%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:45:16 AM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 71 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 30 ~; 30 |; 9 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 7 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t106_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t106_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(assume_negation,[status(cth)],[t106_zfmisc_1]) ).
cnf(c_18,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_19,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_20,plain,
( in(A,C)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_21,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_22,plain,
( in(B,D)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_23,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_24,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_18,c_23]) ).
fof(nnf_12,plain,
? [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1_neg]) ).
fof(sk_t106_zfmisc_1_neg_sk,plain,
( ( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( ( in(sK1,sK3)
& in(sK0,sK2) )
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_12]) ).
fof(sk_t106_zfmisc_1_neg,plain,
( ( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( in(sK0,sK2)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ),
inference(cnf_transformation,[status(thm)],[sk_t106_zfmisc_1_neg_sk]) ).
cnf(c_25,negated_conjecture,
( in(sK0,sK2)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t106_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
( in(sK0,sK2)
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)) ),
inference(paramod,[status(thm)],[c_18,c_25]) ).
cnf(c_27,negated_conjecture,
( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t106_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
( in(sK1,sK3)
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)) ),
inference(paramod,[status(thm)],[c_18,c_27]) ).
cnf(c_29,negated_conjecture,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t106_zfmisc_1_neg]) ).
cnf(c_30,negated_conjecture,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)) ),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_62,negated_conjecture,
( in(sK0,sK2)
| in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_26,c_20]) ).
cnf(c_41,negated_conjecture,
in(sK0,sK2),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_42,negated_conjecture,
( ~ in(sK1,sK3)
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_41,c_30]) ).
cnf(c_63,negated_conjecture,
( in(sK1,sK3)
| in(sK1,sK3) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_45,negated_conjecture,
in(sK1,sK3),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_46,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)),
inference(resolve,[status(thm)],[c_45,c_42]) ).
cnf(c_64,negated_conjecture,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(resolve,[status(thm)],[c_24,c_46]) ).
cnf(c_65,negated_conjecture,
~ in(sK1,sK3),
inference(resolve,[status(thm)],[c_64,c_41]) ).
cnf(c_61,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_45,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n006.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 08:42:40 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 846559 was started by sandbox2 on n006,
% 0.16/0.42 % Sat Sep 26 08:42:40 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 21.
% 0.16/0.44 % Level of proof is 6.
% 0.16/0.44 % Maximum clause weight is 16.000.
% 0.16/0.44 % Given clauses 19.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------