0,sK6(X0,X2,X5)) = X5
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ exact(X0,X1)
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4)
| element(sK6(X0,X2,X5),X2)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ commute(X0,X1,X2,X3)
| ~ element(X8,X4)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(cnf_transformation,[],[f49]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f112,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f55]) ).
fof(f114,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f117,plain,
( injection(g)
| element(sK1(g,b),b) ),
inference(resolution,[],[f89,f75]) ).
fof(f118,plain,
element(sK1(g,b),b),
inference(forward_subsumption_resolution,[],[f117,f87]) ).
fof(f119,plain,
( injection(g)
| element(sK0(g,b),b) ),
inference(resolution,[],[f90,f75]) ).
fof(f120,plain,
element(sK0(g,b),b),
inference(forward_subsumption_resolution,[],[f119,f87]) ).
fof(f121,plain,
! [X0] :
( element(apply(g,X0),e)
| ~ element(X0,b) ),
inference(resolution,[],[f111,f75]) ).
fof(f124,plain,
apply(g,zero(b)) = zero(e),
inference(resolution,[],[f110,f75]) ).
fof(f139,plain,
apply(f,zero(a)) = zero(d),
inference(resolution,[],[f74,f110]) ).
fof(f140,plain,
! [X0] :
( element(apply(f,X0),d)
| ~ element(X0,a) ),
inference(resolution,[],[f74,f111]) ).
fof(f183,plain,
( injection(g)
| apply(g,sK0(g,b)) = apply(g,sK1(g,b)) ),
inference(resolution,[],[f88,f75]) ).
fof(f185,plain,
apply(g,sK0(g,b)) = apply(g,sK1(g,b)),
inference(forward_subsumption_resolution,[],[f183,f87]) ).
fof(f186,plain,
( element(apply(g,sK0(g,b)),e)
| ~ element(sK1(g,b),b) ),
inference(superposition,[],[f121,f185]) ).
fof(f187,plain,
element(apply(g,sK0(g,b)),e),
inference(forward_subsumption_resolution,[],[f186,f118]) ).
fof(f191,plain,
zero(c) = apply(beta,zero(b)),
inference(resolution,[],[f71,f110]) ).
fof(f192,plain,
! [X0] :
( element(apply(beta,X0),c)
| ~ element(X0,b) ),
inference(resolution,[],[f71,f111]) ).
fof(f210,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(alpha,X1,X2)
| apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,X1)
| ~ morphism(g,X2,X3)
| ~ morphism(f,X1,X4)
| ~ morphism(gamma,X4,X3) ),
inference(resolution,[],[f108,f83]) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(h,X2,X3)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0))
| ~ morphism(beta,X1,X2)
| ~ element(X0,X1)
| ~ morphism(g,X1,X4)
| ~ morphism(delta,X4,X3) ),
inference(resolution,[],[f108,f84]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ morphism(delta,X2,r)
| ~ morphism(beta,X1,c)
| ~ element(X0,X1)
| ~ morphism(g,X1,X2)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0)) ),
inference(resolution,[],[f211,f76]) ).
fof(f213,plain,
! [X0,X1] :
( ~ morphism(g,X0,e)
| ~ element(X1,X0)
| ~ morphism(beta,X0,c)
| apply(h,apply(beta,X1)) = apply(delta,apply(g,X1)) ),
inference(resolution,[],[f212,f73]) ).
fof(f214,plain,
! [X0] :
( ~ element(X0,b)
| ~ morphism(beta,b,c)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0)) ),
inference(resolution,[],[f213,f75]) ).
fof(f215,plain,
! [X0] :
( ~ element(X0,b)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0)) ),
inference(forward_subsumption_resolution,[],[f214,f71]) ).
fof(f216,plain,
apply(h,apply(beta,sK1(g,b))) = apply(delta,apply(g,sK1(g,b))),
inference(resolution,[],[f215,f118]) ).
fof(f217,plain,
apply(delta,apply(g,sK0(g,b))) = apply(h,apply(beta,sK0(g,b))),
inference(resolution,[],[f215,f120]) ).
fof(f218,plain,
apply(delta,apply(g,sK0(g,b))) = apply(h,apply(beta,sK1(g,b))),
inference(forward_demodulation,[],[f216,f185]) ).
fof(f221,definition,
( spl8_14
<=> element(apply(beta,sK1(g,b)),c) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
fof(f222,plain,
( ~ element(apply(beta,sK1(g,b)),c)
| spl8_14 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f229,plain,
( ~ element(sK1(g,b),b)
| spl8_14 ),
inference(resolution,[],[f222,f192]) ).
fof(f232,plain,
( $false
| spl8_14 ),
inference(forward_subsumption_resolution,[],[f229,f118]) ).
fof(f233,plain,
spl8_14,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f235,plain,
! [X2,X0,X1] :
( apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,a)
| ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) ),
inference(resolution,[],[f70,f210]) ).
fof(f237,plain,
zero(b) = apply(alpha,zero(a)),
inference(resolution,[],[f70,f110]) ).
fof(f242,definition,
( spl8_16
<=> ! [X2,X1] :
( ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
fof(f243,plain,
( ! [X2,X1] :
( ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl8_17
<=> ! [X0] :
( apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,a) ) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
fof(f246,plain,
( ! [X0] :
( ~ element(X0,a)
| apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0)) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( spl8_16
| spl8_17 ),
inference(avatar_split_clause,[],[f235,f245,f242]) ).
fof(f248,plain,
( $false
| ~ spl8_16 ),
inference(unit_resulting_resolution,[],[f243,f72,f74,f75]) ).
fof(f250,plain,
~ spl8_16,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( apply(alpha,X0) != apply(alpha,X2)
| ~ element(X2,X1)
| ~ element(X0,X1)
| X0 = X2
| ~ morphism(alpha,X1,X3) ),
inference(resolution,[],[f92,f77]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( apply(gamma,X0) != apply(gamma,X2)
| ~ element(X2,X1)
| ~ element(X0,X1)
| X0 = X2
| ~ morphism(gamma,X1,X3) ),
inference(resolution,[],[f92,f78]) ).
fof(f259,plain,
! [X2,X3,X0,X1] :
( ~ morphism(f,X1,X3)
| ~ element(X2,X1)
| apply(f,X0) != apply(f,X2)
| X0 = X2
| ~ element(X0,X1) ),
inference(resolution,[],[f92,f85]) ).
fof(f260,plain,
! [X2,X3,X0,X1] :
( ~ morphism(h,X1,X3)
| ~ element(X2,X1)
| apply(h,X0) != apply(h,X2)
| X0 = X2
| ~ element(X0,X1) ),
inference(resolution,[],[f92,f86]) ).
fof(f261,plain,
! [X0,X1] :
( apply(f,X0) != apply(f,X1)
| ~ element(X0,a)
| X0 = X1
| ~ element(X1,a) ),
inference(resolution,[],[f259,f74]) ).
fof(f262,plain,
! [X0,X1] :
( ~ element(X1,c)
| apply(h,X0) != apply(h,X1)
| X0 = X1
| ~ element(X0,c) ),
inference(resolution,[],[f260,f76]) ).
fof(f273,plain,
! [X0] :
( ~ element(X0,b)
| sK1(g,b) = subtract(b,X0,subtract(b,X0,sK1(g,b))) ),
inference(resolution,[],[f113,f118]) ).
fof(f274,plain,
! [X0] :
( ~ element(X0,b)
| sK0(g,b) = subtract(b,X0,subtract(b,X0,sK0(g,b))) ),
inference(resolution,[],[f113,f120]) ).
fof(f283,plain,
sK0(g,b) = subtract(b,sK1(g,b),subtract(b,sK1(g,b),sK0(g,b))),
inference(resolution,[],[f274,f118]) ).
fof(f288,plain,
sK1(g,b) = subtract(b,sK1(g,b),subtract(b,sK1(g,b),sK1(g,b))),
inference(resolution,[],[f273,f118]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( zero(X2) != apply(beta,X0)
| ~ element(X0,X1)
| apply(alpha,sK6(alpha,X3,X0)) = X0
| ~ morphism(alpha,X3,X1)
| ~ morphism(beta,X1,X2) ),
inference(resolution,[],[f102,f81]) ).
fof(f306,definition,
( spl8_19
<=> element(apply(beta,sK0(g,b)),c) ),
introduced(definition,[new_symbols(definition,[spl8_19])],[avatar_definition]) ).
fof(f307,plain,
( element(apply(beta,sK0(g,b)),c)
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f314,plain,
( element(apply(beta,sK1(g,b)),c)
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f319,plain,
zero(b) = subtract(b,sK1(g,b),sK1(g,b)),
inference(resolution,[],[f112,f118]) ).
fof(f320,plain,
zero(b) = subtract(b,sK0(g,b),sK0(g,b)),
inference(resolution,[],[f112,f120]) ).
fof(f326,plain,
zero(e) = subtract(e,apply(g,sK0(g,b)),apply(g,sK0(g,b))),
inference(resolution,[],[f112,f187]) ).
fof(f331,plain,
( element(zero(b),b)
| ~ element(sK0(g,b),b)
| ~ element(sK0(g,b),b) ),
inference(superposition,[],[f114,f320]) ).
fof(f332,plain,
( element(zero(b),b)
| ~ element(sK0(g,b),b) ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f336,plain,
element(zero(b),b),
inference(forward_subsumption_resolution,[],[f332,f120]) ).
fof(f347,plain,
sK1(g,b) = subtract(b,sK1(g,b),zero(b)),
inference(superposition,[],[f288,f319]) ).
fof(f354,plain,
! [X2,X3,X0,X1] :
( ~ morphism(beta,X1,X2)
| zero(X2) != apply(beta,X0)
| element(sK6(alpha,X3,X0),X3)
| ~ morphism(alpha,X3,X1)
| ~ element(X0,X1) ),
inference(resolution,[],[f103,f81]) ).
fof(f356,plain,
! [X0,X1] :
( ~ morphism(alpha,X1,b)
| element(sK6(alpha,X1,X0),X1)
| apply(beta,X0) != zero(c)
| ~ element(X0,b) ),
inference(resolution,[],[f354,f71]) ).
fof(f357,plain,
! [X0] :
( apply(beta,X0) != zero(c)
| element(sK6(alpha,a,X0),a)
| ~ element(X0,b) ),
inference(resolution,[],[f356,f70]) ).
fof(f389,plain,
( zero(c) != zero(c)
| element(sK6(alpha,a,zero(b)),a)
| ~ element(zero(b),b) ),
inference(superposition,[],[f357,f191]) ).
fof(f390,plain,
! [X2,X0,X1] :
( zero(X0) != zero(c)
| ~ element(zero(b),X1)
| zero(b) = apply(alpha,sK6(alpha,X2,zero(b)))
| ~ morphism(alpha,X2,X1)
| ~ morphism(beta,X1,X0) ),
inference(superposition,[],[f293,f191]) ).
fof(f392,plain,
( element(sK6(alpha,a,zero(b)),a)
| ~ element(zero(b),b) ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f394,plain,
element(sK6(alpha,a,zero(b)),a),
inference(forward_subsumption_resolution,[],[f392,f336]) ).
fof(f398,plain,
( apply(g,apply(alpha,sK6(alpha,a,zero(b)))) = apply(gamma,apply(f,sK6(alpha,a,zero(b))))
| ~ spl8_17 ),
inference(resolution,[],[f394,f246]) ).
fof(f400,plain,
zero(a) = subtract(a,sK6(alpha,a,zero(b)),sK6(alpha,a,zero(b))),
inference(resolution,[],[f394,f112]) ).
fof(f408,plain,
( element(zero(a),a)
| ~ element(sK6(alpha,a,zero(b)),a)
| ~ element(sK6(alpha,a,zero(b)),a) ),
inference(superposition,[],[f114,f400]) ).
fof(f409,plain,
( element(zero(a),a)
| ~ element(sK6(alpha,a,zero(b)),a) ),
inference(duplicate_literal_removal,[],[f408]) ).
fof(f413,plain,
element(zero(a),a),
inference(forward_subsumption_resolution,[],[f409,f394]) ).
fof(f423,plain,
( ! [X2,X0,X1] :
( ~ element(apply(f,sK6(alpha,a,zero(b))),X1)
| ~ element(X0,X1)
| apply(gamma,X0) != apply(g,apply(alpha,sK6(alpha,a,zero(b))))
| apply(f,sK6(alpha,a,zero(b))) = X0
| ~ morphism(gamma,X1,X2) )
| ~ spl8_17 ),
inference(superposition,[],[f257,f398]) ).
fof(f569,plain,
! [X0,X1] :
( ~ element(X1,b)
| ~ element(X0,b)
| apply(beta,subtract(b,X0,X1)) = subtract(c,apply(beta,X0),apply(beta,X1)) ),
inference(resolution,[],[f109,f71]) ).
fof(f573,plain,
! [X0,X1] :
( ~ element(X1,b)
| ~ element(X0,b)
| apply(g,subtract(b,X0,X1)) = subtract(e,apply(g,X0),apply(g,X1)) ),
inference(resolution,[],[f109,f75]) ).
fof(f578,plain,
! [X0] :
( ~ element(X0,b)
| apply(g,subtract(b,X0,sK0(g,b))) = subtract(e,apply(g,X0),apply(g,sK0(g,b))) ),
inference(resolution,[],[f573,f120]) ).
fof(f587,plain,
apply(g,subtract(b,sK1(g,b),sK0(g,b))) = subtract(e,apply(g,sK1(g,b)),apply(g,sK0(g,b))),
inference(resolution,[],[f578,f118]) ).
fof(f589,plain,
subtract(e,apply(g,sK0(g,b)),apply(g,sK0(g,b))) = apply(g,subtract(b,sK1(g,b),sK0(g,b))),
inference(forward_demodulation,[],[f587,f185]) ).
fof(f592,plain,
zero(e) = apply(g,subtract(b,sK1(g,b),sK0(g,b))),
inference(forward_demodulation,[],[f589,f326]) ).
fof(f639,plain,
! [X0] :
( ~ element(X0,b)
| apply(beta,subtract(b,X0,sK0(g,b))) = subtract(c,apply(beta,X0),apply(beta,sK0(g,b))) ),
inference(resolution,[],[f569,f120]) ).
fof(f646,plain,
apply(beta,subtract(b,sK0(g,b),sK0(g,b))) = subtract(c,apply(beta,sK0(g,b)),apply(beta,sK0(g,b))),
inference(resolution,[],[f639,f120]) ).
fof(f647,plain,
apply(beta,subtract(b,sK1(g,b),sK0(g,b))) = subtract(c,apply(beta,sK1(g,b)),apply(beta,sK0(g,b))),
inference(resolution,[],[f639,f118]) ).
fof(f649,plain,
apply(beta,zero(b)) = subtract(c,apply(beta,sK0(g,b)),apply(beta,sK0(g,b))),
inference(forward_demodulation,[],[f646,f320]) ).
fof(f651,plain,
zero(c) = subtract(c,apply(beta,sK0(g,b)),apply(beta,sK0(g,b))),
inference(forward_demodulation,[],[f649,f191]) ).
fof(f665,plain,
( ~ element(apply(beta,sK0(g,b)),c)
| spl8_19 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f672,plain,
( ~ element(sK0(g,b),b)
| spl8_19 ),
inference(resolution,[],[f665,f192]) ).
fof(f675,plain,
( $false
| spl8_19 ),
inference(forward_subsumption_resolution,[],[f672,f120]) ).
fof(f676,plain,
spl8_19,
inference(avatar_contradiction_clause,[],[f675]) ).
fof(f700,plain,
( ! [X0,X1] :
( ~ element(X0,d)
| apply(gamma,X0) != apply(g,apply(alpha,sK6(alpha,a,zero(b))))
| apply(f,sK6(alpha,a,zero(b))) = X0
| ~ morphism(gamma,d,X1)
| ~ element(sK6(alpha,a,zero(b)),a) )
| ~ spl8_17 ),
inference(resolution,[],[f423,f140]) ).
fof(f701,plain,
( ! [X0,X1] :
( ~ element(X0,d)
| apply(gamma,X0) != apply(g,apply(alpha,sK6(alpha,a,zero(b))))
| apply(f,sK6(alpha,a,zero(b))) = X0
| ~ morphism(gamma,d,X1) )
| ~ spl8_17 ),
inference(forward_subsumption_resolution,[],[f700,f394]) ).
fof(f703,definition,
( spl8_40
<=> ! [X1] : ~ morphism(gamma,d,X1) ),
introduced(definition,[new_symbols(definition,[spl8_40])],[avatar_definition]) ).
fof(f704,plain,
( ! [X1] : ~ morphism(gamma,d,X1)
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f706,definition,
( spl8_41
<=> ! [X0] :
( ~ element(X0,d)
| apply(f,sK6(alpha,a,zero(b))) = X0
| apply(gamma,X0) != apply(g,apply(alpha,sK6(alpha,a,zero(b)))) ) ),
introduced(definition,[new_symbols(definition,[spl8_41])],[avatar_definition]) ).
fof(f707,plain,
( ! [X0] :
( apply(gamma,X0) != apply(g,apply(alpha,sK6(alpha,a,zero(b))))
| apply(f,sK6(alpha,a,zero(b))) = X0
| ~ element(X0,d) )
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f708,plain,
( spl8_40
| spl8_41
| ~ spl8_17 ),
inference(avatar_split_clause,[],[f701,f245,f706,f703]) ).
fof(f709,plain,
( $false
| ~ spl8_40 ),
inference(unit_resulting_resolution,[],[f704,f72]) ).
fof(f712,plain,
~ spl8_40,
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f724,plain,
( ! [X0] :
( apply(h,X0) != apply(h,apply(beta,sK0(g,b)))
| apply(beta,sK0(g,b)) = X0
| ~ element(X0,c) )
| ~ spl8_19 ),
inference(resolution,[],[f262,f307]) ).
fof(f730,plain,
( ! [X0] :
( apply(h,X0) != apply(delta,apply(g,sK0(g,b)))
| apply(beta,sK0(g,b)) = X0
| ~ element(X0,c) )
| ~ spl8_19 ),
inference(forward_demodulation,[],[f724,f217]) ).
fof(f731,plain,
( apply(delta,apply(g,sK0(g,b))) != apply(delta,apply(g,sK0(g,b)))
| apply(beta,sK1(g,b)) = apply(beta,sK0(g,b))
| ~ element(apply(beta,sK1(g,b)),c)
| ~ spl8_19 ),
inference(superposition,[],[f730,f218]) ).
fof(f733,plain,
( apply(beta,sK1(g,b)) = apply(beta,sK0(g,b))
| ~ element(apply(beta,sK1(g,b)),c)
| ~ spl8_19 ),
inference(trivial_inequality_removal,[],[f731]) ).
fof(f741,plain,
( apply(beta,sK1(g,b)) = apply(beta,sK0(g,b))
| ~ spl8_14
| ~ spl8_19 ),
inference(forward_subsumption_resolution,[],[f733,f314]) ).
fof(f747,plain,
( subtract(c,apply(beta,sK0(g,b)),apply(beta,sK0(g,b))) = apply(beta,subtract(b,sK1(g,b),sK0(g,b)))
| ~ spl8_14
| ~ spl8_19 ),
inference(superposition,[],[f647,f741]) ).
fof(f753,plain,
( zero(c) = apply(beta,subtract(b,sK1(g,b),sK0(g,b)))
| ~ spl8_14
| ~ spl8_19 ),
inference(forward_demodulation,[],[f747,f651]) ).
fof(f758,plain,
( zero(c) != zero(c)
| element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a)
| ~ element(subtract(b,sK1(g,b),sK0(g,b)),b)
| ~ spl8_14
| ~ spl8_19 ),
inference(superposition,[],[f357,f753]) ).
fof(f759,plain,
( ! [X2,X0,X1] :
( zero(X0) != zero(c)
| ~ element(subtract(b,sK1(g,b),sK0(g,b)),X1)
| subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X2,subtract(b,sK1(g,b),sK0(g,b))))
| ~ morphism(alpha,X2,X1)
| ~ morphism(beta,X1,X0) )
| ~ spl8_14
| ~ spl8_19 ),
inference(superposition,[],[f293,f753]) ).
fof(f761,plain,
( element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a)
| ~ element(subtract(b,sK1(g,b),sK0(g,b)),b)
| ~ spl8_14
| ~ spl8_19 ),
inference(trivial_inequality_removal,[],[f758]) ).
fof(f763,definition,
( spl8_46
<=> element(subtract(b,sK1(g,b),sK0(g,b)),b) ),
introduced(definition,[new_symbols(definition,[spl8_46])],[avatar_definition]) ).
fof(f764,plain,
( ~ element(subtract(b,sK1(g,b),sK0(g,b)),b)
| spl8_46 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f766,definition,
( spl8_47
<=> element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a) ),
introduced(definition,[new_symbols(definition,[spl8_47])],[avatar_definition]) ).
fof(f767,plain,
( element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a)
| ~ spl8_47 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f768,plain,
( ~ spl8_46
| spl8_47
| ~ spl8_14
| ~ spl8_19 ),
inference(avatar_split_clause,[],[f761,f306,f221,f766,f763]) ).
fof(f770,plain,
( ~ element(sK1(g,b),b)
| ~ element(sK0(g,b),b)
| spl8_46 ),
inference(resolution,[],[f764,f114]) ).
fof(f772,plain,
( ~ element(sK0(g,b),b)
| spl8_46 ),
inference(forward_subsumption_resolution,[],[f770,f118]) ).
fof(f773,plain,
( $false
| spl8_46 ),
inference(forward_subsumption_resolution,[],[f772,f120]) ).
fof(f774,plain,
spl8_46,
inference(avatar_contradiction_clause,[],[f773]) ).
fof(f776,plain,
( apply(g,apply(alpha,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))) = apply(gamma,apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))))
| ~ spl8_17
| ~ spl8_47 ),
inference(resolution,[],[f767,f246]) ).
fof(f780,plain,
( apply(g,apply(alpha,sK6(alpha,a,zero(b)))) != apply(g,apply(alpha,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))))
| apply(f,sK6(alpha,a,zero(b))) = apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))
| ~ element(apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))),d)
| ~ spl8_17
| ~ spl8_41
| ~ spl8_47 ),
inference(superposition,[],[f707,f776]) ).
fof(f785,definition,
( spl8_48
<=> element(apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))),d) ),
introduced(definition,[new_symbols(definition,[spl8_48])],[avatar_definition]) ).
fof(f786,plain,
( ~ element(apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))),d)
| spl8_48 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f792,definition,
( spl8_50
<=> apply(f,sK6(alpha,a,zero(b))) = apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))) ),
introduced(definition,[new_symbols(definition,[spl8_50])],[avatar_definition]) ).
fof(f793,plain,
( apply(f,sK6(alpha,a,zero(b))) = apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))
| ~ spl8_50 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f795,definition,
( spl8_51
<=> apply(g,apply(alpha,sK6(alpha,a,zero(b)))) = apply(g,apply(alpha,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))) ),
introduced(definition,[new_symbols(definition,[spl8_51])],[avatar_definition]) ).
fof(f796,plain,
( apply(g,apply(alpha,sK6(alpha,a,zero(b)))) != apply(g,apply(alpha,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))))
| spl8_51 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f797,plain,
( ~ spl8_48
| spl8_50
| ~ spl8_51
| ~ spl8_17
| ~ spl8_41
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f780,f766,f706,f245,f795,f792,f785]) ).
fof(f800,plain,
( ~ element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a)
| spl8_48 ),
inference(resolution,[],[f786,f140]) ).
fof(f803,plain,
( $false
| ~ spl8_47
| spl8_48 ),
inference(forward_subsumption_resolution,[],[f800,f767]) ).
fof(f804,plain,
( ~ spl8_47
| spl8_48 ),
inference(avatar_contradiction_clause,[],[f803]) ).
fof(f1201,definition,
( spl8_88
<=> ! [X1] : ~ morphism(alpha,a,X1) ),
introduced(definition,[new_symbols(definition,[spl8_88])],[avatar_definition]) ).
fof(f1202,plain,
( ! [X1] : ~ morphism(alpha,a,X1)
| ~ spl8_88 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f1353,plain,
! [X0,X1] :
( ~ element(zero(b),X0)
| zero(b) = apply(alpha,sK6(alpha,X1,zero(b)))
| ~ morphism(alpha,X1,X0)
| ~ morphism(beta,X0,c) ),
inference(equality_resolution,[],[f390]) ).
fof(f1354,plain,
! [X0] :
( zero(b) = apply(alpha,sK6(alpha,X0,zero(b)))
| ~ morphism(alpha,X0,b)
| ~ morphism(beta,b,c) ),
inference(resolution,[],[f1353,f336]) ).
fof(f1355,plain,
! [X0] :
( ~ morphism(alpha,X0,b)
| zero(b) = apply(alpha,sK6(alpha,X0,zero(b))) ),
inference(forward_subsumption_resolution,[],[f1354,f71]) ).
fof(f1356,plain,
zero(b) = apply(alpha,sK6(alpha,a,zero(b))),
inference(resolution,[],[f1355,f70]) ).
fof(f1371,plain,
! [X2,X0,X1] :
( ~ element(sK6(alpha,a,zero(b)),X1)
| ~ element(X0,X1)
| apply(alpha,X0) != zero(b)
| sK6(alpha,a,zero(b)) = X0
| ~ morphism(alpha,X1,X2) ),
inference(superposition,[],[f255,f1356]) ).
fof(f1385,plain,
! [X0,X1] :
( ~ element(X0,a)
| apply(alpha,X0) != zero(b)
| sK6(alpha,a,zero(b)) = X0
| ~ morphism(alpha,a,X1) ),
inference(resolution,[],[f1371,f394]) ).
fof(f1387,definition,
( spl8_100
<=> ! [X0] :
( ~ element(X0,a)
| sK6(alpha,a,zero(b)) = X0
| apply(alpha,X0) != zero(b) ) ),
introduced(definition,[new_symbols(definition,[spl8_100])],[avatar_definition]) ).
fof(f1388,plain,
( ! [X0] :
( apply(alpha,X0) != zero(b)
| sK6(alpha,a,zero(b)) = X0
| ~ element(X0,a) )
| ~ spl8_100 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f1389,plain,
( spl8_88
| spl8_100 ),
inference(avatar_split_clause,[],[f1385,f1387,f1201]) ).
fof(f1390,plain,
( $false
| ~ spl8_88 ),
inference(unit_resulting_resolution,[],[f1202,f70]) ).
fof(f1393,plain,
~ spl8_88,
inference(avatar_contradiction_clause,[],[f1390]) ).
fof(f1394,plain,
( zero(b) != zero(b)
| zero(a) = sK6(alpha,a,zero(b))
| ~ element(zero(a),a)
| ~ spl8_100 ),
inference(superposition,[],[f1388,f237]) ).
fof(f1395,plain,
( zero(a) = sK6(alpha,a,zero(b))
| ~ element(zero(a),a)
| ~ spl8_100 ),
inference(trivial_inequality_removal,[],[f1394]) ).
fof(f1396,plain,
( zero(a) = sK6(alpha,a,zero(b))
| ~ spl8_100 ),
inference(forward_subsumption_resolution,[],[f1395,f413]) ).
fof(f1720,plain,
( ! [X0,X1] :
( ~ element(subtract(b,sK1(g,b),sK0(g,b)),X0)
| subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X1,subtract(b,sK1(g,b),sK0(g,b))))
| ~ morphism(alpha,X1,X0)
| ~ morphism(beta,X0,c) )
| ~ spl8_14
| ~ spl8_19 ),
inference(equality_resolution,[],[f759]) ).
fof(f1721,plain,
( ! [X0] :
( subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X0,subtract(b,sK1(g,b),sK0(g,b))))
| ~ morphism(alpha,X0,b)
| ~ morphism(beta,b,c)
| ~ element(sK1(g,b),b)
| ~ element(sK0(g,b),b) )
| ~ spl8_14
| ~ spl8_19 ),
inference(resolution,[],[f1720,f114]) ).
fof(f1722,plain,
( ! [X0] :
( subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X0,subtract(b,sK1(g,b),sK0(g,b))))
| ~ morphism(alpha,X0,b)
| ~ element(sK1(g,b),b)
| ~ element(sK0(g,b),b) )
| ~ spl8_14
| ~ spl8_19 ),
inference(forward_subsumption_resolution,[],[f1721,f71]) ).
fof(f1723,plain,
( ! [X0] :
( subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X0,subtract(b,sK1(g,b),sK0(g,b))))
| ~ morphism(alpha,X0,b)
| ~ element(sK0(g,b),b) )
| ~ spl8_14
| ~ spl8_19 ),
inference(forward_subsumption_resolution,[],[f1722,f118]) ).
fof(f1724,plain,
( ! [X0] :
( ~ morphism(alpha,X0,b)
| subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,X0,subtract(b,sK1(g,b),sK0(g,b)))) )
| ~ spl8_14
| ~ spl8_19 ),
inference(forward_subsumption_resolution,[],[f1723,f120]) ).
fof(f1725,plain,
( subtract(b,sK1(g,b),sK0(g,b)) = apply(alpha,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))
| ~ spl8_14
| ~ spl8_19 ),
inference(resolution,[],[f1724,f70]) ).
fof(f1727,plain,
( apply(g,apply(alpha,sK6(alpha,a,zero(b)))) != apply(g,subtract(b,sK1(g,b),sK0(g,b)))
| ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(superposition,[],[f796,f1725]) ).
fof(f1733,plain,
( zero(e) != apply(g,apply(alpha,sK6(alpha,a,zero(b))))
| ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(forward_demodulation,[],[f1727,f592]) ).
fof(f1736,plain,
( apply(g,zero(b)) != zero(e)
| ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(forward_demodulation,[],[f1733,f1356]) ).
fof(f1741,definition,
( spl8_108
<=> zero(a) = sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))) ),
introduced(definition,[new_symbols(definition,[spl8_108])],[avatar_definition]) ).
fof(f1742,plain,
( zero(a) = sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))
| ~ spl8_108 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f1744,plain,
( $false
| ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(forward_subsumption_resolution,[],[f1736,f124]) ).
fof(f1745,plain,
( ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(avatar_contradiction_clause,[],[f1744]) ).
fof(f1746,plain,
( apply(f,zero(a)) = apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))
| ~ spl8_50
| ~ spl8_100 ),
inference(forward_demodulation,[],[f793,f1396]) ).
fof(f1747,plain,
( zero(d) = apply(f,sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))))
| ~ spl8_50
| ~ spl8_100 ),
inference(forward_demodulation,[],[f1746,f139]) ).
fof(f1787,plain,
( ! [X0] :
( apply(f,X0) != zero(d)
| ~ element(sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))),a)
| sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))) = X0
| ~ element(X0,a) )
| ~ spl8_50
| ~ spl8_100 ),
inference(superposition,[],[f261,f1747]) ).
fof(f1789,plain,
( ! [X0] :
( apply(f,X0) != zero(d)
| sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b))) = X0
| ~ element(X0,a) )
| ~ spl8_47
| ~ spl8_50
| ~ spl8_100 ),
inference(forward_subsumption_resolution,[],[f1787,f767]) ).
fof(f1798,plain,
( zero(d) != zero(d)
| zero(a) = sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))
| ~ element(zero(a),a)
| ~ spl8_47
| ~ spl8_50
| ~ spl8_100 ),
inference(superposition,[],[f1789,f139]) ).
fof(f1799,plain,
( zero(a) = sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))
| ~ element(zero(a),a)
| ~ spl8_47
| ~ spl8_50
| ~ spl8_100 ),
inference(trivial_inequality_removal,[],[f1798]) ).
fof(f1800,plain,
( zero(a) = sK6(alpha,a,subtract(b,sK1(g,b),sK0(g,b)))
| ~ spl8_47
| ~ spl8_50
| ~ spl8_100 ),
inference(forward_subsumption_resolution,[],[f1799,f413]) ).
fof(f1801,plain,
( spl8_108
| ~ spl8_47
| ~ spl8_50
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f1800,f1387,f792,f766,f1741]) ).
fof(f1809,plain,
( apply(alpha,zero(a)) = subtract(b,sK1(g,b),sK0(g,b))
| ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(superposition,[],[f1725,f1742]) ).
fof(f1812,plain,
( zero(b) = subtract(b,sK1(g,b),sK0(g,b))
| ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(forward_demodulation,[],[f1809,f237]) ).
fof(f1822,plain,
( sK0(g,b) = subtract(b,sK1(g,b),zero(b))
| ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(superposition,[],[f283,f1812]) ).
fof(f1846,plain,
( sK0(g,b) = sK1(g,b)
| ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(superposition,[],[f347,f1822]) ).
fof(f1848,plain,
( $false
| ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(unit_resulting_resolution,[],[f91,f87,f75,f1846]) ).
fof(f1898,plain,
( ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(avatar_contradiction_clause,[],[f1848]) ).
cnf(s12,plain,
spl8_14,
inference(sat_conversion,[],[f233]) ).
cnf(s13,plain,
( spl8_16
| spl8_17 ),
inference(sat_conversion,[],[f247]) ).
cnf(s14,plain,
~ spl8_16,
inference(sat_conversion,[],[f250]) ).
cnf(s50,plain,
spl8_19,
inference(sat_conversion,[],[f676]) ).
cnf(s54,plain,
( ~ spl8_17
| spl8_40
| spl8_41 ),
inference(sat_conversion,[],[f708]) ).
cnf(s56,plain,
~ spl8_40,
inference(sat_conversion,[],[f712]) ).
cnf(s59,plain,
( ~ spl8_14
| ~ spl8_19
| ~ spl8_46
| spl8_47 ),
inference(sat_conversion,[],[f768]) ).
cnf(s61,plain,
spl8_46,
inference(sat_conversion,[],[f774]) ).
cnf(s63,plain,
( ~ spl8_17
| ~ spl8_41
| ~ spl8_47
| ~ spl8_48
| spl8_50
| ~ spl8_51 ),
inference(sat_conversion,[],[f797]) ).
cnf(s66,plain,
( ~ spl8_47
| spl8_48 ),
inference(sat_conversion,[],[f804]) ).
cnf(s113,plain,
( spl8_88
| spl8_100 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s115,plain,
~ spl8_88,
inference(sat_conversion,[],[f1393]) ).
cnf(s128,plain,
( ~ spl8_14
| ~ spl8_19
| spl8_51 ),
inference(sat_conversion,[],[f1745]) ).
cnf(s130,plain,
( ~ spl8_47
| ~ spl8_50
| ~ spl8_100
| spl8_108 ),
inference(sat_conversion,[],[f1801]) ).
cnf(s132,plain,
( ~ spl8_14
| ~ spl8_19
| ~ spl8_108 ),
inference(sat_conversion,[],[f1898]) ).
cnf(s134,plain,
spl8_100,
inference(rat,[],[s113,s115]) ).
cnf(s139,plain,
( ~ spl8_14
| ~ spl8_19
| spl8_47 ),
inference(rat,[],[s59,s61]) ).
cnf(s140,plain,
( ~ spl8_17
| spl8_41 ),
inference(rat,[],[s54,s56]) ).
cnf(s149,plain,
spl8_17,
inference(rat,[],[s13,s14]) ).
cnf(s150,plain,
spl8_41,
inference(rat,[],[s140,s149]) ).
cnf(s153,plain,
~ spl8_108,
inference(rat,[],[s132,s50,s12]) ).
cnf(s154,plain,
spl8_51,
inference(rat,[],[s128,s50,s12]) ).
cnf(s157,plain,
spl8_47,
inference(rat,[],[s139,s50,s12]) ).
cnf(s161,plain,
~ spl8_50,
inference(rat,[],[s130,s153,s134,s157]) ).
cnf(s162,plain,
spl8_48,
inference(rat,[],[s66,s157]) ).
cnf(s165,plain,
$false,
inference(rat,[],[s63,s154,s161,s150,s149,s162,s157]) ).
fof(f1949,plain,
$false,
inference(avatar_sat_refutation,[],[s165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HAL001+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:48:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.06/2.23 % (3332802)Detected formulas, will run a generic FOF schedule.
% 10.06/2.23 % (3332807)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=303487174:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.06/2.23 % (3332809)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4231530685:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.06/2.23 % (3332811)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3786613793:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.06/2.23 % (3332813)dis-21_1_sil=8000:lcm=predicate:random_seed=2704097143:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.06/2.23 % (3332810)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3826734649:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.06/2.23 % (3332808)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=183149250:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.06/2.23 % (3332810)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332810)------------------------------
% 10.06/2.23 % (3332810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332810)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332810)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332810)Time elapsed: 0.001 s
% 10.06/2.23 % (3332810)Peak memory usage: 87 MB
% 10.06/2.23 % (3332812)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=165657838:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.06/2.23 % (3332811)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332811)------------------------------
% 10.06/2.23 % (3332811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332811)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332811)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332811)Time elapsed: 0.001 s
% 10.06/2.23 % (3332811)Peak memory usage: 87 MB
% 10.06/2.23 % (3332811)Instructions burned: 1 (million)
% 10.06/2.23 % (3332813)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332813)------------------------------
% 10.06/2.23 % (3332813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332813)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332813)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332813)Time elapsed: 0.007 s
% 10.06/2.23 % (3332813)Peak memory usage: 88 MB
% 10.06/2.23 % (3332813)Instructions burned: 10 (million)
% 10.06/2.23 % (3332812)Instruction limit reached!
% 10.06/2.23 % (3332812)------------------------------
% 10.06/2.23 % (3332812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332812)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332812)Termination reason: Instruction limit
% 10.06/2.23 % (3332812)Termination phase: Saturation
% 10.06/2.23 % (3332812)Time elapsed: 0.097 s
% 10.06/2.23 % (3332812)Peak memory usage: 90 MB
% 10.06/2.23 % (3332812)Instructions burned: 139 (million)
% 10.06/2.23 % (3332813)------------------------------
% 10.06/2.23 % (3332813)------------------------------
% 10.06/2.23 % (3332811)------------------------------
% 10.06/2.23 % (3332811)------------------------------
% 10.06/2.23 % (3332810)------------------------------
% 10.06/2.23 % (3332810)------------------------------
% 10.06/2.23 % (3332821)lrs+10_1_sil=8000:sp=occurrence:random_seed=1098861077:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.06/2.23 % (3332823)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3417630892:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.06/2.23 % (3332823)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332823)------------------------------
% 10.06/2.23 % (3332823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332823)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332823)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332823)Time elapsed: 0.001 s
% 10.06/2.23 % (3332823)Peak memory usage: 88 MB
% 10.06/2.23 % (3332823)Instructions burned: 2 (million)
% 10.06/2.23 % (3332822)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1284031288:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 10.06/2.23 % (3332824)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=860537345:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.06/2.23 % (3332822)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332822)------------------------------
% 10.06/2.23 % (3332822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332822)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332822)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332822)Time elapsed: 0.002 s
% 10.06/2.23 % (3332822)Peak memory usage: 88 MB
% 10.06/2.23 % (3332822)Instructions burned: 1 (million)
% 10.06/2.23 % (3332821)Instruction limit reached!
% 10.06/2.23 % (3332821)------------------------------
% 10.06/2.23 % (3332821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332821)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332821)Termination reason: Instruction limit
% 10.06/2.23 % (3332821)Termination phase: Saturation
% 10.06/2.23 % (3332821)Time elapsed: 0.166 s
% 10.06/2.23 % (3332821)Peak memory usage: 91 MB
% 10.06/2.23 % (3332821)Instructions burned: 286 (million)
% 10.06/2.23 % (3332824)Instruction limit reached!
% 10.06/2.23 % (3332824)------------------------------
% 10.06/2.23 % (3332824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332824)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332824)Termination reason: Instruction limit
% 10.06/2.23 % (3332824)Termination phase: Saturation
% 10.06/2.23 % (3332824)Time elapsed: 0.143 s
% 10.06/2.23 % (3332824)Peak memory usage: 91 MB
% 10.06/2.23 % (3332824)Instructions burned: 248 (million)
% 10.06/2.23 % (3332823)------------------------------
% 10.06/2.23 % (3332823)------------------------------
% 10.06/2.23 % (3332829)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3616995350:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 10.06/2.23 % (3332829)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332829)------------------------------
% 10.06/2.23 % (3332829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332829)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332829)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332829)Time elapsed: 0.002 s
% 10.06/2.23 % (3332829)Peak memory usage: 88 MB
% 10.06/2.23 % (3332829)Instructions burned: 2 (million)
% 10.06/2.23 % (3332822)------------------------------
% 10.06/2.23 % (3332822)------------------------------
% 10.06/2.23 % (3332831)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=67162007:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 10.06/2.23 % (3332830)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2276018740:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 10.06/2.23 % (3332831)Instruction limit reached!
% 10.06/2.23 % (3332831)------------------------------
% 10.06/2.23 % (3332831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332831)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332831)Termination reason: Instruction limit
% 10.06/2.23 % (3332831)Termination phase: Saturation
% 10.06/2.23 % (3332831)Time elapsed: 0.044 s
% 10.06/2.23 % (3332831)Peak memory usage: 90 MB
% 10.06/2.23 % (3332831)Instructions burned: 114 (million)
% 10.06/2.23 % (3332833)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2247822845:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 10.06/2.23 % (3332836)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=396297218:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.06/2.23 % (3332836)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332836)------------------------------
% 10.06/2.23 % (3332836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332836)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332836)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332836)Time elapsed: 0.0000 s
% 10.06/2.23 % (3332836)Peak memory usage: 87 MB
% 10.06/2.23 % (3332829)------------------------------
% 10.06/2.23 % (3332829)------------------------------
% 10.06/2.23 % (3332833)Instruction limit reached!
% 10.06/2.23 % (3332833)------------------------------
% 10.06/2.23 % (3332833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332833)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332833)Termination reason: Instruction limit
% 10.06/2.23 % (3332833)Termination phase: Saturation
% 10.06/2.23 % (3332833)Time elapsed: 0.064 s
% 10.06/2.23 % (3332833)Peak memory usage: 89 MB
% 10.06/2.23 % (3332833)Instructions burned: 127 (million)
% 10.06/2.23 % (3332808)First to succeed.
% 10.06/2.23 % (3332808)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3332802"
% 10.06/2.23 % (3332836)------------------------------
% 10.06/2.23 % (3332836)------------------------------
% 10.06/2.23 % (3332840)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3683347535:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 10.06/2.23 % (3332839)lrs+10_1_sil=8000:sp=occurrence:random_seed=620380467:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 10.06/2.23 % (3332840)Refutation not found, incomplete strategy
% 10.06/2.23 % (3332840)------------------------------
% 10.06/2.23 % (3332840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.23 % (3332840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.23 % (3332840)CaDiCaL version: 2.1.3
% 10.06/2.23 % (3332840)Termination reason: Refutation not found, incomplete strategy
% 10.06/2.23 % (3332840)Time elapsed: 0.002 s
% 10.06/2.23 % (3332840)Peak memory usage: 88 MB
% 10.06/2.23 % (3332840)Instructions burned: 2 (million)
% 10.06/2.23 % (3332807)Also succeeded, but the first one will report.
% 10.06/2.23 % (3332841)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3687673285:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 10.06/2.23 % (3332808)Refutation found. Thanks to Tanya!
% 10.06/2.23 % SZS status Theorem for theBenchmark
% 10.06/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 10.47/2.43 % (3332808)------------------------------
% 10.47/2.43 % (3332808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.43 % (3332808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.43 % (3332808)CaDiCaL version: 2.1.3
% 10.47/2.43 % (3332808)Termination reason: Refutation
% 10.47/2.43 % (3332808)Time elapsed: 0.956 s
% 10.47/2.43 % (3332808)Peak memory usage: 133 MB
% 10.47/2.43 % (3332808)Instructions burned: 1392 (million)
% 10.47/2.43 % (3332808)------------------------------
% 10.47/2.43 % (3332808)------------------------------
% 10.47/2.43 % (3332802)Success in time 1.402 s
% 10.47/2.43 % Vampire exiting
%------------------------------------------------------------------------------