%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET735+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 : n012.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 02:47:59 PM UTC 2026
% Result : Theorem 2.87s 0.98s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 158 ( 34 unt; 0 def)
% Number of atoms : 575 ( 91 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 694 ( 277 ~; 279 |; 103 &)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 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 : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-5 aty)
% Number of variables : 464 ( 0 sgn 434 !; 30 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
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(f23,axiom,
! [X0,X1,X2,X3] :
( member(X3,image3(X0,X1,X2))
<=> ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image3) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( equal_set(image3(X0,X3,X4),image3(X1,X3,X4))
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X3,X4) )
=> equal_maps(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII26) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( equal_set(image3(X0,X3,X4),image3(X1,X3,X4))
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X3,X4) )
=> equal_maps(X0,X1,X3,X4) ),
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] :
( equal_set(X0,X1)
=> ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f37,plain,
? [X0,X1,X2,X3,X4] :
( equal_set(image3(X0,X3,X4),image3(X1,X3,X4))
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X3,X4)
& ~ equal_maps(X0,X1,X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
? [X0,X1,X2,X3,X4] :
( equal_set(image3(X0,X3,X4),image3(X1,X3,X4))
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X3,X4)
& ~ equal_maps(X0,X1,X3,X4) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ identity(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f48,plain,
( equal_set(image3(sK0,sK3,sK4),image3(sK1,sK3,sK4))
& identity(compose_function(sK2,sK1,sK3,sK4,sK3),sK3)
& identity(compose_function(sK2,sK0,sK3,sK4,sK3),sK3)
& maps(sK2,sK4,sK3)
& maps(sK1,sK3,sK4)
& maps(sK0,sK3,sK4)
& ~ equal_maps(sK0,sK1,sK3,sK4) ),
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)],[f38]) ).
fof(f49,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))],[f41]) ).
fof(f50,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))],[f43]) ).
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)
| ? [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,[],[f46]) ).
fof(f52,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,[],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,image3(X0,X1,X2))
| ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) ) )
& ( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2)
| member(X3,image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,image3(X0,X1,X2))
| ( ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) )
& member(X3,X2) ) )
& ( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2)
| member(X3,image3(X0,X1,X2)) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,image3(X0,X1,X2))
| ( ? [X5] :
( apply(X0,X5,X3)
& member(X5,X1) )
& member(X3,X2) ) )
& ( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2)
| member(X3,image3(X0,X1,X2)) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,image3(X0,X1,X2))
| ( apply(X0,sK10(X0,X1,X3),X3)
& member(sK10(X0,X1,X3),X1)
& member(X3,X2) ) )
& ( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
| ~ member(X3,X2)
| member(X3,image3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X5,sK10(X0,X1,X3))],[f56]) ).
fof(f58,plain,
equal_set(image3(sK0,sK3,sK4),image3(sK1,sK3,sK4)),
inference(cnf_transformation,[],[f48]) ).
fof(f59,plain,
identity(compose_function(sK2,sK1,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f60,plain,
identity(compose_function(sK2,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f61,plain,
maps(sK2,sK4,sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f62,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
~ equal_maps(sK0,sK1,sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f67,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,[],[f49]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f73,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,[],[f50]) ).
fof(f74,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,[],[f50]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f77,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,[],[f53]) ).
fof(f78,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,[],[f53]) ).
fof(f79,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,[],[f53]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| apply(X0,sK10(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f57]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(sK10(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1)
| ~ member(X3,X2)
| member(X3,image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ equal_maps(sK0,sK1,sK3,sK4),
inference(cnf_transformation,[],[f64]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f63]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f62]) ).
tcf(c_52,negated_conjecture,
maps(sK2,sK4,sK3),
inference(cnf_transformation,[],[f61]) ).
tcf(c_53,negated_conjecture,
identity(compose_function(sK2,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,negated_conjecture,
identity(compose_function(sK2,sK1,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f59]) ).
tcf(c_55,negated_conjecture,
equal_set(image3(sK0,sK3,sK4),image3(sK1,sK3,sK4)),
inference(cnf_transformation,[],[f58]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_58,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,[],[f69]) ).
tcf(c_59,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,[],[f68]) ).
tcf(c_60,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,[],[f67]) ).
tcf(c_61,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,[],[f75]) ).
tcf(c_62,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,[],[f74]) ).
tcf(c_63,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,[],[f73]) ).
tcf(c_64,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,[],[f72]) ).
tcf(c_65,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,[],[f71]) ).
tcf(c_66,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,[],[f70]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_69,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,[],[f79]) ).
tcf(c_70,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,[],[f78]) ).
tcf(c_71,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,[],[f77]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X2,image3(X0,X4,X3))
| ~ member(X2,X3)
| ~ member(X1,X4)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK10(X1,X2,X0),X2)
| ~ member(X0,image3(X1,X2,X3)) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,sK10(X1,X2,X0),X0)
| ~ member(X0,image3(X1,X2,X3)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ( image3(sK1,sK3,sK4) != X1 )
| ( image3(sK0,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_372,plain,
subset(image3(sK1,sK3,sK4),image3(sK0,sK3,sK4)),
inference(unflattening,[status(thm)],[c_371]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK3 )
| ( compose_function(sK2,sK0,sK3,sK4,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_67]) ).
tcf(c_384,plain,
! [X0: $i] :
( apply(compose_function(sK2,sK0,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_383]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK3 )
| ( compose_function(sK2,sK1,sK3,sK4,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_67]) ).
tcf(c_393,plain,
! [X0: $i] :
( apply(compose_function(sK2,sK1,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_392]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ( image3(sK1,sK3,sK4) != X0 )
| ( image3(sK0,sK3,sK4) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_372]) ).
tcf(c_406,plain,
! [X0: $i] :
( member(X0,image3(sK0,sK3,sK4))
| ~ member(X0,image3(sK1,sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_405]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X2,X3),X3)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_66]) ).
tcf(c_428,plain,
member(sK8(sK0,sK1,sK3,sK4),sK4),
inference(unflattening,[status(thm)],[c_427]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2,X3),X3)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_65]) ).
tcf(c_433,plain,
member(sK7(sK0,sK1,sK3,sK4),sK4),
inference(unflattening,[status(thm)],[c_432]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X2)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_64]) ).
tcf(c_438,plain,
member(sK6(sK0,sK1,sK3,sK4),sK3),
inference(unflattening,[status(thm)],[c_437]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_443,plain,
apply(sK0,sK6(sK0,sK1,sK3,sK4),sK7(sK0,sK1,sK3,sK4)),
inference(unflattening,[status(thm)],[c_442]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 )
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_448,plain,
sK7(sK0,sK1,sK3,sK4) != sK8(sK0,sK1,sK3,sK4),
inference(unflattening,[status(thm)],[c_447]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_453,plain,
apply(sK1,sK6(sK0,sK1,sK3,sK4),sK8(sK0,sK1,sK3,sK4)),
inference(unflattening,[status(thm)],[c_452]) ).
tcf(c_463,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_60]) ).
tcf(c_464,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_463]) ).
tcf(c_502,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 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_60]) ).
tcf(c_503,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK4)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_502]) ).
tcf(c_541,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 != sK2 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_60]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X2)
| ~ apply(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_541]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X2,X3,sK5(X2,X0,X3))
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_59]) ).
tcf(c_563,plain,
! [X0: $i] :
( apply(sK2,X0,sK5(sK2,sK3,X0))
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_562]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X2,X0,X3),X0)
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_58]) ).
tcf(c_572,plain,
! [X0: $i] :
( member(sK5(sK2,sK3,X0),sK3)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_571]) ).
tcf(c_610,plain,
! [X0: $i] :
( ~ member(X0,image3(sK1,sK3,sK4))
| member(X0,image3(sK0,sK3,sK4)) ),
inference(prop_impl_just,[status(thm)],[c_406]) ).
tcf(c_611,plain,
! [X0: $i] :
( member(X0,image3(sK0,sK3,sK4))
| ~ member(X0,image3(sK1,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_610]) ).
tcf(c_626,plain,
! [X0: $i] :
( apply(compose_function(sK2,sK0,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(prop_impl_just,[status(thm)],[c_384]) ).
tcf(c_628,plain,
! [X0: $i] :
( apply(compose_function(sK2,sK1,sK3,sK4,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(prop_impl_just,[status(thm)],[c_393]) ).
tcf(c_650,plain,
! [X0: $i] :
( apply(sK2,X0,sK5(sK2,sK3,X0))
| ~ member(X0,sK4) ),
inference(prop_impl_just,[status(thm)],[c_563]) ).
tcf(c_1843,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK2,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK5(sK2,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_650,c_542]) ).
tcf(c_1918,plain,
! [X0: $i] :
( member(sK9(sK2,sK0,sK4,X0,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_626,c_69]) ).
tcf(c_1934,plain,
! [X0: $i] :
( member(sK9(sK2,sK1,sK4,X0,X0),sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_628,c_69]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i] :
( member(sK8(sK0,sK1,sK3,sK4),image3(sK1,X1,X0))
| ~ member(sK6(sK0,sK1,sK3,sK4),X1)
| ~ member(sK8(sK0,sK1,sK3,sK4),X0) ),
inference(superposition,[status(thm)],[c_453,c_72]) ).
tcf(c_2041,plain,
( member(sK8(sK0,sK1,sK3,sK4),image3(sK0,sK3,sK4))
| ~ member(sK6(sK0,sK1,sK3,sK4),sK3)
| ~ member(sK8(sK0,sK1,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_1972,c_611]) ).
tcf(c_2042,plain,
member(sK8(sK0,sK1,sK3,sK4),image3(sK0,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_2041,c_438,c_428]) ).
tcf(c_2051,plain,
apply(sK0,sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK8(sK0,sK1,sK3,sK4)),
inference(superposition,[status(thm)],[c_2042,c_75]) ).
tcf(c_2052,plain,
member(sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK3),
inference(superposition,[status(thm)],[c_2042,c_74]) ).
tcf(c_2070,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK2,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1843,c_572,c_1843]) ).
tcf(c_2168,plain,
! [X0: $i] :
( apply(sK0,X0,sK9(sK2,sK0,sK4,X0,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_626,c_70]) ).
tcf(c_2169,plain,
! [X0: $i] :
( apply(sK1,X0,sK9(sK2,sK1,sK4,X0,X0))
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_628,c_70]) ).
tcf(c_2202,plain,
! [X0: $i] :
( apply(sK2,sK9(sK2,sK0,sK4,X0,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_626,c_71]) ).
tcf(c_2203,plain,
! [X0: $i] :
( apply(sK2,sK9(sK2,sK1,sK4,X0,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_628,c_71]) ).
tcf(c_2249,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK0,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1)
| ~ member(sK9(sK2,sK0,sK4,X0,X0),sK4) ),
inference(superposition,[status(thm)],[c_2168,c_464]) ).
tcf(c_2280,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK0,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2249,c_1918,c_2249]) ).
tcf(c_2291,plain,
( ( sK9(sK2,sK0,sK4,sK6(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4)) = sK7(sK0,sK1,sK3,sK4) )
| ~ member(sK6(sK0,sK1,sK3,sK4),sK3)
| ~ member(sK7(sK0,sK1,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_443,c_2280]) ).
tcf(c_2297,plain,
sK9(sK2,sK0,sK4,sK6(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4)) = sK7(sK0,sK1,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_2291,c_438,c_433]) ).
tcf(c_2345,plain,
( ( sK9(sK2,sK0,sK4,sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4))) = sK8(sK0,sK1,sK3,sK4) )
| ~ member(sK8(sK0,sK1,sK3,sK4),sK4)
| ~ member(sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_2051,c_2280]) ).
tcf(c_2356,plain,
sK9(sK2,sK0,sK4,sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4))) = sK8(sK0,sK1,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_2345,c_428,c_2052]) ).
tcf(c_2388,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK1,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1)
| ~ member(sK9(sK2,sK1,sK4,X0,X0),sK4) ),
inference(superposition,[status(thm)],[c_2169,c_503]) ).
tcf(c_2430,plain,
( apply(sK2,sK8(sK0,sK1,sK3,sK4),sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)))
| ~ member(sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_2356,c_2202]) ).
tcf(c_2443,plain,
apply(sK2,sK8(sK0,sK1,sK3,sK4),sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4))),
inference(forward_subsumption_resolution,[status(thm)],[c_2430,c_2052]) ).
tcf(c_2645,plain,
( ( sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)) = sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)) )
| ~ member(sK8(sK0,sK1,sK3,sK4),sK4)
| ~ member(sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_2443,c_2070]) ).
tcf(c_2646,plain,
! [X0: $i] :
( ( sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ member(sK8(sK0,sK1,sK3,sK4),sK4)
| ~ apply(sK2,sK8(sK0,sK1,sK3,sK4),X0)
| ~ member(sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_2443,c_542]) ).
tcf(c_2650,plain,
sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)) = sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_2645,c_428,c_2052]) ).
tcf(c_2651,plain,
! [X0: $i] :
( ( sK10(sK0,sK3,sK8(sK0,sK1,sK3,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK2,sK8(sK0,sK1,sK3,sK4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2646,c_428,c_2052]) ).
tcf(c_2661,plain,
sK9(sK2,sK0,sK4,sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)),sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4))) = sK8(sK0,sK1,sK3,sK4),
inference(demodulation,[status(thm)],[c_2356,c_2650]) ).
tcf(c_3044,plain,
! [X0: $i] :
( ( sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK2,sK8(sK0,sK1,sK3,sK4),X0) ),
inference(light_normalisation,[status(thm)],[c_2651,c_2650]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK2,sK1,sK4,X0,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2388,c_1934,c_2388]) ).
tcf(c_3066,plain,
( ( sK9(sK2,sK1,sK4,sK6(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4)) = sK8(sK0,sK1,sK3,sK4) )
| ~ member(sK6(sK0,sK1,sK3,sK4),sK3)
| ~ member(sK8(sK0,sK1,sK3,sK4),sK4) ),
inference(superposition,[status(thm)],[c_453,c_3055]) ).
tcf(c_3074,plain,
sK9(sK2,sK1,sK4,sK6(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4)) = sK8(sK0,sK1,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_3066,c_438,c_428]) ).
tcf(c_3094,plain,
( apply(sK2,sK8(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4))
| ~ member(sK6(sK0,sK1,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_3074,c_2203]) ).
tcf(c_3097,plain,
apply(sK2,sK8(sK0,sK1,sK3,sK4),sK6(sK0,sK1,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_3094,c_438]) ).
tcf(c_3114,plain,
( ( sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)) = sK6(sK0,sK1,sK3,sK4) )
| ~ member(sK6(sK0,sK1,sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_3097,c_3044]) ).
tcf(c_3115,plain,
sK5(sK2,sK3,sK8(sK0,sK1,sK3,sK4)) = sK6(sK0,sK1,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_3114,c_438]) ).
tcf(c_3169,plain,
sK7(sK0,sK1,sK3,sK4) = sK8(sK0,sK1,sK3,sK4),
inference(light_normalisation,[status(thm)],[c_2661,c_2297,c_3115]) ).
tcf(c_3170,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3169,c_448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET735+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 11:47:51 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.87/0.98 % SZS status Started for theBenchmark.p
% 2.87/0.98 % SZS status Theorem for theBenchmark.p
% 2.87/0.98
% 2.87/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.87/0.98
% 2.87/0.98 % ------ iProver source info
% 2.87/0.98
% 2.87/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 2.87/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.87/0.98 % git: non_committed_changes: false
% 2.87/0.98
% 2.87/0.98 % ------ Parsing...
% 2.87/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.87/0.98
% 2.87/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 2.87/0.98
% 2.87/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.87/0.98
% 2.87/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.87/0.98 % ------ Proving...
% 2.87/0.98 % ------ Problem Properties
% 2.87/0.98
% 2.87/0.98 %
% 2.87/0.98 % clauses 27
% 2.87/0.98 % conjectures 0
% 2.87/0.98 % EPR 3
% 2.87/0.98 % Horn 27
% 2.87/0.98 % unary 6
% 2.87/0.98 % binary 13
% 2.87/0.98 % lits 72
% 2.87/0.98 % lits eq 4
% 2.87/0.98 % fd_pure 0
% 2.87/0.98 % fd_pseudo 0
% 2.87/0.98 % fd_cond 0
% 2.87/0.98 % fd_pseudo_cond 3
% 2.87/0.98 % AC symbols 0
% 2.87/0.98
% 2.87/0.98 % ------ Schedule dynamic 5 is on
% 2.87/0.98
% 2.87/0.98 % ------ no conjectures: strip conj schedule
% 2.87/0.98
% 2.87/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.87/0.98
% 2.87/0.98
% 2.87/0.98 % ------
% 2.87/0.98 % Current options:
% 2.87/0.98 % ------
% 2.87/0.98
% 2.87/0.98
% 2.87/0.98 %
% 2.87/0.98
% 2.87/0.98 % ------ Proving...
% 2.87/0.98 %
% 2.87/0.98
% 2.87/0.98 % SZS status Theorem for theBenchmark.p
% 2.87/0.98
% 2.87/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/0.99
% 2.87/0.99
%------------------------------------------------------------------------------