%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 01:47:30 PM UTC 2026
% Result : Theorem 8.13s 1.71s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 129 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 53 ~; 60 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 105 !; 4 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ( p(s(tyop_2Emin_2Ebool,X0))
<=> p(s(tyop_2Emin_2Ebool,X1)) )
=> s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(f28,axiom,
! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
<=> ! [X3] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
fof(f29,axiom,
! [X0,X1,X2,X3] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
<=> ( s(X0,X2) != s(X0,X3)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
fof(f30,axiom,
! [X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
fof(f31,conjecture,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
? [X0,X1] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))),
inference(ennf_transformation,[],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( ( p(s(tyop_2Emin_2Ebool,X0))
<~> p(s(tyop_2Emin_2Ebool,X1)) )
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
<=> ! [X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f37,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
fof(f39,plain,
! [X0,X1] :
( ( ( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X1)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,X1)) ) )
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(nnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) )
& ( ? [X3] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) )
& ( ? [X3] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) )
& ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
| ( s(X0,X2) != s(X0,X3)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ) )
& ( s(X0,X2) = s(X0,X3)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
| ( s(X0,X2) != s(X0,X3)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ) )
& ( s(X0,X2) = s(X0,X3)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(cnf_transformation,[],[f37]) ).
fof(f47,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_49,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(cnf_transformation,[],[f45]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),
inference(cnf_transformation,[],[f49]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(X0,X3)))))) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( p(X0)
| ~ p(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_409,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) = s(tyop_2Emin_2Ebool,X0) ) ),
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i] :
( p(X0)
| ~ p(s(tyop_2Emin_2Ebool,X1))
| ( X0 != s(tyop_2Emin_2Ebool,X1) ) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_731,plain,
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_763,plain,
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ( s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))) ) ),
inference(superposition,[status(thm)],[c_409,c_54]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,X1))
| ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
inference(instantiation,[status(thm)],[c_729]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = s(tyop_2Emin_2Ebool,X0) )
| ( X2 != X1 )
| ( s(tyop_2Emin_2Ebool,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_1331,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| ~ p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
inference(instantiation,[status(thm)],[c_920]) ).
tcf(c_1345,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),
inference(superposition,[status(thm)],[c_785,c_49]) ).
tcf(c_1372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = s(tyop_2Emin_2Ebool,X0) )
| ( X2 != s(tyop_2Emin_2Ebool,X1) )
| ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
inference(instantiation,[status(thm)],[c_923]) ).
tcf(c_1790,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))) ) ),
inference(instantiation,[status(thm)],[c_1331]) ).
tcf(c_1958,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X0) )
| ( s(tyop_2Emin_2Ebool,X2) != s(tyop_2Emin_2Ebool,X1) )
| ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
inference(instantiation,[status(thm)],[c_1372]) ).
tcf(c_2155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(X0,X3))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) ) ),
inference(superposition,[status(thm)],[c_409,c_58]) ).
tcf(c_2796,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) ) ),
inference(instantiation,[status(thm)],[c_1790]) ).
tcf(c_3437,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1),s(sK0,X0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) ) ),
inference(superposition,[status(thm)],[c_1345,c_2155]) ).
tcf(c_3474,plain,
! [X0: $i] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1),s(sK0,X0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_3437,c_49]) ).
tcf(c_3756,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),
inference(superposition,[status(thm)],[c_53,c_3474]) ).
tcf(c_4723,plain,
! [X0: $i] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) )
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) != s(tyop_2Emin_2Ebool,X0) )
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) != s(tyop_2Emin_2Ebool,X0) ) ),
inference(instantiation,[status(thm)],[c_1958]) ).
tcf(c_14057,plain,
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) )
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) != s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) )
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) != s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))) ) ),
inference(instantiation,[status(thm)],[c_4723]) ).
tcf(c_14058,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14057,c_3756,c_2796,c_1345,c_763,c_731,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/0.34 % Computer : n001.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Wed Sep 23 17:34:06 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.13/1.71 % SZS status Started for theBenchmark.p
% 8.13/1.71 % SZS status Theorem for theBenchmark.p
% 8.13/1.71
% 8.13/1.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.13/1.71
% 8.13/1.71 % ------ iProver source info
% 8.13/1.71
% 8.13/1.71 % git: date: 2026-07-19 20:42:38 +0200
% 8.13/1.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.13/1.71 % git: non_committed_changes: false
% 8.13/1.71
% 8.13/1.71 % ------ Parsing...
% 8.13/1.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.13/1.71
% 8.13/1.71 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.13/1.71
% 8.13/1.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.13/1.71
% 8.13/1.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.13/1.71 % ------ Proving...
% 8.13/1.71 % ------ Problem Properties
% 8.13/1.71
% 8.13/1.71 %
% 8.13/1.71 % clauses 11
% 8.13/1.71 % conjectures 1
% 8.13/1.71 % EPR 0
% 8.13/1.71 % Horn 8
% 8.13/1.71 % unary 2
% 8.13/1.71 % binary 5
% 8.13/1.71 % lits 24
% 8.13/1.71 % lits eq 7
% 8.13/1.71 % fd_pure 0
% 8.13/1.71 % fd_pseudo 0
% 8.13/1.71 % fd_cond 0
% 8.13/1.71 % fd_pseudo_cond 0
% 8.13/1.71 % AC symbols 0
% 8.13/1.71
% 8.13/1.71 % ------ Schedule dynamic 5 is on
% 8.13/1.71
% 8.13/1.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.13/1.71
% 8.13/1.71
% 8.13/1.71 % ------
% 8.13/1.71 % Current options:
% 8.13/1.71 % ------
% 8.13/1.71
% 8.13/1.71
% 8.13/1.71 %
% 8.13/1.71
% 8.13/1.71 % ------ Proving...
% 8.13/1.71 %
% 8.13/1.71
% 8.13/1.71 % SZS status Theorem for theBenchmark.p
% 8.13/1.71
% 8.13/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.13/1.71
% 8.13/1.71
%------------------------------------------------------------------------------