%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET717+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:47:57 PM UTC 2026
% Result : Theorem 79.20s 14.61s
% Output : CNFRefutation 79.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 101 ( 14 unt; 0 def)
% Number of atoms : 422 ( 52 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 557 ( 236 ~; 234 |; 66 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-5 aty)
% Number of variables : 332 ( 0 sgn 306 !; 26 ?; 149 :)
% 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/sandbox/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/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( surjective(X1,X3,X4)
& surjective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> surjective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII08) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( surjective(X1,X3,X4)
& surjective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> surjective(compose_function(X1,X0,X2,X3,X4),X2,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,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(f33,plain,
? [X0,X1,X2,X3,X4] :
( surjective(X1,X3,X4)
& surjective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ surjective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( surjective(X1,X3,X4)
& surjective(X0,X2,X3)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ surjective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(flattening,[],[f33]) ).
fof(f35,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,[],[f32]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f40,plain,
( surjective(sK1,sK3,sK4)
& surjective(sK0,sK2,sK3)
& maps(sK1,sK3,sK4)
& maps(sK0,sK2,sK3)
& ~ surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,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)],[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)
| ( 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))],[f36]) ).
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) ) )
& ( ! [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,[],[f38]) ).
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)
| ? [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,[],[f42]) ).
fof(f44,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,sK6(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK6(X0,X1,X3,X5,X6))
& member(sK6(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,[sK6]),skolemize(X8,sK6(X0,X1,X3,X5,X6))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ? [X6] :
( apply(X0,X6,X5)
& member(X6,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ( apply(X0,sK8(X0,X1,X5),X5)
& member(sK8(X0,X1,X5),X1) ) ) )
& ( ( member(sK7(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X5))],[f46]) ).
fof(f48,plain,
surjective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f49,plain,
surjective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f50,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f51,plain,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
~ surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f53,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,[],[f41]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f44]) ).
fof(f60,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| apply(X0,sK8(X0,X1,X5),X5) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| member(sK8(X0,X1,X5),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f52]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f51]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f50]) ).
tcf(c_52,negated_conjecture,
surjective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f49]) ).
tcf(c_53,negated_conjecture,
surjective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
tcf(c_54,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,[],[f55]) ).
tcf(c_55,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,[],[f54]) ).
tcf(c_56,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,[],[f53]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(compose_function(X0,X3,X7,X6,X5),X4,X2)
| ~ member(X4,X7)
| ~ member(X2,X5)
| ~ member(X1,X6)
| ~ apply(X3,X4,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK7(X0,X2,X3)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK8(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_260,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 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_260]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).
tcf(c_282,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK3,X0))
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_281]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_291,plain,
! [X0: $i] :
( member(sK5(sK0,sK3,X0),sK3)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_290]) ).
tcf(c_299,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_56]) ).
tcf(c_300,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_299]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_321,plain,
! [X0: $i] :
( apply(sK1,X0,sK5(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_320]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_330,plain,
! [X0: $i] :
( member(sK5(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_329]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X0,X1,X2),X2)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_412,plain,
member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4),
inference(unflattening,[status(thm)],[c_411]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_63]) ).
tcf(c_426,plain,
! [X0: $i] :
( member(sK8(sK0,sK2,X0),sK2)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_425]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_63]) ).
tcf(c_444,plain,
! [X0: $i] :
( member(sK8(sK1,sK3,X0),sK3)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_443]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ member(sK5(sK0,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_282,c_261]) ).
tcf(c_915,plain,
! [X0: $i] :
( member(sK8(sK1,sK3,X0),sK3)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_53,c_63]) ).
tcf(c_932,plain,
! [X0: $i] :
( apply(sK0,sK8(sK0,sK2,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_52,c_64]) ).
tcf(c_933,plain,
! [X0: $i] :
( apply(sK1,sK8(sK1,sK3,X0),X0)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_53,c_64]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1)
| ~ member(sK5(sK1,sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_321,c_300]) ).
tcf(c_1040,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_869,c_291,c_869]) ).
tcf(c_1052,plain,
! [X0: $i] :
( ( sK5(sK0,sK3,sK8(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK3)
| ~ member(sK8(sK0,sK2,X0),sK2) ),
inference(superposition,[status(thm)],[c_932,c_1040]) ).
tcf(c_1057,plain,
! [X0: $i] :
( ( sK5(sK0,sK3,sK8(sK0,sK2,X0)) = X0 )
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_1052,c_426,c_1052]) ).
tcf(c_1066,plain,
! [X0: $i] :
( ( sK5(sK0,sK3,sK8(sK0,sK2,sK8(sK1,sK3,X0))) = sK8(sK1,sK3,X0) )
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_915,c_1057]) ).
tcf(c_1155,plain,
! [X0: $i,X1: $i] :
( surjective(X0,X1,sK4)
| ( sK5(sK0,sK3,sK8(sK0,sK2,sK8(sK1,sK3,sK7(X0,X1,sK4)))) = sK8(sK1,sK3,sK7(X0,X1,sK4)) ) ),
inference(superposition,[status(thm)],[c_62,c_1066]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(sK8(X3,X4,sK7(X0,X1,X2)),X4)
| ~ surjective(X3,X4,X2)
| ~ member(sK7(X0,X1,X2),X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1228,plain,
sK5(sK0,sK3,sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))) = sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),
inference(superposition,[status(thm)],[c_1155,c_49]) ).
tcf(c_1243,plain,
( apply(sK0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)))
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2) ),
inference(superposition,[status(thm)],[c_1228,c_282]) ).
tcf(c_1289,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK1,sK4,X0) = X1 )
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_998,c_330,c_998]) ).
tcf(c_1301,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK8(sK1,sK3,X0)) = X0 )
| ~ member(X0,sK4)
| ~ member(sK8(sK1,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_933,c_1289]) ).
tcf(c_1309,plain,
! [X0: $i] :
( ( sK5(sK1,sK4,sK8(sK1,sK3,X0)) = X0 )
| ~ member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_1301,c_444,c_1301]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i] :
( surjective(X0,X1,sK4)
| ( sK5(sK1,sK4,sK8(sK1,sK3,sK7(X0,X1,sK4))) = sK7(X0,X1,sK4) ) ),
inference(superposition,[status(thm)],[c_62,c_1309]) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i] :
( member(sK8(X0,X1,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X1)
| ~ surjective(X0,X1,sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_1179]) ).
tcf(c_1498,plain,
sK5(sK1,sK4,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) = sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(superposition,[status(thm)],[c_1316,c_49]) ).
tcf(c_1541,plain,
( apply(sK1,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_1498,c_321]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X2,X3,sK8(X0,X1,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),X3)
| ~ surjective(X2,X3,X1)
| ~ member(sK8(X0,X1,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1833,plain,
! [X0: $i] :
( member(sK8(X0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ surjective(X0,sK3,sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_2736,plain,
( member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ surjective(sK1,sK3,sK4)
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_1833]) ).
tcf(c_3118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( surjective(X0,X2,X5)
| ~ member(sK8(X1,X2,sK8(X3,X4,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),X2)
| ~ apply(X0,sK8(X1,X2,sK8(X3,X4,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(X0,X2,X5)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_5227,plain,
! [X0: $i,X1: $i] :
( member(sK8(X0,X1,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),X1)
| ~ surjective(X0,X1,sK3)
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_1824]) ).
tcf(c_7413,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ~ member(sK8(X0,sK2,sK8(X1,X2,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK8(X0,sK2,sK8(X1,X2,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_3118]) ).
tcf(c_8833,plain,
! [X0: $i] :
( surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ~ member(sK8(sK0,sK2,sK8(X0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK8(sK0,sK2,sK8(X0,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_7413]) ).
tcf(c_12281,plain,
( member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ surjective(sK0,sK2,sK3)
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_5227]) ).
tcf(c_17890,plain,
( surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_8833]) ).
tcf(c_95727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(compose_function(X4,X0,sK2,X6,X7),sK8(sK0,sK2,sK8(sK1,sK3,sK7(X1,X2,sK4))),X5)
| ~ member(X5,X7)
| ~ member(X3,X6)
| ~ apply(X4,X3,X5)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(X1,X2,sK4))),sK2)
| ~ apply(X0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(X1,X2,sK4))),X3) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_104477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(compose_function(X2,sK0,sK2,X4,X5),sK8(sK0,sK2,sK8(sK1,sK3,sK7(X0,X1,sK4))),X3)
| ~ member(X3,X5)
| ~ member(sK8(sK1,sK3,sK7(X0,X1,sK4)),X4)
| ~ apply(X2,sK8(sK1,sK3,sK7(X0,X1,sK4)),X3)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(X0,X1,sK4))),sK2)
| ~ apply(sK0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(X0,X1,sK4))),sK8(sK1,sK3,sK7(X0,X1,sK4))) ),
inference(instantiation,[status(thm)],[c_95727]) ).
tcf(c_119343,plain,
! [X0: $i,X1: $i] :
( apply(compose_function(sK1,sK0,sK2,X0,X1),sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),X1)
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(sK1,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ apply(sK0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(instantiation,[status(thm)],[c_104477]) ).
tcf(c_131697,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK2,X0,sK4),sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),X0)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(sK1,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ apply(sK0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(instantiation,[status(thm)],[c_119343]) ).
tcf(c_131699,plain,
( apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ member(sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),sK4)
| ~ member(sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK3)
| ~ member(sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK2)
| ~ apply(sK1,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)),sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))
| ~ apply(sK0,sK8(sK0,sK2,sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))),sK8(sK1,sK3,sK7(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4))) ),
inference(instantiation,[status(thm)],[c_131697]) ).
tcf(c_131700,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_131699,c_17890,c_12281,c_2736,c_1541,c_1243,c_412,c_49,c_52,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET717+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 11:45:35 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.47 % Detected problem language: tptp
% 0.14/0.49 % Proving...
% 79.20/14.61 % SZS status Started for theBenchmark.p
% 79.20/14.61 % SZS status Theorem for theBenchmark.p
% 79.20/14.61
% 79.20/14.61 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 79.20/14.61
% 79.20/14.61 % ------ iProver source info
% 79.20/14.61
% 79.20/14.61 % git: date: 2026-07-19 20:42:38 +0200
% 79.20/14.61 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 79.20/14.61 % git: non_committed_changes: false
% 79.20/14.61
% 79.20/14.61 % ------ Parsing...
% 79.20/14.61 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 79.20/14.61
% 79.20/14.61 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 79.20/14.61
% 79.20/14.61 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 79.20/14.61
% 79.20/14.61 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 79.20/14.61 % ------ Proving...
% 79.20/14.61 % ------ Problem Properties
% 79.20/14.61
% 79.20/14.61 %
% 79.20/14.61 % clauses 17
% 79.20/14.61 % conjectures 3
% 79.20/14.61 % EPR 4
% 79.20/14.61 % Horn 16
% 79.20/14.61 % unary 3
% 79.20/14.61 % binary 5
% 79.20/14.61 % lits 52
% 79.20/14.61 % lits eq 2
% 79.20/14.61 % fd_pure 0
% 79.20/14.61 % fd_pseudo 0
% 79.20/14.61 % fd_cond 0
% 79.20/14.61 % fd_pseudo_cond 2
% 79.20/14.61 % AC symbols 0
% 79.20/14.61
% 79.20/14.61 % ------ Schedule dynamic 5 is on
% 79.20/14.61
% 79.20/14.61 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 79.20/14.61
% 79.20/14.61
% 79.20/14.61 % ------
% 79.20/14.61 % Current options:
% 79.20/14.61 % ------
% 79.20/14.61
% 79.20/14.61
% 79.20/14.61 %
% 79.20/14.61
% 79.20/14.61 % ------ Proving...
% 79.20/14.61 % Proof_search_loop: time out after: 2601 full_loop iterations
% 79.20/14.61
% 79.20/14.61 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 79.20/14.61
% 79.20/14.61
% 79.20/14.61 % ------
% 79.20/14.61 % Current options:
% 79.20/14.61 % ------
% 79.20/14.61
% 79.20/14.61
% 79.20/14.61 %
% 79.20/14.61
% 79.20/14.61 % ------ Proving...
% 79.20/14.61 %
% 79.20/14.61
% 79.20/14.61 % SZS status Theorem for theBenchmark.p
% 79.20/14.61
% 79.20/14.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 79.20/14.61
% 79.20/14.61
%------------------------------------------------------------------------------