%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ITP004+4 : 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 : n008.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 26.56s 5.39s
% Output : CNFRefutation 26.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Epred__set_2EDELETE__DEF,axiom,
! [A_27a,V0s_2E0,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,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))),
file('theBenchmark.p',thm_2Epred__set_2EDELETE__DEF) ).
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_2EDIFF__SUBSET,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),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
file('theBenchmark.p',thm_2Epred__set_2EDIFF__SUBSET) ).
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_9298,plain,
s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A,C),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = 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))),
inference(clausify,[status(thm)],[thm_2Epred__set_2EDELETE__DEF]) ).
cnf(c_9299,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))) = s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A,C),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))),
inference(copy,[status(thm)],[c_9298]) ).
cnf(c_9302,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]) ).
cnf(c_9656,plain,
s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(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_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))),
inference(paramod,[status(thm)],[c_9299,c_9302]) ).
cnf(c_9303,plain,
s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))) = s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(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_2EEMPTY_2E0))))),
inference(copy,[status(thm)],[c_9656]) ).
cnf(c_9505,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C))),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B)))),
inference(clausify,[status(thm)],[thm_2Epred__set_2EDIFF__SUBSET]) ).
fof(nnf_3099,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(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(A_27a,sK0),skolemize(V0s_2E0,sK1)],[nnf_3099]) ).
cnf(c_9654,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(split_conjunct,[status(thm)],[sk_thm_2Epred__set_2EREST__SUBSET_neg]) ).
cnf(c_9657,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(sK0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(paramod,[status(thm)],[c_9303,c_9654]) ).
cnf(c_9655,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9505,c_9657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 17:03:41 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1501859 was started by sandbox2 on n008,
% 0.12/0.38 % Fri Sep 25 17:03:41 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 1.17/1.50
% 1.17/1.50 % From the command line: assign(max_seconds, 300).
% 1.17/1.50
% 1.17/1.50 % SInE: 1503 to sos, 1670 to usable, of 3173 axioms (tolerance 2.00, depth 0 fixpoint).
% 26.56/5.39
% 26.56/5.39 % SZS status Theorem for theBenchmark
% 26.56/5.39
% 26.56/5.39 % Proof 1 at 2.92 (+ 0.49) seconds.
% 26.56/5.39 % Length of proof is 11.
% 26.56/5.39 % Level of proof is 4.
% 26.56/5.39 % Maximum clause weight is 151.000.
% 26.56/5.39 % Given clauses 0.
% 26.56/5.39
% 26.56/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------