%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET968+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 : n014.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 08:37:22 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 24 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 11 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 14 !; 4 ?)
% 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(t4_xboole_1,axiom,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
file('theBenchmark.p',t4_xboole_1) ).
fof(t121_zfmisc_1,conjecture,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
file('theBenchmark.p',t121_zfmisc_1) ).
fof(t121_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).
cnf(c_16,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_17,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_18,plain,
set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(clausify,[status(thm)],[t4_xboole_1]) ).
fof(nnf_9,plain,
? [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) != set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(fof_nnf,[status(thm)],[t121_zfmisc_1_neg]) ).
fof(sk_t121_zfmisc_1_neg,plain,
cartesian_product2(set_union2(sK0,sK1),set_union2(sK2,sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,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_9]) ).
cnf(c_19,negated_conjecture,
cartesian_product2(set_union2(sK0,sK1),set_union2(sK2,sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(split_conjunct,[status(thm)],[sk_t121_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
set_union2(cartesian_product2(set_union2(sK0,sK1),sK2),cartesian_product2(set_union2(sK0,sK1),sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(paramod,[status(thm)],[c_17,c_19]) ).
cnf(c_26,negated_conjecture,
set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(set_union2(sK0,sK1),sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(paramod,[status(thm)],[c_16,c_25]) ).
cnf(c_27,negated_conjecture,
set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK3))) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_28,negated_conjecture,
set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK1,sK2),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK3)))) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(paramod,[status(thm)],[c_18,c_27]) ).
cnf(c_29,negated_conjecture,
set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK1,sK2),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK3)))) != set_union2(set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2))),cartesian_product2(sK1,sK3)),
inference(paramod,[status(thm)],[c_18,c_28]) ).
cnf(c_30,negated_conjecture,
set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK1,sK2),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK3)))) != set_union2(cartesian_product2(sK0,sK2),set_union2(set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_20,negated_conjecture,
set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK1,sK2),set_union2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK3)))) != set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK0,sK3),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3)))),
inference(paramod,[status(thm)],[c_18,c_30]) ).
cnf(c_31,plain,
set_union2(cartesian_product2(set_union2(A,B),C),cartesian_product2(set_union2(A,B),D)) = set_union2(cartesian_product2(A,set_union2(C,D)),cartesian_product2(B,set_union2(C,D))),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_32,plain,
set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),cartesian_product2(set_union2(A,B),D)) = set_union2(cartesian_product2(A,set_union2(C,D)),cartesian_product2(B,set_union2(C,D))),
inference(paramod,[status(thm)],[c_16,c_31]) ).
cnf(c_33,plain,
set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),set_union2(cartesian_product2(A,D),cartesian_product2(B,D))) = set_union2(cartesian_product2(A,set_union2(C,D)),cartesian_product2(B,set_union2(C,D))),
inference(paramod,[status(thm)],[c_16,c_32]) ).
cnf(c_34,plain,
set_union2(cartesian_product2(A,C),set_union2(cartesian_product2(B,C),set_union2(cartesian_product2(A,D),cartesian_product2(B,D)))) = set_union2(cartesian_product2(A,set_union2(C,D)),cartesian_product2(B,set_union2(C,D))),
inference(paramod,[status(thm)],[c_18,c_33]) ).
cnf(c_35,plain,
set_union2(cartesian_product2(A,C),set_union2(cartesian_product2(B,C),set_union2(cartesian_product2(A,D),cartesian_product2(B,D)))) = set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,set_union2(C,D))),
inference(paramod,[status(thm)],[c_17,c_34]) ).
cnf(c_36,plain,
set_union2(cartesian_product2(A,C),set_union2(cartesian_product2(B,C),set_union2(cartesian_product2(A,D),cartesian_product2(B,D)))) = set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),set_union2(cartesian_product2(B,C),cartesian_product2(B,D))),
inference(paramod,[status(thm)],[c_17,c_35]) ).
cnf(c_23,plain,
set_union2(cartesian_product2(A,B),set_union2(cartesian_product2(C,B),set_union2(cartesian_product2(A,D),cartesian_product2(C,D)))) = set_union2(cartesian_product2(A,B),set_union2(cartesian_product2(A,D),set_union2(cartesian_product2(C,B),cartesian_product2(C,D)))),
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_24,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:28:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2646993 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 08:28:03 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 10.
% 0.14/0.38 % Level of proof is 3.
% 0.14/0.38 % Maximum clause weight is 31.000.
% 0.14/0.38 % Given clauses 8.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------