%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET979+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 : n001.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 08:37:24 AM UTC 2026
% Result : Theorem 0.08s 5.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 7 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t120_zfmisc_1,axiom,
! [A,B,C] :
( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
file('theBenchmark.p',t120_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('theBenchmark.p',t41_enumset1) ).
fof(t132_zfmisc_1,conjecture,
! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
file('theBenchmark.p',t132_zfmisc_1) ).
fof(t132_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).
cnf(c_18,plain,
cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(clausify,[status(thm)],[t120_zfmisc_1]) ).
cnf(c_19,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(C,B)) = cartesian_product2(set_union2(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,plain,
cartesian_product2(A,set_union2(B,C)) = set_union2(cartesian_product2(A,B),cartesian_product2(A,C)),
inference(clausify,[status(thm)],[t120_zfmisc_1]) ).
cnf(c_21,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(A,C)) = cartesian_product2(A,set_union2(B,C)),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(clausify,[status(thm)],[t41_enumset1]) ).
cnf(c_23,plain,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(copy,[status(thm)],[c_22]) ).
fof(nnf_10,plain,
? [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) != set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
| cartesian_product2(unordered_pair(A,B),C) != set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(fof_nnf,[status(thm)],[t132_zfmisc_1_neg]) ).
fof(sk_t132_zfmisc_1_neg,plain,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_10]) ).
cnf(c_24,negated_conjecture,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t132_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(paramod,[status(thm)],[c_23,c_24]) ).
cnf(c_27,negated_conjecture,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) != cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) ),
inference(paramod,[status(thm)],[c_19,c_26]) ).
cnf(c_28,negated_conjecture,
( cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1))) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) != cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) ),
inference(paramod,[status(thm)],[c_23,c_27]) ).
cnf(c_29,negated_conjecture,
( cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1))) != cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1)))
| cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) != cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2) ),
inference(paramod,[status(thm)],[c_21,c_28]) ).
cnf(c_30,negated_conjecture,
cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1))) != cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1))),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_25,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 08:34:48 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 1383603 was started by sandbox on n001,
% 0.08/5.37 % Sat Sep 26 08:34:48 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 0.08/5.38
% 0.08/5.38 % SZS status Theorem for theBenchmark
% 0.08/5.38
% 0.08/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/5.38 % Length of proof is 11.
% 0.08/5.38 % Level of proof is 3.
% 0.08/5.38 % Maximum clause weight is 13.000.
% 0.08/5.38 % Given clauses 0.
% 0.08/5.38
% 0.08/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------