%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:37:21 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 41 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 9 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 50 ( 7 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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(t107_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
file('theBenchmark.p',t107_zfmisc_1) ).
fof(t107_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
inference(assume_negation,[status(cth)],[t107_zfmisc_1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_11,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_14,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_15,plain,
( in(A,C)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_16,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_17,plain,
( in(B,D)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_18,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_19,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_11,c_18]) ).
fof(nnf_8,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(B,A),cartesian_product2(D,C))
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(fof_nnf,[status(thm)],[t107_zfmisc_1_neg]) ).
fof(sk_t107_zfmisc_1_neg,plain,
( ~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,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_8]) ).
cnf(c_22,negated_conjecture,
in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t107_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(sK2,sK3)),
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_24,negated_conjecture,
~ in(ordered_pair(sK1,sK0),cartesian_product2(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_t107_zfmisc_1_neg]) ).
cnf(c_51,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK1,sK0),singleton(sK1)),cartesian_product2(sK3,sK2)),
inference(paramod,[status(thm)],[c_11,c_24]) ).
cnf(c_25,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK1)),cartesian_product2(sK3,sK2)),
inference(paramod,[status(thm)],[c_10,c_51]) ).
cnf(c_33,negated_conjecture,
in(sK1,sK3),
inference(resolve,[status(thm)],[c_17,c_23]) ).
cnf(c_34,negated_conjecture,
in(sK0,sK2),
inference(resolve,[status(thm)],[c_15,c_23]) ).
cnf(c_52,plain,
( ~ in(A,B)
| in(unordered_pair(unordered_pair(sK1,A),singleton(sK1)),cartesian_product2(sK3,B)) ),
inference(resolve,[status(thm)],[c_19,c_33]) ).
cnf(c_53,plain,
in(unordered_pair(unordered_pair(sK1,sK0),singleton(sK1)),cartesian_product2(sK3,sK2)),
inference(resolve,[status(thm)],[c_52,c_34]) ).
cnf(c_54,plain,
in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK1)),cartesian_product2(sK3,sK2)),
inference(paramod,[status(thm)],[c_10,c_53]) ).
cnf(c_50,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_25,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:26:36 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 1238981 was started by sandbox on n004,
% 0.10/0.37 % Sat Sep 26 08:26:36 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).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 19.
% 0.14/0.39 % Level of proof is 4.
% 0.14/0.39 % Maximum clause weight is 16.000.
% 0.14/0.39 % Given clauses 18.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------