%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET733+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 : n018.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 4.80s 1.52s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 112 ( 23 unt; 0 def)
% Number of atoms : 413 ( 76 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 501 ( 200 ~; 202 |; 71 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 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; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 326 ( 0 sgn 302 !; 24 ?; 121 :)
% 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(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(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) )
=> injective(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII24) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) )
=> injective(X0,X2,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,X2] :
( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) )
=> injective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f33,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
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] :
( identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3)
& ~ injective(X0,X2,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3)
& ~ injective(X0,X2,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] :
( ~ identity(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ),
inference(flattening,[],[f40]) ).
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,
( identity(compose_function(sK1,sK0,sK2,sK3,sK2),sK2)
& maps(sK1,sK3,sK2)
& maps(sK0,sK2,sK3)
& ~ injective(sK0,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).
fof(f45,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,sK4(X0,X2,X3))
& member(sK4(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X2,X3))],[f38]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( member(sK7(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1)
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
& sK5(X0,X1,X2) != sK6(X0,X1,X2) )
| injective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X4,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2))],[f41]) ).
fof(f47,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(f48,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,[],[f47]) ).
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)
| ( apply(X0,sK8(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK8(X0,X1,X3,X5,X6))
& member(sK8(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,[sK8]),skolemize(X8,sK8(X0,X1,X3,X5,X6))],[f48]) ).
fof(f50,plain,
identity(compose_function(sK1,sK0,sK2,sK3,sK2),sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f51,plain,
maps(sK1,sK3,sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f52,plain,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f44]) ).
fof(f53,plain,
~ injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f44]) ).
fof(f54,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,[],[f45]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK4(X0,X2,X3)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK4(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,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,sK8(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f49]) ).
fof(f65,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,sK8(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f66,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(sK8(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_49,negated_conjecture,
~ injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
maps(sK1,sK3,sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,negated_conjecture,
identity(compose_function(sK1,sK0,sK2,sK3,sK2),sK2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK4(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_55,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,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK8(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,[],[f66]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X1,X5,sK8(X0,X1,X3,X5,X6))
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK8(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,[],[f64]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK2 )
| ( compose_function(sK1,sK0,sK2,sK3,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_281,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK2,sK3,sK2),X0,X0)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_280]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X0,X1,X2),X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_292,plain,
member(sK7(sK0,sK2,sK3),sK3),
inference(unflattening,[status(thm)],[c_291]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_297,plain,
member(sK6(sK0,sK2,sK3),sK2),
inference(unflattening,[status(thm)],[c_296]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK5(X0,X1,X2),X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_302,plain,
member(sK5(sK0,sK2,sK3),sK2),
inference(unflattening,[status(thm)],[c_301]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_307,plain,
apply(sK0,sK6(sK0,sK2,sK3),sK7(sK0,sK2,sK3)),
inference(unflattening,[status(thm)],[c_306]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_312,plain,
apply(sK0,sK5(sK0,sK2,sK3),sK7(sK0,sK2,sK3)),
inference(unflattening,[status(thm)],[c_311]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 )
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_317,plain,
sK5(sK0,sK2,sK3) != sK6(sK0,sK2,sK3),
inference(unflattening,[status(thm)],[c_316]) ).
tcf(c_327,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_55]) ).
tcf(c_328,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_327]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK4(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_349,plain,
! [X0: $i] :
( apply(sK0,X0,sK4(sK0,sK3,X0))
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_348]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_53]) ).
tcf(c_358,plain,
! [X0: $i] :
( member(sK4(sK0,sK3,X0),sK3)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_357]) ).
tcf(c_366,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 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK2)
| ~ member(X1,sK2)
| ~ member(X0,sK3)
| ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_366]) ).
tcf(c_1029,plain,
! [X0: $i] :
( apply(sK1,sK8(sK1,sK0,sK3,X0,X0),X0)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_281,c_66]) ).
tcf(c_1030,plain,
! [X0: $i] :
( apply(sK0,X0,sK8(sK1,sK0,sK3,X0,X0))
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_281,c_65]) ).
tcf(c_1031,plain,
! [X0: $i] :
( member(sK8(sK1,sK0,sK3,X0,X0),sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_281,c_64]) ).
tcf(c_1076,plain,
! [X0: $i] :
( ( sK7(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK3)
| ~ member(sK7(sK0,sK2,sK3),sK3)
| ~ member(sK6(sK0,sK2,sK3),sK2)
| ~ apply(sK0,sK6(sK0,sK2,sK3),X0) ),
inference(superposition,[status(thm)],[c_307,c_328]) ).
tcf(c_1077,plain,
! [X0: $i] :
( ( sK7(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK3)
| ~ member(sK7(sK0,sK2,sK3),sK3)
| ~ member(sK5(sK0,sK2,sK3),sK2)
| ~ apply(sK0,sK5(sK0,sK2,sK3),X0) ),
inference(superposition,[status(thm)],[c_312,c_328]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i] :
( ( sK4(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ member(sK4(sK0,sK3,X0),sK3) ),
inference(superposition,[status(thm)],[c_349,c_328]) ).
tcf(c_1084,plain,
! [X0: $i] :
( ( sK7(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK0,sK5(sK0,sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1077,c_292,c_302]) ).
tcf(c_1088,plain,
! [X0: $i] :
( ( sK7(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK3)
| ~ apply(sK0,sK6(sK0,sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1076,c_292,c_297]) ).
tcf(c_1146,plain,
( ( sK4(sK0,sK3,sK5(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK5(sK0,sK2,sK3),sK2)
| ~ member(sK4(sK0,sK3,sK5(sK0,sK2,sK3)),sK3) ),
inference(superposition,[status(thm)],[c_349,c_1084]) ).
tcf(c_1148,plain,
( ( sK4(sK0,sK3,sK5(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK4(sK0,sK3,sK5(sK0,sK2,sK3)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1146,c_302]) ).
tcf(c_1161,plain,
( ( sK4(sK0,sK3,sK6(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK6(sK0,sK2,sK3),sK2)
| ~ member(sK4(sK0,sK3,sK6(sK0,sK2,sK3)),sK3) ),
inference(superposition,[status(thm)],[c_349,c_1088]) ).
tcf(c_1163,plain,
( ( sK4(sK0,sK3,sK6(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK4(sK0,sK3,sK6(sK0,sK2,sK3)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1161,c_297]) ).
tcf(c_1173,plain,
( ( sK4(sK0,sK3,sK5(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK5(sK0,sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_358,c_1148]) ).
tcf(c_1174,plain,
sK4(sK0,sK3,sK5(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1173,c_302]) ).
tcf(c_1181,plain,
( ( sK4(sK0,sK3,sK6(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3) )
| ~ member(sK6(sK0,sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_358,c_1163]) ).
tcf(c_1182,plain,
sK4(sK0,sK3,sK6(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1181,c_297]) ).
tcf(c_1411,plain,
! [X0: $i,X1: $i] :
( ( sK4(sK0,sK3,X0) = X1 )
| ~ member(X1,sK3)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1078,c_358,c_1078]) ).
tcf(c_1425,plain,
! [X0: $i] :
( ( sK8(sK1,sK0,sK3,X0,X0) = sK4(sK0,sK3,X0) )
| ~ member(X0,sK2)
| ~ member(sK8(sK1,sK0,sK3,X0,X0),sK3) ),
inference(superposition,[status(thm)],[c_1030,c_1411]) ).
tcf(c_1436,plain,
! [X0: $i] :
( ( sK8(sK1,sK0,sK3,X0,X0) = sK4(sK0,sK3,X0) )
| ~ member(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_1425,c_1031,c_1425]) ).
tcf(c_1443,plain,
sK8(sK1,sK0,sK3,sK6(sK0,sK2,sK3),sK6(sK0,sK2,sK3)) = sK4(sK0,sK3,sK6(sK0,sK2,sK3)),
inference(superposition,[status(thm)],[c_297,c_1436]) ).
tcf(c_1444,plain,
sK8(sK1,sK0,sK3,sK5(sK0,sK2,sK3),sK5(sK0,sK2,sK3)) = sK4(sK0,sK3,sK5(sK0,sK2,sK3)),
inference(superposition,[status(thm)],[c_302,c_1436]) ).
tcf(c_1446,plain,
sK8(sK1,sK0,sK3,sK5(sK0,sK2,sK3),sK5(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3),
inference(light_normalisation,[status(thm)],[c_1444,c_1174]) ).
tcf(c_1447,plain,
sK8(sK1,sK0,sK3,sK6(sK0,sK2,sK3),sK6(sK0,sK2,sK3)) = sK7(sK0,sK2,sK3),
inference(light_normalisation,[status(thm)],[c_1443,c_1182]) ).
tcf(c_1454,plain,
( apply(sK1,sK7(sK0,sK2,sK3),sK5(sK0,sK2,sK3))
| ~ member(sK5(sK0,sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_1446,c_1029]) ).
tcf(c_1456,plain,
apply(sK1,sK7(sK0,sK2,sK3),sK5(sK0,sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1454,c_302]) ).
tcf(c_1460,plain,
! [X0: $i] :
( ( sK5(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK2)
| ~ member(sK7(sK0,sK2,sK3),sK3)
| ~ member(sK5(sK0,sK2,sK3),sK2)
| ~ apply(sK1,sK7(sK0,sK2,sK3),X0) ),
inference(superposition,[status(thm)],[c_1456,c_367]) ).
tcf(c_1461,plain,
! [X0: $i] :
( ( sK5(sK0,sK2,sK3) = X0 )
| ~ member(X0,sK2)
| ~ apply(sK1,sK7(sK0,sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1460,c_292,c_302]) ).
tcf(c_1600,plain,
( apply(sK1,sK7(sK0,sK2,sK3),sK6(sK0,sK2,sK3))
| ~ member(sK6(sK0,sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_1447,c_1029]) ).
tcf(c_1602,plain,
apply(sK1,sK7(sK0,sK2,sK3),sK6(sK0,sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1600,c_297]) ).
tcf(c_1791,plain,
( ( sK5(sK0,sK2,sK3) = sK6(sK0,sK2,sK3) )
| ~ member(sK6(sK0,sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_1602,c_1461]) ).
tcf(c_1792,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1791,c_317,c_297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET733+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.44 % Computer : n018.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 11:50:04 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.28/0.52
% 0.28/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.28/0.52
% 0.28/0.52 % Detected problem language: tptp
% 0.28/0.53 % Proving...
% 4.80/1.52 % SZS status Started for theBenchmark.p
% 4.80/1.52 % SZS status Theorem for theBenchmark.p
% 4.80/1.52
% 4.80/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.80/1.52
% 4.80/1.52 % ------ iProver source info
% 4.80/1.52
% 4.80/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 4.80/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.80/1.52 % git: non_committed_changes: false
% 4.80/1.52
% 4.80/1.52 % ------ Parsing...
% 4.80/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.80/1.52
% 4.80/1.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 4.80/1.52
% 4.80/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.80/1.52
% 4.80/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.80/1.52 % ------ Proving...
% 4.80/1.52 % ------ Problem Properties
% 4.80/1.52
% 4.80/1.52 %
% 4.80/1.52 % clauses 17
% 4.80/1.52 % conjectures 0
% 4.80/1.52 % EPR 2
% 4.80/1.52 % Horn 17
% 4.80/1.52 % unary 6
% 4.80/1.52 % binary 5
% 4.80/1.52 % lits 46
% 4.80/1.52 % lits eq 3
% 4.80/1.52 % fd_pure 0
% 4.80/1.52 % fd_pseudo 0
% 4.80/1.52 % fd_cond 0
% 4.80/1.52 % fd_pseudo_cond 2
% 4.80/1.52 % AC symbols 0
% 4.80/1.52
% 4.80/1.52 % ------ Schedule dynamic 5 is on
% 4.80/1.52
% 4.80/1.52 % ------ no conjectures: strip conj schedule
% 4.80/1.52
% 4.80/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.80/1.52
% 4.80/1.52
% 4.80/1.52 % ------
% 4.80/1.52 % Current options:
% 4.80/1.52 % ------
% 4.80/1.52
% 4.80/1.52
% 4.80/1.52 %
% 4.80/1.52
% 4.80/1.52 % ------ Proving...
% 4.80/1.52 %
% 4.80/1.52
% 4.80/1.52 % SZS status Theorem for theBenchmark.p
% 4.80/1.52
% 4.80/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.80/1.52
% 4.80/1.52
%------------------------------------------------------------------------------