%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU417+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 : n011.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 08:46:15 AM UTC 2026
% Result : Theorem 13.07s 2.41s
% Output : CNFRefutation 13.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 107 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 102 ( 42 ~; 35 |; 9 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 77 ( 2 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k4_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ),
file('theBenchmark.p',dt_k4_subset_1) ).
fof(dt_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ),
file('theBenchmark.p',dt_k5_subset_1) ).
fof(redefinition_k1_relset_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k1_relset_2(A,B,C) = k3_xboole_0(B,C) ),
file('theBenchmark.p',redefinition_k1_relset_2) ).
fof(redefinition_k4_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k4_subset_1(A,B,C) = k2_xboole_0(B,C) ),
file('theBenchmark.p',redefinition_k4_subset_1) ).
fof(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,C) = k3_xboole_0(B,C) ),
file('theBenchmark.p',redefinition_k5_subset_1) ).
fof(t29_xboole_1,axiom,
! [A,B,C] : r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C)),
file('theBenchmark.p',t29_xboole_1) ).
fof(t59_setfam_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B)) ) ) ),
file('theBenchmark.p',t59_setfam_1) ).
fof(t8_mssubfam,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( B = k4_subset_1(k1_zfmisc_1(A),C,D)
=> k8_setfam_1(A,B) = k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D)) ) ) ) ),
file('theBenchmark.p',t8_mssubfam) ).
fof(t7_relset_2,conjecture,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> r1_tarski(k5_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)),k8_setfam_1(A,k1_relset_2(A,B,C))) ) ),
file('theBenchmark.p',t7_relset_2) ).
fof(t7_relset_2_neg,negated_conjecture,
~ ! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> r1_tarski(k5_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)),k8_setfam_1(A,k1_relset_2(A,B,C))) ) ),
inference(assume_negation,[status(cth)],[t7_relset_2]) ).
fof(nnf_50,plain,
? [A,B] :
( ? [C] :
( ~ r1_tarski(k5_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)),k8_setfam_1(A,k1_relset_2(A,B,C)))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(fof_nnf,[status(thm)],[t7_relset_2_neg]) ).
fof(sk_t7_relset_2_neg,plain,
( ~ r1_tarski(k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)),k8_setfam_1(sK0,k1_relset_2(sK0,sK1,sK2)))
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
& m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_50]) ).
cnf(c_51,negated_conjecture,
~ r1_tarski(k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)),k8_setfam_1(sK0,k1_relset_2(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_t7_relset_2_neg]) ).
cnf(c_52,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(split_conjunct,[status(thm)],[sk_t7_relset_2_neg]) ).
cnf(c_53,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(split_conjunct,[status(thm)],[sk_t7_relset_2_neg]) ).
cnf(c_54,plain,
( k5_subset_1(B,k8_setfam_1(B,C),k8_setfam_1(B,D)) = k8_setfam_1(B,A)
| k4_subset_1(k1_zfmisc_1(B),C,D) != A
| ~ m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(clausify,[status(thm)],[t8_mssubfam]) ).
cnf(c_59,plain,
( r1_tarski(k8_setfam_1(B,C),k8_setfam_1(B,A))
| ~ r1_tarski(A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(clausify,[status(thm)],[t59_setfam_1]) ).
cnf(c_65,plain,
r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C)),
inference(clausify,[status(thm)],[t29_xboole_1]) ).
cnf(c_69,plain,
( k3_xboole_0(A,C) = k5_subset_1(B,A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[redefinition_k5_subset_1]) ).
cnf(c_70,plain,
( k5_subset_1(B,A,C) = k3_xboole_0(A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_71,plain,
( k4_subset_1(B,A,C) = k2_xboole_0(A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[redefinition_k4_subset_1]) ).
cnf(c_72,plain,
( k3_xboole_0(A,C) = k1_relset_2(B,A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(clausify,[status(thm)],[redefinition_k1_relset_2]) ).
cnf(c_73,plain,
( k1_relset_2(B,A,C) = k3_xboole_0(A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_95,plain,
( m1_subset_1(k5_subset_1(B,A,C),k1_zfmisc_1(B))
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[dt_k5_subset_1]) ).
cnf(c_96,plain,
( m1_subset_1(k4_subset_1(B,A,C),k1_zfmisc_1(B))
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[dt_k4_subset_1]) ).
cnf(c_121,plain,
( k5_subset_1(sK0,k8_setfam_1(sK0,B),k8_setfam_1(sK0,sK2)) = k8_setfam_1(sK0,A)
| k4_subset_1(k1_zfmisc_1(sK0),B,sK2) != A
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_54,c_52]) ).
cnf(c_142,plain,
( r1_tarski(k8_setfam_1(C,k2_xboole_0(A,D)),k8_setfam_1(C,k3_xboole_0(A,B)))
| ~ m1_subset_1(k2_xboole_0(A,D),k1_zfmisc_1(k1_zfmisc_1(C)))
| ~ m1_subset_1(k3_xboole_0(A,B),k1_zfmisc_1(k1_zfmisc_1(C))) ),
inference(resolve,[status(thm)],[c_65,c_59]) ).
cnf(c_148,plain,
( k5_subset_1(k1_zfmisc_1(sK0),sK1,A) = k3_xboole_0(sK1,A)
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_70,c_53]) ).
cnf(c_152,plain,
( k4_subset_1(k1_zfmisc_1(sK0),sK1,A) = k2_xboole_0(sK1,A)
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_71,c_53]) ).
cnf(c_156,plain,
( k1_relset_2(sK0,sK1,A) = k3_xboole_0(sK1,A)
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_73,c_53]) ).
cnf(c_222,plain,
( m1_subset_1(k5_subset_1(k1_zfmisc_1(sK0),sK1,A),k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_95,c_53]) ).
cnf(c_230,plain,
( m1_subset_1(k4_subset_1(k1_zfmisc_1(sK0),sK1,A),k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_96,c_53]) ).
cnf(c_1269,plain,
k5_subset_1(k1_zfmisc_1(sK0),sK1,sK2) = k3_xboole_0(sK1,sK2),
inference(resolve,[status(thm)],[c_148,c_52]) ).
cnf(c_1463,plain,
k4_subset_1(k1_zfmisc_1(sK0),sK1,sK2) = k2_xboole_0(sK1,sK2),
inference(resolve,[status(thm)],[c_152,c_52]) ).
cnf(c_1987,plain,
k1_relset_2(sK0,sK1,sK2) = k3_xboole_0(sK1,sK2),
inference(resolve,[status(thm)],[c_156,c_52]) ).
cnf(c_2001,negated_conjecture,
~ r1_tarski(k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)),k8_setfam_1(sK0,k3_xboole_0(sK1,sK2))),
inference(paramod,[status(thm)],[c_1987,c_51]) ).
cnf(c_12030,plain,
( k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)) = k8_setfam_1(sK0,k2_xboole_0(sK1,sK2))
| ~ m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m1_subset_1(k2_xboole_0(sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_1463,c_121]) ).
cnf(c_4270,negated_conjecture,
( k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)) = k8_setfam_1(sK0,k2_xboole_0(sK1,sK2))
| ~ m1_subset_1(k2_xboole_0(sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_53,c_12030]) ).
cnf(c_12031,negated_conjecture,
m1_subset_1(k5_subset_1(k1_zfmisc_1(sK0),sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(resolve,[status(thm)],[c_222,c_52]) ).
cnf(c_5135,negated_conjecture,
m1_subset_1(k3_xboole_0(sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(paramod,[status(thm)],[c_1269,c_12031]) ).
cnf(c_12032,negated_conjecture,
m1_subset_1(k4_subset_1(k1_zfmisc_1(sK0),sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(resolve,[status(thm)],[c_230,c_52]) ).
cnf(c_6337,negated_conjecture,
m1_subset_1(k2_xboole_0(sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(paramod,[status(thm)],[c_1463,c_12032]) ).
cnf(c_6339,negated_conjecture,
k5_subset_1(sK0,k8_setfam_1(sK0,sK1),k8_setfam_1(sK0,sK2)) = k8_setfam_1(sK0,k2_xboole_0(sK1,sK2)),
inference(resolve,[status(thm)],[c_6337,c_4270]) ).
cnf(c_6343,negated_conjecture,
~ r1_tarski(k8_setfam_1(sK0,k2_xboole_0(sK1,sK2)),k8_setfam_1(sK0,k3_xboole_0(sK1,sK2))),
inference(paramod,[status(thm)],[c_6339,c_2001]) ).
cnf(c_12033,plain,
( r1_tarski(k8_setfam_1(sK0,k2_xboole_0(sK1,sK2)),k8_setfam_1(sK0,k3_xboole_0(sK1,A)))
| ~ m1_subset_1(k3_xboole_0(sK1,A),k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(resolve,[status(thm)],[c_142,c_6337]) ).
cnf(c_12034,negated_conjecture,
~ m1_subset_1(k3_xboole_0(sK1,sK2),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(resolve,[status(thm)],[c_12033,c_6343]) ).
cnf(c_12029,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5135,c_12034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU417+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 09:34:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 214145 was started by sandbox2 on n011,
% 0.08/0.35 % Sat Sep 26 09:34:14 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 13.07/2.41
% 13.07/2.41 % given #500 (A,wt=31): 171 v1_xboole_0(A) | -m1_subset_1(B,k1_zfmisc_1(A)) | k5_subset_1(A,f2(A),B) = k3_xboole_0(f2(A),B). [resolve(80,b,70,a)].
% 13.07/2.41
% 13.07/2.41 % given #1000 (T,wt=25): 1127 k5_subset_1(k2_xboole_0(A,B),k3_xboole_0(A,C),k1_xboole_0) = k1_xboole_0. [resolve(141,a,382,a)].
% 13.07/2.41
% 13.07/2.41 % SZS status Theorem for theBenchmark
% 13.07/2.41
% 13.07/2.41 % Proof 1 at 1.50 (+ 0.44) seconds.
% 13.07/2.41 % Length of proof is 39.
% 13.07/2.41 % Level of proof is 7.
% 13.07/2.41 % Maximum clause weight is 55.000.
% 13.07/2.41 % Given clauses 1492.
% 13.07/2.41
% 13.07/2.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------