%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU429+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 : n009.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 08:46:19 AM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 18 ~; 11 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(s8_domain_1__e1_38__relset_2,axiom,
! [A,B,C,D] :
( ( m2_relset_1(D,A,B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(A) )
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ),
file('theBenchmark.p',s8_domain_1__e1_38__relset_2) ).
fof(t28_relset_2,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
file('theBenchmark.p',t28_relset_2) ).
fof(t28_relset_2_neg,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
inference(assume_negation,[status(cth)],[t28_relset_2]) ).
cnf(c_59,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_60,plain,
( ~ m1_relset_1(A,B,C)
| m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_61,plain,
( m1_subset_1(a_4_1_relset_2(A,D,B,C),k1_zfmisc_1(k1_zfmisc_1(D)))
| ~ m2_relset_1(C,A,D)
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[s8_domain_1__e1_38__relset_2]) ).
fof(nnf_51,plain,
? [A] :
( ? [B,C] :
( ? [D] :
( ~ m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B)))
& m2_relset_1(D,A,B) )
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t28_relset_2_neg]) ).
fof(sk_t28_relset_2_neg,plain,
( ~ m1_subset_1(a_4_1_relset_2(sK1,sK2,sK3,sK0),k1_zfmisc_1(k1_zfmisc_1(sK2)))
& m2_relset_1(sK0,sK1,sK2)
& m1_subset_1(sK3,k1_zfmisc_1(k1_zfmisc_1(sK1)))
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK3,sK0,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK0)],[nnf_51]) ).
cnf(c_62,negated_conjecture,
m2_relset_1(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t28_relset_2_neg]) ).
cnf(c_75,plain,
( ~ m1_relset_1(D,A,C)
| m1_subset_1(a_4_1_relset_2(A,C,B,D),k1_zfmisc_1(k1_zfmisc_1(C)))
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_61,c_60]) ).
cnf(c_76,negated_conjecture,
m1_relset_1(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_62,c_59]) ).
cnf(c_81,negated_conjecture,
( m1_subset_1(a_4_1_relset_2(sK1,sK2,A,sK0),k1_zfmisc_1(k1_zfmisc_1(sK2)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK1)))
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_76,c_75]) ).
cnf(c_111,negated_conjecture,
~ m1_subset_1(a_4_1_relset_2(sK1,sK2,sK3,sK0),k1_zfmisc_1(k1_zfmisc_1(sK2))),
inference(split_conjunct,[status(thm)],[sk_t28_relset_2_neg]) ).
cnf(c_112,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(split_conjunct,[status(thm)],[sk_t28_relset_2_neg]) ).
cnf(c_113,negated_conjecture,
~ v1_xboole_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t28_relset_2_neg]) ).
cnf(c_160,negated_conjecture,
( m1_subset_1(a_4_1_relset_2(sK1,sK2,A,sK0),k1_zfmisc_1(k1_zfmisc_1(sK2)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK1))) ),
inference(resolve,[status(thm)],[c_113,c_81]) ).
cnf(c_399,negated_conjecture,
m1_subset_1(a_4_1_relset_2(sK1,sK2,sK3,sK0),k1_zfmisc_1(k1_zfmisc_1(sK2))),
inference(resolve,[status(thm)],[c_160,c_112]) ).
cnf(c_398,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_111,c_399]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU429+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 09:44:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 4010990 was started by sandbox2 on n009,
% 0.09/0.37 % Sat Sep 26 09:44:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.43 % Length of proof is 15.
% 0.14/0.43 % Level of proof is 5.
% 0.14/0.43 % Maximum clause weight is 31.000.
% 0.14/0.43 % Given clauses 67.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------