%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU449+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 : 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 08:46:24 AM UTC 2026
% Result : Theorem 3.64s 1.00s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 111 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 110 ( 47 ~; 39 |; 9 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 83 ( 1 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(redefinition_k6_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k6_relset_1(A,B,C) = k4_relat_1(C) ),
file('theBenchmark.p',redefinition_k6_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(dt_k6_relset_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> m2_relset_1(k6_relset_1(A,B,C),B,A) ),
file('theBenchmark.p',dt_k6_relset_1) ).
fof(dt_k8_relset_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B)) ),
file('theBenchmark.p',dt_k8_relset_2) ).
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(t61_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E)))
<=> r1_tarski(D,k8_relset_2(A,B,C,E)) ) ) ) ),
file('theBenchmark.p',t61_relset_2) ).
fof(t63_relset_2,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
file('theBenchmark.p',t63_relset_2) ).
fof(t63_relset_2_neg,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
inference(assume_negation,[status(cth)],[t63_relset_2]) ).
cnf(c_56,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,
( m2_relset_1(k6_relset_1(B,C,A),C,B)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[dt_k6_relset_1]) ).
cnf(c_61,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_62,plain,
( r1_tarski(C,k8_relset_2(B,D,A,E))
| ~ r1_tarski(A,k8_relset_2(D,B,C,k6_relset_1(B,D,E)))
| ~ m2_relset_1(E,B,D)
| ~ m1_subset_1(C,k1_zfmisc_1(D))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[t61_relset_2]) ).
cnf(c_63,plain,
( ~ r1_tarski(C,k8_relset_2(B,D,A,E))
| r1_tarski(A,k8_relset_2(D,B,C,k6_relset_1(B,D,E)))
| ~ m2_relset_1(E,B,D)
| ~ m1_subset_1(C,k1_zfmisc_1(D))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[t61_relset_2]) ).
fof(nnf_55,plain,
? [A,B,C] :
( ? [D] :
( ? [E] :
( ( ~ r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
| ~ r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) )
& m2_relset_1(E,A,B) )
& m1_subset_1(D,k1_zfmisc_1(B)) )
& m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[t63_relset_2_neg]) ).
fof(sk_t63_relset_2_neg,plain,
( ( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK0)),sK0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k6_relset_1(sK1,sK2,sK0))) )
& m2_relset_1(sK0,sK1,sK2)
& m1_subset_1(sK4,k1_zfmisc_1(sK2))
& m1_subset_1(sK3,k1_zfmisc_1(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK4,sK2,sK0]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK4),skolemize(E,sK0)],[nnf_55]) ).
cnf(c_64,negated_conjecture,
m2_relset_1(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t63_relset_2_neg]) ).
cnf(c_68,negated_conjecture,
m1_relset_1(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_64,c_56]) ).
cnf(c_69,negated_conjecture,
m1_subset_1(sK0,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))),
inference(resolve,[status(thm)],[c_64,c_61]) ).
cnf(c_70,negated_conjecture,
( r1_tarski(B,k8_relset_2(sK1,sK2,A,sK0))
| ~ r1_tarski(A,k8_relset_2(sK2,sK1,B,k6_relset_1(sK1,sK2,sK0)))
| ~ m1_subset_1(B,k1_zfmisc_1(sK2))
| ~ m1_subset_1(A,k1_zfmisc_1(sK1)) ),
inference(resolve,[status(thm)],[c_64,c_62]) ).
cnf(c_71,negated_conjecture,
( ~ r1_tarski(B,k8_relset_2(sK1,sK2,A,sK0))
| r1_tarski(A,k8_relset_2(sK2,sK1,B,k6_relset_1(sK1,sK2,sK0)))
| ~ m1_subset_1(B,k1_zfmisc_1(sK2))
| ~ m1_subset_1(A,k1_zfmisc_1(sK1)) ),
inference(resolve,[status(thm)],[c_64,c_63]) ).
cnf(c_83,plain,
( ~ m1_relset_1(C,A,B)
| m1_subset_1(k6_relset_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(B,A))) ),
inference(resolve,[status(thm)],[c_61,c_60]) ).
cnf(c_87,negated_conjecture,
( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK0)),sK0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k6_relset_1(sK1,sK2,sK0))) ),
inference(split_conjunct,[status(thm)],[sk_t63_relset_2_neg]) ).
cnf(c_88,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(sK2)),
inference(split_conjunct,[status(thm)],[sk_t63_relset_2_neg]) ).
cnf(c_89,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(sK1)),
inference(split_conjunct,[status(thm)],[sk_t63_relset_2_neg]) ).
cnf(c_93,plain,
( m1_subset_1(k8_relset_2(B,D,A,C),k1_zfmisc_1(D))
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,D)))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[dt_k8_relset_2]) ).
cnf(c_95,plain,
( k4_relat_1(A) = k6_relset_1(B,C,A)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k6_relset_1]) ).
cnf(c_96,plain,
( k6_relset_1(B,C,A) = k4_relat_1(A)
| ~ m1_relset_1(A,B,C) ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_98,plain,
r1_tarski(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_183,plain,
m1_subset_1(k6_relset_1(sK1,sK2,sK0),k1_zfmisc_1(k2_zfmisc_1(sK2,sK1))),
inference(resolve,[status(thm)],[c_83,c_68]) ).
cnf(c_206,plain,
( r1_tarski(sK4,k8_relset_2(sK1,sK2,A,sK0))
| ~ r1_tarski(A,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(sK1)) ),
inference(resolve,[status(thm)],[c_88,c_70]) ).
cnf(c_219,plain,
( ~ r1_tarski(A,k8_relset_2(sK1,sK2,sK3,sK0))
| r1_tarski(sK3,k8_relset_2(sK2,sK1,A,k6_relset_1(sK1,sK2,sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(sK2)) ),
inference(resolve,[status(thm)],[c_89,c_71]) ).
cnf(c_225,plain,
( m1_subset_1(k8_relset_2(sK1,B,sK3,A),k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(sK1,B))) ),
inference(resolve,[status(thm)],[c_93,c_89]) ).
cnf(c_226,plain,
( m1_subset_1(k8_relset_2(sK2,B,sK4,A),k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(sK2,B))) ),
inference(resolve,[status(thm)],[c_93,c_88]) ).
cnf(c_238,plain,
k6_relset_1(sK1,sK2,sK0) = k4_relat_1(sK0),
inference(resolve,[status(thm)],[c_96,c_68]) ).
cnf(c_266,plain,
( ~ r1_tarski(A,k8_relset_2(sK1,sK2,sK3,sK0))
| r1_tarski(sK3,k8_relset_2(sK2,sK1,A,k4_relat_1(sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(sK2)) ),
inference(paramod,[status(thm)],[c_238,c_219]) ).
cnf(c_267,plain,
( r1_tarski(sK4,k8_relset_2(sK1,sK2,A,sK0))
| ~ r1_tarski(A,k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)))
| ~ m1_subset_1(A,k1_zfmisc_1(sK1)) ),
inference(paramod,[status(thm)],[c_238,c_206]) ).
cnf(c_270,plain,
m1_subset_1(k4_relat_1(sK0),k1_zfmisc_1(k2_zfmisc_1(sK2,sK1))),
inference(paramod,[status(thm)],[c_238,c_183]) ).
cnf(c_2755,negated_conjecture,
( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k6_relset_1(sK1,sK2,sK0)),sK0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k4_relat_1(sK0))) ),
inference(paramod,[status(thm)],[c_238,c_87]) ).
cnf(c_273,negated_conjecture,
( ~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),sK0))
| ~ r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k4_relat_1(sK0))) ),
inference(paramod,[status(thm)],[c_238,c_2755]) ).
cnf(c_1226,plain,
m1_subset_1(k8_relset_2(sK1,sK2,sK3,sK0),k1_zfmisc_1(sK2)),
inference(resolve,[status(thm)],[c_225,c_69]) ).
cnf(c_2756,plain,
( ~ r1_tarski(k8_relset_2(sK1,sK2,sK3,sK0),k8_relset_2(sK1,sK2,sK3,sK0))
| r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k4_relat_1(sK0))) ),
inference(resolve,[status(thm)],[c_266,c_1226]) ).
cnf(c_2684,plain,
r1_tarski(sK3,k8_relset_2(sK2,sK1,k8_relset_2(sK1,sK2,sK3,sK0),k4_relat_1(sK0))),
inference(resolve,[status(thm)],[c_98,c_2756]) ).
cnf(c_2696,negated_conjecture,
~ r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),sK0)),
inference(resolve,[status(thm)],[c_2684,c_273]) ).
cnf(c_2757,plain,
( r1_tarski(sK4,k8_relset_2(sK1,sK2,k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),sK0))
| ~ m1_subset_1(k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),k1_zfmisc_1(sK1)) ),
inference(resolve,[status(thm)],[c_267,c_98]) ).
cnf(c_2708,negated_conjecture,
~ m1_subset_1(k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),k1_zfmisc_1(sK1)),
inference(resolve,[status(thm)],[c_2696,c_2757]) ).
cnf(c_2758,plain,
m1_subset_1(k8_relset_2(sK2,sK1,sK4,k4_relat_1(sK0)),k1_zfmisc_1(sK1)),
inference(resolve,[status(thm)],[c_270,c_226]) ).
cnf(c_2754,plain,
$false,
inference(resolve,[status(thm)],[c_2708,c_2758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU449+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 10:00:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 281045 was started by sandbox on n011,
% 0.10/0.37 % Sat Sep 26 10:00:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 3.64/1.00
% 3.64/1.00 % SZS status Theorem for theBenchmark
% 3.64/1.00
% 3.64/1.00 % Proof 1 at 0.51 (+ 0.10) seconds.
% 3.64/1.00 % Length of proof is 41.
% 3.64/1.00 % Level of proof is 8.
% 3.64/1.00 % Maximum clause weight is 48.000.
% 3.64/1.00 % Given clauses 390.
% 3.64/1.00
% 3.64/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------