%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:46:25 AM UTC 2026
% Result : Theorem 0.08s 0.44s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 21 unt; 0 def)
% Number of atoms : 69 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 14 |; 6 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 75 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k6_partfun1,axiom,
! [A] :
( m2_relset_1(k6_partfun1(A),A,A)
& v1_partfun1(k6_partfun1(A),A,A) ),
file('theBenchmark.p',dt_k6_partfun1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k7_relset_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(F,C,D)
& m1_relset_1(E,A,B) )
=> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ),
file('theBenchmark.p',redefinition_k7_relset_1) ).
fof(redefinition_k9_relset_2,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C)))
& m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> k9_relset_2(A,B,C,D,E) = k5_relat_1(D,E) ),
file('theBenchmark.p',redefinition_k9_relset_2) ).
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(t23_funct_2,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C
& k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C ) ),
file('theBenchmark.p',t23_funct_2) ).
fof(t65_relset_2,conjecture,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> k9_relset_2(A,A,B,k6_partfun1(A),C) = k9_relset_2(A,B,B,C,k6_partfun1(B)) ),
file('theBenchmark.p',t65_relset_2) ).
fof(t65_relset_2_neg,negated_conjecture,
~ ! [A,B,C] :
( m2_relset_1(C,A,B)
=> k9_relset_2(A,A,B,k6_partfun1(A),C) = k9_relset_2(A,B,B,C,k6_partfun1(B)) ),
inference(assume_negation,[status(cth)],[t65_relset_2]) ).
cnf(c_49,plain,
( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_52,plain,
m2_relset_1(k6_partfun1(A),A,A),
inference(clausify,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_54,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_56,plain,
( k7_relset_1(B,B,B,C,k6_partfun1(B),A) = A
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t23_funct_2]) ).
cnf(c_57,plain,
( k7_relset_1(B,C,C,C,A,k6_partfun1(C)) = A
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t23_funct_2]) ).
fof(nnf_48,plain,
? [A,B,C] :
( k9_relset_2(A,B,B,C,k6_partfun1(B)) != k9_relset_2(A,A,B,k6_partfun1(A),C)
& m2_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[t65_relset_2_neg]) ).
fof(sk_t65_relset_2_neg,plain,
( k9_relset_2(sK1,sK2,sK2,sK0,k6_partfun1(sK2)) != k9_relset_2(sK1,sK1,sK2,k6_partfun1(sK1),sK0)
& m2_relset_1(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_48]) ).
cnf(c_58,negated_conjecture,
m2_relset_1(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t65_relset_2_neg]) ).
cnf(c_66,negated_conjecture,
m1_subset_1(sK0,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))),
inference(resolve,[status(thm)],[c_58,c_49]) ).
cnf(c_67,negated_conjecture,
m1_relset_1(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_58,c_54]) ).
cnf(c_68,negated_conjecture,
k7_relset_1(sK1,sK1,sK1,sK2,k6_partfun1(sK1),sK0) = sK0,
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_69,negated_conjecture,
k7_relset_1(sK1,sK2,sK2,sK2,sK0,k6_partfun1(sK2)) = sK0,
inference(resolve,[status(thm)],[c_58,c_57]) ).
cnf(c_80,plain,
m1_relset_1(k6_partfun1(A),A,A),
inference(resolve,[status(thm)],[c_54,c_52]) ).
cnf(c_85,plain,
m1_subset_1(k6_partfun1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))),
inference(resolve,[status(thm)],[c_49,c_52]) ).
cnf(c_88,negated_conjecture,
k9_relset_2(sK1,sK2,sK2,sK0,k6_partfun1(sK2)) != k9_relset_2(sK1,sK1,sK2,k6_partfun1(sK1),sK0),
inference(split_conjunct,[status(thm)],[sk_t65_relset_2_neg]) ).
cnf(c_96,plain,
( k5_relat_1(A,D) = k9_relset_2(B,C,E,A,D)
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,E)))
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(clausify,[status(thm)],[redefinition_k9_relset_2]) ).
cnf(c_97,plain,
( k9_relset_2(B,C,E,A,D) = k5_relat_1(A,D)
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,E)))
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_98,plain,
( k7_relset_1(B,C,E,F,A,D) = k5_relat_1(A,D)
| ~ m1_relset_1(D,E,F)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k7_relset_1]) ).
cnf(c_444,plain,
( k9_relset_2(B,B,C,k6_partfun1(B),A) = k5_relat_1(k6_partfun1(B),A)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(resolve,[status(thm)],[c_97,c_85]) ).
cnf(c_310,negated_conjecture,
k9_relset_2(sK1,sK1,sK2,k6_partfun1(sK1),sK0) = k5_relat_1(k6_partfun1(sK1),sK0),
inference(resolve,[status(thm)],[c_444,c_66]) ).
cnf(c_445,negated_conjecture,
( k9_relset_2(sK1,sK2,B,sK0,A) = k5_relat_1(sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(sK2,B))) ),
inference(resolve,[status(thm)],[c_97,c_66]) ).
cnf(c_316,negated_conjecture,
k9_relset_2(sK1,sK2,sK2,sK0,k6_partfun1(sK2)) = k5_relat_1(sK0,k6_partfun1(sK2)),
inference(resolve,[status(thm)],[c_445,c_85]) ).
cnf(c_446,negated_conjecture,
k5_relat_1(sK0,k6_partfun1(sK2)) != k9_relset_2(sK1,sK1,sK2,k6_partfun1(sK1),sK0),
inference(paramod,[status(thm)],[c_316,c_88]) ).
cnf(c_447,negated_conjecture,
k5_relat_1(sK0,k6_partfun1(sK2)) != k5_relat_1(k6_partfun1(sK1),sK0),
inference(paramod,[status(thm)],[c_310,c_446]) ).
cnf(c_335,negated_conjecture,
k5_relat_1(k6_partfun1(sK1),sK0) != k5_relat_1(sK0,k6_partfun1(sK2)),
inference(copy,[status(thm)],[c_447]) ).
cnf(c_448,plain,
( k7_relset_1(D,D,B,C,k6_partfun1(D),A) = k5_relat_1(k6_partfun1(D),A)
| ~ m1_relset_1(A,B,C) ),
inference(resolve,[status(thm)],[c_98,c_80]) ).
cnf(c_395,negated_conjecture,
k7_relset_1(A,A,sK1,sK2,k6_partfun1(A),sK0) = k5_relat_1(k6_partfun1(A),sK0),
inference(resolve,[status(thm)],[c_448,c_67]) ).
cnf(c_449,negated_conjecture,
( k7_relset_1(sK1,sK2,B,C,sK0,A) = k5_relat_1(sK0,A)
| ~ m1_relset_1(A,B,C) ),
inference(resolve,[status(thm)],[c_98,c_67]) ).
cnf(c_397,negated_conjecture,
k7_relset_1(sK1,sK2,A,A,sK0,k6_partfun1(A)) = k5_relat_1(sK0,k6_partfun1(A)),
inference(resolve,[status(thm)],[c_449,c_80]) ).
cnf(c_426,negated_conjecture,
k5_relat_1(k6_partfun1(sK1),sK0) = sK0,
inference(paramod,[status(thm)],[c_395,c_68]) ).
cnf(c_435,negated_conjecture,
k5_relat_1(sK0,k6_partfun1(sK2)) = sK0,
inference(paramod,[status(thm)],[c_397,c_69]) ).
cnf(c_450,negated_conjecture,
sK0 != k5_relat_1(sK0,k6_partfun1(sK2)),
inference(paramod,[status(thm)],[c_426,c_335]) ).
cnf(c_451,negated_conjecture,
sK0 != sK0,
inference(paramod,[status(thm)],[c_435,c_450]) ).
cnf(c_443,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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 : Sat Sep 26 10:04:55 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 783732 was started by sandbox on n026,
% 0.08/0.37 % Sat Sep 26 10:04:55 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.44
% 0.08/0.44 % SZS status Theorem for theBenchmark
% 0.08/0.44
% 0.08/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.08/0.44 % Length of proof is 31.
% 0.08/0.44 % Level of proof is 5.
% 0.08/0.44 % Maximum clause weight is 37.000.
% 0.08/0.44 % Given clauses 33.
% 0.08/0.44
% 0.08/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------