%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:57:52 AM UTC 2026
% Result : Theorem 1.67s 1.99s
% Output : Proof 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 29 unt; 0 def)
% Number of atoms : 56 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 12 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 64 ( 0 sgn 32 !; 14 ?)
% 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(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(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(f_7_1,plain,
! [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)) ),
inference(fof_nnf,[status(thm)],[t120_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_12,U_11,U_10] :
( cartesian_product2(U_10,set_union2(U_12,U_11)) = set_union2(cartesian_product2(U_10,U_12),cartesian_product2(U_10,U_11))
& cartesian_product2(set_union2(U_12,U_11),U_10) = set_union2(cartesian_product2(U_12,U_10),cartesian_product2(U_11,U_10)) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_18,U_16,U_14] : cartesian_product2(U_14,set_union2(U_18,U_16)) = set_union2(cartesian_product2(U_14,U_18),cartesian_product2(U_14,U_16))
& ! [U_17,U_15,U_13] : cartesian_product2(set_union2(U_17,U_15),U_13) = set_union2(cartesian_product2(U_17,U_13),cartesian_product2(U_15,U_13)) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
cartesian_product2(set_union2(U_17,U_15),U_13) = set_union2(cartesian_product2(U_17,U_13),cartesian_product2(U_15,U_13)),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
cartesian_product2(U_14,set_union2(U_18,U_16)) = set_union2(cartesian_product2(U_14,U_18),cartesian_product2(U_14,U_16)),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,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(negate,[status(cth)],[t121_zfmisc_1]) ).
fof(f_8_2,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(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_22,U_21,U_20,U_19] : cartesian_product2(set_union2(U_22,U_21),set_union2(U_20,U_19)) != set_union2(set_union2(set_union2(cartesian_product2(U_22,U_20),cartesian_product2(U_22,U_19)),cartesian_product2(U_21,U_20)),cartesian_product2(U_21,U_19)),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_21,U_20,U_19] : cartesian_product2(set_union2(sK3,U_21),set_union2(U_20,U_19)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,U_20),cartesian_product2(sK3,U_19)),cartesian_product2(U_21,U_20)),cartesian_product2(U_21,U_19)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
? [U_20,U_19] : cartesian_product2(set_union2(sK3,sK4),set_union2(U_20,U_19)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,U_20),cartesian_product2(sK3,U_19)),cartesian_product2(sK4,U_20)),cartesian_product2(sK4,U_19)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
? [U_19] : cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,U_19)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,U_19)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,U_19)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_19,sK6)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(definitional_conversion,[status(esa)],[f_8_7]) ).
cnf(f_8_9,negated_conjecture,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(clausify,[status(thm)],[f_8_8]) ).
fof(f_9_1,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(fof_nnf,[status(thm)],[t4_xboole_1]) ).
fof(f_9_2,plain,
! [U_25,U_24,U_23] : set_union2(set_union2(U_25,U_24),U_23) = set_union2(U_25,set_union2(U_24,U_23)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
set_union2(set_union2(U_25,U_24),U_23) = set_union2(U_25,set_union2(U_24,U_23)),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(start,[status(thm),parent(0:0)],[f_8_9]) ).
cnf(t2,plain,
( set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6))
| cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6)))
| cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) = set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))),
inference(extension,[status(thm),parent(t2:2)],[f_7_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6))
| set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))) != set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6)))
| set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))) = set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( cartesian_product2(sK4,set_union2(sK5,sK6)) != set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))
| cartesian_product2(sK3,set_union2(sK5,sK6)) != set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6))
| set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))) = set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))) ),
inference(extension,[status(thm),parent(t6:2)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
cartesian_product2(sK3,set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),
inference(extension,[status(thm),parent(t8:2)],[f_7_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
cartesian_product2(sK4,set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6)),
inference(extension,[status(thm),parent(t8:3)],[f_7_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) != set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6)))
| set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))) = set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) = set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))),
inference(extension,[status(thm),parent(t14:2)],[f_9_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:08:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 1.67/1.99 % SZS status Theorem for theBenchmark
% 1.67/1.99 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------