%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU435+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:46:20 AM UTC 2026
% Result : Theorem 0.02s 5.44s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 21 ( 8 ~; 3 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-6 aty)
% Number of variables : 34 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s8_domain_1__e1_46__relset_2,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(F,k1_zfmisc_1(D))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) )
=> m1_subset_1(a_6_0_relset_2(A,B,C,D,E,F),k1_zfmisc_1(k1_zfmisc_1(E))) ),
file('theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
fof(t36_relset_2,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B))))
=> ! [D,E,F] :
( m1_subset_1(F,k1_zfmisc_1(D))
=> m1_subset_1(a_6_0_relset_2(A,B,C,D,E,F),k1_zfmisc_1(k1_zfmisc_1(E))) ) ),
file('theBenchmark.p',t36_relset_2) ).
fof(t36_relset_2_neg,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B))))
=> ! [D,E,F] :
( m1_subset_1(F,k1_zfmisc_1(D))
=> m1_subset_1(a_6_0_relset_2(A,B,C,D,E,F),k1_zfmisc_1(k1_zfmisc_1(E))) ) ),
inference(assume_negation,[status(cth)],[t36_relset_2]) ).
fof(nnf_51,plain,
? [A,B,C] :
( ? [D,E,F] :
( ~ m1_subset_1(a_6_0_relset_2(A,B,C,D,E,F),k1_zfmisc_1(k1_zfmisc_1(E)))
& m1_subset_1(F,k1_zfmisc_1(D)) )
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) ),
inference(fof_nnf,[status(thm)],[t36_relset_2_neg]) ).
fof(sk_t36_relset_2_neg,plain,
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
& m1_subset_1(sK5,k1_zfmisc_1(sK3))
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK5,sK3,sK4]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK4),skolemize(F,sK5)],[nnf_51]) ).
cnf(c_75,negated_conjecture,
~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4))),
inference(split_conjunct,[status(thm)],[sk_t36_relset_2_neg]) ).
cnf(c_76,negated_conjecture,
m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(split_conjunct,[status(thm)],[sk_t36_relset_2_neg]) ).
cnf(c_77,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))),
inference(split_conjunct,[status(thm)],[sk_t36_relset_2_neg]) ).
cnf(c_87,plain,
( m1_subset_1(a_6_0_relset_2(B,C,A,E,F,D),k1_zfmisc_1(k1_zfmisc_1(F)))
| ~ m1_subset_1(D,k1_zfmisc_1(E))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(B,C)))) ),
inference(clausify,[status(thm)],[s8_domain_1__e1_46__relset_2]) ).
cnf(c_176,negated_conjecture,
( m1_subset_1(a_6_0_relset_2(B,C,A,sK3,D,sK5),k1_zfmisc_1(k1_zfmisc_1(D)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(B,C)))) ),
inference(resolve,[status(thm)],[c_87,c_76]) ).
cnf(c_177,negated_conjecture,
~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))),
inference(resolve,[status(thm)],[c_176,c_75]) ).
cnf(c_175,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_77,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU435+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/5.40 % Computer : n020.cluster.edu
% 0.02/5.40 % Model : x86_64 x86_64
% 0.02/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/5.40 % Memory : 8046.5625MB
% 0.02/5.40 % OS : Linux 6.8.0-71-generic
% 0.02/5.40 % CPULimit : 300
% 0.02/5.40 % WCLimit : 300
% 0.02/5.40 % DateTime : Sat Sep 26 09:50:58 UTC 2026
% 0.02/5.40 % CPUTime :
% 0.02/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/5.40 % Process 1271671 was started by sandbox2 on n020,
% 0.02/5.40 % Sat Sep 26 09:50:58 2026
% 0.02/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/5.42
% 0.02/5.42 % From the command line: assign(max_seconds, 300).
% 0.02/5.44
% 0.02/5.44 % SZS status Theorem for theBenchmark
% 0.02/5.44
% 0.02/5.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.02/5.44 % Length of proof is 7.
% 0.02/5.44 % Level of proof is 2.
% 0.02/5.44 % Maximum clause weight is 46.000.
% 0.02/5.44 % Given clauses 20.
% 0.02/5.44
% 0.02/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------