%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET979+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 : n016.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 08:57:54 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 23 unt; 0 def)
% Number of atoms : 77 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 37 ~; 24 |; 6 &)
% ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 27 !; 27 ?)
% 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(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(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('theBenchmark.p',t41_enumset1) ).
fof(f_8_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_8_2,plain,
! [U_14,U_13,U_12] :
( cartesian_product2(U_12,set_union2(U_14,U_13)) = set_union2(cartesian_product2(U_12,U_14),cartesian_product2(U_12,U_13))
& cartesian_product2(set_union2(U_14,U_13),U_12) = set_union2(cartesian_product2(U_14,U_12),cartesian_product2(U_13,U_12)) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_20,U_18,U_16] : cartesian_product2(U_16,set_union2(U_20,U_18)) = set_union2(cartesian_product2(U_16,U_20),cartesian_product2(U_16,U_18))
& ! [U_19,U_17,U_15] : cartesian_product2(set_union2(U_19,U_17),U_15) = set_union2(cartesian_product2(U_19,U_15),cartesian_product2(U_17,U_15)) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
cartesian_product2(set_union2(U_19,U_17),U_15) = set_union2(cartesian_product2(U_19,U_15),cartesian_product2(U_17,U_15)),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
cartesian_product2(U_16,set_union2(U_20,U_18)) = set_union2(cartesian_product2(U_16,U_20),cartesian_product2(U_16,U_18)),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,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(negate,[status(cth)],[t132_zfmisc_1]) ).
fof(f_9_2,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(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_23,U_22,U_21] :
( cartesian_product2(U_21,unordered_pair(U_23,U_22)) != set_union2(cartesian_product2(U_21,singleton(U_23)),cartesian_product2(U_21,singleton(U_22)))
| cartesian_product2(unordered_pair(U_23,U_22),U_21) != set_union2(cartesian_product2(singleton(U_23),U_21),cartesian_product2(singleton(U_22),U_21)) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_29,U_27,U_25] : cartesian_product2(U_25,unordered_pair(U_29,U_27)) != set_union2(cartesian_product2(U_25,singleton(U_29)),cartesian_product2(U_25,singleton(U_27)))
| ? [U_28,U_26,U_24] : cartesian_product2(unordered_pair(U_28,U_26),U_24) != set_union2(cartesian_product2(singleton(U_28),U_24),cartesian_product2(singleton(U_26),U_24)) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_29,U_27,U_25] : cartesian_product2(U_25,unordered_pair(U_29,U_27)) != set_union2(cartesian_product2(U_25,singleton(U_29)),cartesian_product2(U_25,singleton(U_27)))
| ? [U_26,U_24] : cartesian_product2(unordered_pair(sK3,U_26),U_24) != set_union2(cartesian_product2(singleton(sK3),U_24),cartesian_product2(singleton(U_26),U_24)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_29,U_27,U_25] : cartesian_product2(U_25,unordered_pair(U_29,U_27)) != set_union2(cartesian_product2(U_25,singleton(U_29)),cartesian_product2(U_25,singleton(U_27)))
| ? [U_24] : cartesian_product2(unordered_pair(sK3,sK4),U_24) != set_union2(cartesian_product2(singleton(sK3),U_24),cartesian_product2(singleton(sK4),U_24)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_29,U_27,U_25] : cartesian_product2(U_25,unordered_pair(U_29,U_27)) != set_union2(cartesian_product2(U_25,singleton(U_29)),cartesian_product2(U_25,singleton(U_27)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ? [U_27,U_25] : cartesian_product2(U_25,unordered_pair(sK6,U_27)) != set_union2(cartesian_product2(U_25,singleton(sK6)),cartesian_product2(U_25,singleton(U_27)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ? [U_25] : cartesian_product2(U_25,unordered_pair(sK6,sK7)) != set_union2(cartesian_product2(U_25,singleton(sK6)),cartesian_product2(U_25,singleton(sK7)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7)],[f_9_8]) ).
fof(f_9_10,negated_conjecture,
( cartesian_product2(sK8,unordered_pair(sK6,sK7)) != set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8)],[f_9_9]) ).
fof(f_9_11,negated_conjecture,
( cartesian_product2(sK8,unordered_pair(sK6,sK7)) != set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(definitional_conversion,[status(esa)],[f_9_10]) ).
cnf(f_9_12,negated_conjecture,
( cartesian_product2(sK8,unordered_pair(sK6,sK7)) != set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(clausify,[status(thm)],[f_9_11]) ).
fof(f_10_1,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(fof_nnf,[status(thm)],[t41_enumset1]) ).
fof(f_10_2,plain,
! [U_31,U_30] : unordered_pair(U_31,U_30) = set_union2(singleton(U_31),singleton(U_30)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
unordered_pair(U_31,U_30) = set_union2(singleton(U_31),singleton(U_30)),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_6,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(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(sK8,unordered_pair(sK6,sK7)) != set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7)))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
inference(start,[status(thm),parent(0:0)],[f_9_12]) ).
cnf(t2,plain,
( cartesian_product2(set_union2(singleton(sK3),singleton(sK4)),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) != cartesian_product2(set_union2(singleton(sK3),singleton(sK4)),sK5)
| cartesian_product2(unordered_pair(sK3,sK4),sK5) = set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)) ),
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,
( sK5 != sK5
| unordered_pair(sK3,sK4) != set_union2(singleton(sK3),singleton(sK4))
| cartesian_product2(unordered_pair(sK3,sK4),sK5) = cartesian_product2(set_union2(singleton(sK3),singleton(sK4)),sK5) ),
inference(extension,[status(thm),parent(t2:2)],[equality_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
unordered_pair(sK3,sK4) = set_union2(singleton(sK3),singleton(sK4)),
inference(extension,[status(thm),parent(t4:2)],[f_10_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t4:3)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
cartesian_product2(set_union2(singleton(sK3),singleton(sK4)),sK5) = set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)),
inference(extension,[status(thm),parent(t2:3)],[f_8_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( cartesian_product2(sK8,set_union2(singleton(sK6),singleton(sK7))) != set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7)))
| cartesian_product2(sK8,unordered_pair(sK6,sK7)) != cartesian_product2(sK8,set_union2(singleton(sK6),singleton(sK7)))
| cartesian_product2(sK8,unordered_pair(sK6,sK7)) = set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7))) ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:2]) ).
cnf(t14,plain,
( unordered_pair(sK6,sK7) != set_union2(singleton(sK6),singleton(sK7))
| sK8 != sK8
| cartesian_product2(sK8,unordered_pair(sK6,sK7)) = cartesian_product2(sK8,set_union2(singleton(sK6),singleton(sK7))) ),
inference(extension,[status(thm),parent(t12:2)],[equality_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
unordered_pair(sK6,sK7) = set_union2(singleton(sK6),singleton(sK7)),
inference(extension,[status(thm),parent(t14:3)],[f_10_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
cartesian_product2(sK8,set_union2(singleton(sK6),singleton(sK7))) = set_union2(cartesian_product2(sK8,singleton(sK6)),cartesian_product2(sK8,singleton(sK7))),
inference(extension,[status(thm),parent(t12:3)],[f_8_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+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
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:14:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------