%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU425+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 : n013.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 08:46:17 AM UTC 2026
% Result : Theorem 7.20s 1.33s
% Output : CNFRefutation 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 18 unt; 0 def)
% Number of atoms : 129 ( 31 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 121 ( 46 ~; 43 |; 13 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 9 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d1_funct_2,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( ( B = k1_xboole_0
=> ( ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 )
| A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) ) ) ) ),
file('theBenchmark.p',d1_funct_2) ).
fof(d3_relset_2,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_relat_1(C) )
=> ( C = k5_relset_2(A,B)
<=> ( ! [D] :
( r1_tarski(D,A)
=> k1_funct_1(C,D) = k9_relat_1(B,D) )
& k1_relat_1(C) = k1_zfmisc_1(A) ) ) ) ),
file('theBenchmark.p',d3_relset_2) ).
fof(dt_k5_relset_2,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) ) ),
file('theBenchmark.p',dt_k5_relset_2) ).
fof(fc12_relat_1,axiom,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k4_relset_1(A,B,C) = k1_relat_1(C) ),
file('theBenchmark.p',redefinition_k4_relset_1) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t11_relset_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( ( r1_tarski(k2_relat_1(C),B)
& r1_tarski(k1_relat_1(C),A) )
=> m2_relset_1(C,A,B) ) ),
file('theBenchmark.p',t11_relset_1) ).
fof(t20_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C))) ),
file('theBenchmark.p',t20_relset_2) ).
fof(t21_relset_2,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
file('theBenchmark.p',t21_relset_2) ).
fof(t21_relset_2_neg,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
inference(assume_negation,[status(cth)],[t21_relset_2]) ).
cnf(c_53,plain,
( k1_relat_1(A) = k4_relset_1(B,C,A)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k4_relset_1]) ).
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_58,plain,
( v1_relat_1(A)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_60,plain,
( k4_relset_1(B,C,A) != B
| v1_funct_2(A,B,C)
| k1_xboole_0 = C
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[d1_funct_2]) ).
cnf(c_65,plain,
( k1_relat_1(B) = k1_zfmisc_1(C)
| k5_relset_2(C,A) != B
| ~ v1_funct_1(B)
| ~ v1_relat_1(B)
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[d3_relset_2]) ).
cnf(c_69,plain,
( v1_relat_1(k5_relset_2(B,A))
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[dt_k5_relset_2]) ).
cnf(c_70,plain,
( v1_funct_1(k5_relset_2(B,A))
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[dt_k5_relset_2]) ).
cnf(c_74,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[fc12_relat_1]) ).
cnf(c_76,plain,
~ v1_xboole_0(k1_zfmisc_1(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
cnf(c_96,plain,
r1_tarski(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_97,plain,
( m2_relset_1(A,B,C)
| ~ r1_tarski(k2_relat_1(A),C)
| ~ r1_tarski(k1_relat_1(A),B)
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[t11_relset_1]) ).
cnf(c_99,plain,
( r1_tarski(k2_relat_1(k5_relset_2(B,A)),k1_zfmisc_1(k2_relat_1(A)))
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(clausify,[status(thm)],[t20_relset_2]) ).
fof(nnf_49,plain,
? [A,B,C] :
( ( ~ m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_1(k5_relset_2(A,C)) )
& m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(fof_nnf,[status(thm)],[t21_relset_2_neg]) ).
fof(sk_t21_relset_2_neg,plain,
( ( ~ m2_relset_1(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_funct_1(k5_relset_2(sK1,sK0)) )
& m1_subset_1(sK0,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_49]) ).
cnf(c_108,negated_conjecture,
m1_subset_1(sK0,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_t21_relset_2_neg]) ).
cnf(c_109,negated_conjecture,
( ~ m2_relset_1(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_funct_1(k5_relset_2(sK1,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t21_relset_2_neg]) ).
cnf(c_116,plain,
( k1_relat_1(A) = k4_relset_1(B,C,A)
| ~ m2_relset_1(A,B,C) ),
inference(resolve,[status(thm)],[c_54,c_53]) ).
cnf(c_117,plain,
( k4_relset_1(B,C,A) = k1_relat_1(A)
| ~ m2_relset_1(A,B,C) ),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_137,plain,
( k1_relat_1(k5_relset_2(B,A)) = k1_zfmisc_1(B)
| ~ v1_funct_1(k5_relset_2(B,A))
| ~ v1_relat_1(k5_relset_2(B,A))
| ~ v1_relat_1(A) ),
inference(xxres,[status(thm)],[c_65]) ).
cnf(c_244,plain,
( m2_relset_1(A,k1_relat_1(A),B)
| ~ r1_tarski(k2_relat_1(A),B)
| ~ v1_relat_1(A) ),
inference(resolve,[status(thm)],[c_97,c_96]) ).
cnf(c_281,plain,
r1_tarski(k2_relat_1(k5_relset_2(sK1,sK0)),k1_zfmisc_1(k2_relat_1(sK0))),
inference(resolve,[status(thm)],[c_108,c_99]) ).
cnf(c_282,plain,
v1_relat_1(sK0),
inference(resolve,[status(thm)],[c_108,c_58]) ).
cnf(c_369,plain,
v1_funct_1(k5_relset_2(A,sK0)),
inference(resolve,[status(thm)],[c_282,c_70]) ).
cnf(c_370,plain,
v1_relat_1(k5_relset_2(A,sK0)),
inference(resolve,[status(thm)],[c_282,c_69]) ).
cnf(c_379,negated_conjecture,
( ~ m2_relset_1(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0))) ),
inference(resolve,[status(thm)],[c_369,c_109]) ).
cnf(c_6928,plain,
( k1_relat_1(k5_relset_2(A,sK0)) = k1_zfmisc_1(A)
| ~ v1_funct_1(k5_relset_2(A,sK0))
| ~ v1_relat_1(k5_relset_2(A,sK0)) ),
inference(resolve,[status(thm)],[c_137,c_282]) ).
cnf(c_6929,plain,
( k1_relat_1(k5_relset_2(A,sK0)) = k1_zfmisc_1(A)
| ~ v1_funct_1(k5_relset_2(A,sK0)) ),
inference(resolve,[status(thm)],[c_370,c_6928]) ).
cnf(c_586,plain,
k1_relat_1(k5_relset_2(A,sK0)) = k1_zfmisc_1(A),
inference(resolve,[status(thm)],[c_369,c_6929]) ).
cnf(c_6930,plain,
( m2_relset_1(k5_relset_2(sK1,sK0),k1_relat_1(k5_relset_2(sK1,sK0)),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_relat_1(k5_relset_2(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_281,c_244]) ).
cnf(c_6931,plain,
( m2_relset_1(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| ~ v1_relat_1(k5_relset_2(sK1,sK0)) ),
inference(paramod,[status(thm)],[c_586,c_6930]) ).
cnf(c_3184,plain,
m2_relset_1(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0))),
inference(resolve,[status(thm)],[c_370,c_6931]) ).
cnf(c_3193,negated_conjecture,
~ v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0))),
inference(resolve,[status(thm)],[c_3184,c_379]) ).
cnf(c_6932,plain,
k4_relset_1(k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)),k5_relset_2(sK1,sK0)) = k1_relat_1(k5_relset_2(sK1,sK0)),
inference(resolve,[status(thm)],[c_3184,c_117]) ).
cnf(c_6641,plain,
k4_relset_1(k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)),k5_relset_2(sK1,sK0)) = k1_zfmisc_1(sK1),
inference(paramod,[status(thm)],[c_586,c_6932]) ).
cnf(c_6933,plain,
( k4_relset_1(k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)),k5_relset_2(sK1,sK0)) != k1_zfmisc_1(sK1)
| v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK0)) ),
inference(resolve,[status(thm)],[c_3184,c_60]) ).
cnf(c_6934,plain,
( k1_zfmisc_1(sK1) != k1_zfmisc_1(sK1)
| v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK0)) ),
inference(paramod,[status(thm)],[c_6641,c_6933]) ).
cnf(c_6935,plain,
( k1_zfmisc_1(sK1) != k1_zfmisc_1(sK1)
| v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| k1_zfmisc_1(k2_relat_1(sK0)) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_6934]) ).
cnf(c_6936,plain,
( v1_funct_2(k5_relset_2(sK1,sK0),k1_zfmisc_1(sK1),k1_zfmisc_1(k2_relat_1(sK0)))
| k1_zfmisc_1(k2_relat_1(sK0)) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_6935]) ).
cnf(c_6644,negated_conjecture,
k1_zfmisc_1(k2_relat_1(sK0)) = k1_xboole_0,
inference(resolve,[status(thm)],[c_3193,c_6936]) ).
cnf(c_6937,plain,
~ v1_xboole_0(k1_xboole_0),
inference(paramod,[status(thm)],[c_6644,c_76]) ).
cnf(c_6927,plain,
$false,
inference(resolve,[status(thm)],[c_74,c_6937]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:40:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2466428 was started by sandbox on n013,
% 0.09/0.37 % Sat Sep 26 09:40:36 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 7.20/1.33
% 7.20/1.33 % given #500 (A,wt=30): 213 -v1_relat_1(A) | -v1_funct_1(A) | k5_relset_2(B,c2) = A | k1_relat_1(A) != k1_zfmisc_1(B) | r1_tarski(f1(B,c2,A),B). [resolve(92,a,67,a)].
% 7.20/1.33
% 7.20/1.33 % SZS status Theorem for theBenchmark
% 7.20/1.33
% 7.20/1.33 % Proof 1 at 0.72 (+ 0.18) seconds.
% 7.20/1.33 % Length of proof is 41.
% 7.20/1.33 % Level of proof is 8.
% 7.20/1.33 % Maximum clause weight is 37.000.
% 7.20/1.33 % Given clauses 649.
% 7.20/1.33
% 7.20/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------