%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:41:17 AM UTC 2026
% Result : Theorem 2.39s 0.78s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 56 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 49 ( 21 ~; 16 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 2 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ),
file('theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(thm_2Epred__set_2ESUBSET__DEF,axiom,
! [A_27a,V0s_2E0,V1t_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
file('theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
fof(thm_2Epred__set_2EIN__DELETE,axiom,
! [A_27a,V0s_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0))))))
<=> ( s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ),
file('theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
fof(thm_2Epred__set_2EREST__DEF,axiom,
! [A_27a,V0s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),
file('theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
fof(thm_2Epred__set_2EREST__SUBSET,conjecture,
! [A_27a,V0s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
file('theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
fof(thm_2Epred__set_2EREST__SUBSET_neg,negated_conjecture,
~ ! [A_27a,V0s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
inference(assume_negation,[status(cth)],[thm_2Epred__set_2EREST__SUBSET]) ).
cnf(c_31,plain,
( s(tyop_2Emin_2Ebool,B) = s(tyop_2Emin_2Ebool,A)
| p(s(tyop_2Emin_2Ebool,B))
| p(s(tyop_2Emin_2Ebool,A)) ),
inference(clausify,[status(thm)],[reserved_2Eho_2Eboolext]) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('theBenchmark.p',reserved_2Eho_2Enotfalse) ).
cnf(c_34,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(clausify,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
fof(nnf_26,plain,
! [A_27a,V0s_2E0,V1t_2E0] :
( ( ? [V2x_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( ! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[thm_2Epred__set_2ESUBSET__DEF]) ).
fof(sk_thm_2Epred__set_2ESUBSET__DEF_sk,plain,
! [A_27a,V0s_2E0,V1t_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,sK0(A_27a,V0s_2E0,V1t_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,sK0(A_27a,V0s_2E0,V1t_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( ! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(V2x_2E0,sK0(A_27a,V0s_2E0,V1t_2E0))],[nnf_26]) ).
fof(sk_thm_2Epred__set_2ESUBSET__DEF,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(VAR_0,sK0(VAR_0,VAR_1,VAR_2)),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_2))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_1),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_2)))) )
& ! [VAR_0,VAR_1,VAR_2] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(VAR_0,sK0(VAR_0,VAR_1,VAR_2)),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_1))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_1),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_2)))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(VAR_0,VAR_3),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(VAR_0,VAR_3),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_1),s(tyop_2Emin_2Efun(VAR_0,tyop_2Emin_2Ebool),VAR_2)))) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm_2Epred__set_2ESUBSET__DEF_sk]) ).
cnf(c_85,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,sK0(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) ),
inference(split_conjunct,[status(thm)],[sk_thm_2Epred__set_2ESUBSET__DEF]) ).
cnf(c_86,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,sK0(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) ),
inference(split_conjunct,[status(thm)],[sk_thm_2Epred__set_2ESUBSET__DEF]) ).
cnf(c_87,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C),s(A,D)))))) ),
inference(clausify,[status(thm)],[thm_2Epred__set_2EIN__DELETE]) ).
cnf(c_90,plain,
s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(A,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))))) = s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))),
inference(clausify,[status(thm)],[thm_2Epred__set_2EREST__DEF]) ).
fof(nnf_29,plain,
? [A_27a,V0s_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
inference(fof_nnf,[status(thm)],[thm_2Epred__set_2EREST__SUBSET_neg]) ).
fof(sk_thm_2Epred__set_2EREST__SUBSET_neg,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A_27a,sK1),skolemize(V0s_2E0,sK2)],[nnf_29]) ).
cnf(c_91,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)))),
inference(split_conjunct,[status(thm)],[sk_thm_2Epred__set_2EREST__SUBSET_neg]) ).
cnf(c_101,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,A)
| p(s(tyop_2Emin_2Ebool,A)) ),
inference(resolve,[status(thm)],[c_34,c_31]) ).
cnf(c_318,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK1,sK0(sK1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)),sK2)),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)))),
inference(resolve,[status(thm)],[c_86,c_91]) ).
cnf(c_1168,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),
inference(resolve,[status(thm)],[c_101,c_91]) ).
cnf(c_471,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(copy,[status(thm)],[c_1168]) ).
cnf(c_638,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK1,sK0(sK1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)),sK2)),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2),s(sK1,A)))))),
inference(resolve,[status(thm)],[c_87,c_318]) ).
cnf(c_1160,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK1,sK0(sK1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)),sK2)),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)))))),
inference(paramod,[status(thm)],[c_90,c_638]) ).
cnf(c_1169,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2))),s(tyop_2Emin_2Efun(sK1,tyop_2Emin_2Ebool),sK2)))),
inference(resolve,[status(thm)],[c_1160,c_85]) ).
cnf(c_1170,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(paramod,[status(thm)],[c_471,c_1169]) ).
cnf(c_1167,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_1170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 17:04:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2457238 was started by sandbox2 on n018,
% 0.08/0.36 % Fri Sep 25 17:04:20 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 2.39/0.78
% 2.39/0.78 % SZS status Theorem for theBenchmark
% 2.39/0.78
% 2.39/0.78 % Proof 1 at 0.22 (+ 0.06) seconds.
% 2.39/0.78 % Length of proof is 18.
% 2.39/0.78 % Level of proof is 5.
% 2.39/0.78 % Maximum clause weight is 68.000.
% 2.39/0.78 % Given clauses 116.
% 2.39/0.78
% 2.39/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------