%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:58:01 AM UTC 2026
% Result : Theorem 41.57s 47.10s
% Output : Proof 41.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 34 unt; 0 def)
% Number of atoms : 135 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 38 |; 27 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 3 sgn 56 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(d3_zfmisc_1,axiom,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
file('theBenchmark.p',d3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t19_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('theBenchmark.p',t19_finset_1) ).
fof(t20_finset_1,conjecture,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('theBenchmark.p',t20_finset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_9_2,plain,
! [U_13] :
( ! [U_12] :
( finite(U_12)
| ~ element(U_12,powerset(U_13)) )
| ~ finite(U_13) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_12,U_13] :
( finite(U_12)
| ~ element(U_12,powerset(U_13))
| ~ finite(U_13) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( finite(U_12)
| ~ element(U_12,powerset(U_13))
| ~ finite(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_14_1,plain,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(fof_nnf,[status(thm)],[d3_zfmisc_1]) ).
fof(f_14_2,plain,
! [U_20,U_19,U_18] : cartesian_product3(U_20,U_19,U_18) = cartesian_product2(cartesian_product2(U_20,U_19),U_18),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_18,U_19,U_20] : cartesian_product3(U_20,U_19,U_18) = cartesian_product2(cartesian_product2(U_20,U_19),U_18),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
cartesian_product3(U_20,U_19,U_18) = cartesian_product2(cartesian_product2(U_20,U_19),U_18),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_50_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_50_2,plain,
! [U_61,U_60] : subset(U_61,U_61),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_61] : subset(U_61,U_61),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
! [U_61] : subset(U_61,U_61),
inference(definitional_conversion,[status(esa)],[f_50_3]) ).
cnf(f_50_5,plain,
subset(U_61,U_61),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_1,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[t19_finset_1]) ).
fof(f_51_2,plain,
! [U_63,U_62] :
( finite(cartesian_product2(U_63,U_62))
| ~ finite(U_62)
| ~ finite(U_63) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_62,U_63] :
( finite(cartesian_product2(U_63,U_62))
| ~ finite(U_62)
| ~ finite(U_63) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( finite(cartesian_product2(U_63,U_62))
| ~ finite(U_62)
| ~ finite(U_63) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_53_1,negated_conjecture,
~ ! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
inference(negate,[status(cth)],[t20_finset_1]) ).
fof(f_53_2,negated_conjecture,
? [A,B,C] :
( ~ finite(cartesian_product3(A,B,C))
& finite(C)
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[f_53_1]) ).
fof(f_53_3,negated_conjecture,
? [U_68,U_67,U_66] :
( ~ finite(cartesian_product3(U_68,U_67,U_66))
& finite(U_66)
& finite(U_67)
& finite(U_68) ),
inference(variable_rename,[status(thm)],[f_53_2]) ).
fof(f_53_4,negated_conjecture,
? [U_67,U_66] :
( ~ finite(cartesian_product3(sK27,U_67,U_66))
& finite(U_66)
& finite(U_67)
& finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_68,sK27)],[f_53_3]) ).
fof(f_53_5,negated_conjecture,
? [U_66] :
( ~ finite(cartesian_product3(sK27,sK28,U_66))
& finite(U_66)
& finite(sK28)
& finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_67,sK28)],[f_53_4]) ).
fof(f_53_6,negated_conjecture,
( ~ finite(cartesian_product3(sK27,sK28,sK29))
& finite(sK29)
& finite(sK28)
& finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_66,sK29)],[f_53_5]) ).
fof(f_53_7,negated_conjecture,
( ~ finite(cartesian_product3(sK27,sK28,sK29))
& finite(sK29)
& finite(sK28)
& finite(sK27) ),
inference(definitional_conversion,[status(esa)],[f_53_6]) ).
cnf(f_53_8,negated_conjecture,
finite(sK27),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_9,negated_conjecture,
finite(sK28),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_10,negated_conjecture,
finite(sK29),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_11,negated_conjecture,
~ finite(cartesian_product3(sK27,sK28,sK29)),
inference(clausify,[status(thm)],[f_53_7]) ).
fof(f_55_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_55_2,plain,
! [U_72,U_71] :
( ( element(U_72,powerset(U_71))
| ~ subset(U_72,U_71) )
& ( subset(U_72,U_71)
| ~ element(U_72,powerset(U_71)) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_76,U_74] :
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) )
& ! [U_75,U_73] :
( subset(U_75,U_73)
| ~ element(U_75,powerset(U_73)) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_76,U_74] :
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) )
& ! [U_75,U_73] :
( subset(U_75,U_73)
| ~ element(U_75,powerset(U_73)) ) ),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_6,plain,
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) ),
inference(clausify,[status(thm)],[f_55_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_29,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
finite(sK27),
inference(start,[status(thm),parent(0:0)],[f_53_8]) ).
cnf(t2,plain,
( ~ finite(sK28)
| finite(cartesian_product2(sK27,sK28))
| ~ finite(sK27) ),
inference(extension,[status(thm),parent(t1:1)],[f_51_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ finite(sK29)
| finite(cartesian_product2(cartesian_product2(sK27,sK28),sK29))
| ~ finite(cartesian_product2(sK27,sK28)) ),
inference(extension,[status(thm),parent(t2:2)],[f_51_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ element(cartesian_product3(sK27,sK28,sK29),powerset(cartesian_product2(cartesian_product2(sK27,sK28),sK29)))
| finite(cartesian_product3(sK27,sK28,sK29))
| ~ finite(cartesian_product2(cartesian_product2(sK27,sK28),sK29)) ),
inference(extension,[status(thm),parent(t4:2)],[f_9_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ finite(cartesian_product3(sK27,sK28,sK29)),
inference(extension,[status(thm),parent(t6:2)],[f_53_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ subset(cartesian_product3(sK27,sK28,sK29),cartesian_product2(cartesian_product2(sK27,sK28),sK29))
| element(cartesian_product3(sK27,sK28,sK29),powerset(cartesian_product2(cartesian_product2(sK27,sK28),sK29))) ),
inference(extension,[status(thm),parent(t6:3)],[f_55_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( cartesian_product3(sK27,sK28,sK29) != cartesian_product2(cartesian_product2(sK27,sK28),sK29)
| ~ subset(cartesian_product3(sK27,sK28,sK29),cartesian_product3(sK27,sK28,sK29))
| cartesian_product3(sK27,sK28,sK29) != cartesian_product3(sK27,sK28,sK29)
| subset(cartesian_product3(sK27,sK28,sK29),cartesian_product2(cartesian_product2(sK27,sK28),sK29)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_29]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
cartesian_product3(sK27,sK28,sK29) = cartesian_product3(sK27,sK28,sK29),
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
subset(cartesian_product3(sK27,sK28,sK29),cartesian_product3(sK27,sK28,sK29)),
inference(extension,[status(thm),parent(t12:3)],[f_50_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
cartesian_product3(sK27,sK28,sK29) = cartesian_product2(cartesian_product2(sK27,sK28),sK29),
inference(extension,[status(thm),parent(t12:4)],[f_14_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
finite(sK29),
inference(extension,[status(thm),parent(t4:3)],[f_53_10]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t4:3]) ).
cnf(t22,plain,
finite(sK28),
inference(extension,[status(thm),parent(t2:3)],[f_53_9]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.60 % Computer : n013.cluster.edu
% 0.12/5.60 % Model : x86_64 x86_64
% 0.12/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.60 % Memory : 8046.5625MB
% 0.12/5.60 % OS : Linux 6.8.0-71-generic
% 0.12/5.60 % CPULimit : 300
% 0.12/5.60 % WCLimit : 300
% 0.12/5.60 % DateTime : Sat Sep 19 23:16:59 UTC 2026
% 0.12/5.60 % CPUTime :
% 41.57/47.10 % SZS status Theorem for theBenchmark
% 41.57/47.10 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------