%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET726+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:47:58 PM UTC 2026
% Result : Theorem 3.38s 6.07s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 106 ( 20 unt; 0 def)
% Number of atoms : 426 ( 70 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 523 ( 203 ~; 205 |; 83 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 379 ( 0 sgn 353 !; 26 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X2)
& member(X5,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X6)
& apply(X0,X3,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X4,X2)
& member(X3,X1) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII17) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f34,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4)
& ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4)
& ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f33]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ identity(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4)
& identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3)
& maps(sK2,sK4,sK3)
& maps(sK1,sK4,sK3)
& maps(sK0,sK3,sK4)
& ~ equal_maps(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f36]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK5(X0,X2,X3))
& member(sK5(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f38]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X2)
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0,X1,X2,X3)),skolemize(X5,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f40]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ( apply(X0,sK9(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK9(X0,X1,X3,X5,X6))
& member(sK9(X0,X1,X3,X5,X6),X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( ( ~ apply(X0,X3,X4)
| apply(inverse_function(X0,X1,X2),X4,X3) )
& ( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f54,plain,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f56,plain,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f57,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
~ equal_maps(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK9(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK9(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK9(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_49,negated_conjecture,
~ equal_maps(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(cnf_transformation,[],[f58]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f57]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f56]) ).
tcf(c_53,negated_conjecture,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f54]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK9(X0,X1,X3,X5,X6),X3)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK9(X0,X1,X3,X5,X6))
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK9(X0,X1,X3,X5,X6),X6)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X4,X3)
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ apply(inverse_function(X0,X1,X2),X3,X4) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK3 )
| ( compose_function(sK1,sK0,sK3,sK4,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_64]) ).
tcf(c_323,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_322]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X3,X2,X1),X1)
| ( X3 != sK1 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( inverse_function(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_345,plain,
member(sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3),
inference(unflattening,[status(thm)],[c_344]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X3,X2,X1),X1)
| ( X3 != sK1 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( inverse_function(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_350,plain,
member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3),
inference(unflattening,[status(thm)],[c_349]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X3,X2,X1),X2)
| ( X3 != sK1 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( inverse_function(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_355,plain,
member(sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK4),
inference(unflattening,[status(thm)],[c_354]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X3,X2,X1),sK7(X0,X3,X2,X1))
| ( X3 != sK1 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( inverse_function(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_360,plain,
apply(inverse_function(sK0,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unflattening,[status(thm)],[c_359]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK3 )
| ( X2 != sK4 )
| ( X1 != sK1 )
| ( inverse_function(sK0,sK3,sK4) != X0 )
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_365,plain,
sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) != sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(unflattening,[status(thm)],[c_364]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X3,sK6(X0,X3,X2,X1),sK8(X0,X3,X2,X1))
| ( X3 != sK1 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( inverse_function(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_370,plain,
apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unflattening,[status(thm)],[c_369]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_380]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_402,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_401]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_411,plain,
! [X0: $i] :
( member(sK5(sK0,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_410]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X0)
| ~ member(X4,X0)
| ~ member(X3,X1)
| ~ apply(X2,X3,X5)
| ~ apply(X2,X3,X4)
| ( X2 != sK1 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_419]) ).
tcf(c_1035,plain,
! [X0: $i] :
( apply(sK0,X0,sK9(sK1,sK0,sK4,X0,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_323,c_67]) ).
tcf(c_1036,plain,
! [X0: $i] :
( member(sK9(sK1,sK0,sK4,X0,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_323,c_66]) ).
tcf(c_1059,plain,
( apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3))
| ~ member(sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK4)
| ~ member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_360,c_69]) ).
tcf(c_1060,plain,
apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1059,c_355,c_350]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK5(sK0,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_402,c_381]) ).
tcf(c_1092,plain,
! [X0: $i] :
( ( sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) = X0 )
| ~ member(X0,sK3)
| ~ member(sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK4)
| ~ member(sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3)
| ~ apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),X0) ),
inference(superposition,[status(thm)],[c_370,c_420]) ).
tcf(c_1099,plain,
! [X0: $i] :
( ( sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1092,c_355,c_345]) ).
tcf(c_1250,plain,
! [X0: $i] :
( apply(sK1,sK9(sK1,sK0,sK4,X0,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_323,c_68]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1073,c_411,c_1073]) ).
tcf(c_1319,plain,
! [X0: $i] :
( ( sK9(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3)
| ~ member(sK9(sK1,sK0,sK4,X0,X0),sK4) ),
inference(superposition,[status(thm)],[c_1035,c_1307]) ).
tcf(c_1320,plain,
( ( sK5(sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)) = sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) )
| ~ member(sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK4)
| ~ member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_1060,c_1307]) ).
tcf(c_1328,plain,
sK5(sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)) = sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1320,c_355,c_350]) ).
tcf(c_1335,plain,
! [X0: $i] :
( ( sK9(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1319,c_1036,c_1319]) ).
tcf(c_1343,plain,
sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)) = sK5(sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(superposition,[status(thm)],[c_350,c_1335]) ).
tcf(c_1353,plain,
sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)) = sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(light_normalisation,[status(thm)],[c_1343,c_1328]) ).
tcf(c_2123,plain,
( apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3))
| ~ member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_1353,c_1250]) ).
tcf(c_2126,plain,
apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2123,c_350]) ).
tcf(c_2500,plain,
( ( sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) = sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) )
| ~ member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_2126,c_1099]) ).
tcf(c_2501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2500,c_365,c_350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET726+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.36 % Computer : n011.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Thu Sep 24 11:47:19 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.41 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 3.38/6.07 % SZS status Started for theBenchmark.p
% 3.38/6.07 % SZS status Theorem for theBenchmark.p
% 3.38/6.07
% 3.38/6.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.38/6.07
% 3.38/6.07 % ------ iProver source info
% 3.38/6.07
% 3.38/6.07 % git: date: 2026-07-19 20:42:38 +0200
% 3.38/6.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.38/6.07 % git: non_committed_changes: false
% 3.38/6.07
% 3.38/6.07 % ------ Parsing...
% 3.38/6.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.38/6.07
% 3.38/6.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.38/6.07
% 3.38/6.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.38/6.07
% 3.38/6.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.38/6.07 % ------ Proving...
% 3.38/6.07 % ------ Problem Properties
% 3.38/6.07
% 3.38/6.07 %
% 3.38/6.07 % clauses 23
% 3.38/6.07 % conjectures 0
% 3.38/6.07 % EPR 3
% 3.38/6.07 % Horn 23
% 3.38/6.07 % unary 6
% 3.38/6.07 % binary 8
% 3.38/6.07 % lits 66
% 3.38/6.07 % lits eq 4
% 3.38/6.07 % fd_pure 0
% 3.38/6.07 % fd_pseudo 0
% 3.38/6.07 % fd_cond 0
% 3.38/6.07 % fd_pseudo_cond 3
% 3.38/6.07 % AC symbols 0
% 3.38/6.07
% 3.38/6.07 % ------ Schedule dynamic 5 is on
% 3.38/6.07
% 3.38/6.07 % ------ no conjectures: strip conj schedule
% 3.38/6.07
% 3.38/6.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.38/6.07
% 3.38/6.07
% 3.38/6.07 % ------
% 3.38/6.07 % Current options:
% 3.38/6.07 % ------
% 3.38/6.07
% 3.38/6.07
% 3.38/6.07 %
% 3.38/6.07
% 3.38/6.07 % ------ Proving...
% 3.38/6.07 %
% 3.38/6.07
% 3.38/6.07 % SZS status Theorem for theBenchmark.p
% 3.38/6.07
% 3.38/6.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.38/6.07
% 3.38/6.07
%------------------------------------------------------------------------------