%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n008.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 08:57:15 AM UTC 2026
% Result : Theorem 84.95s 85.22s
% Output : Proof 84.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 103 ( 54 unt; 0 def)
% Number of atoms : 290 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 319 ( 132 ~; 126 |; 34 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 1 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('theBenchmark.p',p3) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('theBenchmark.p',p6) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('theBenchmark.p',p12) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p14) ).
fof(p16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p16) ).
fof(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('theBenchmark.p',p18) ).
fof(p24,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p24) ).
fof(prove_relset_1_29,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
file('theBenchmark.p',prove_relset_1_29) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_3] :
( ! [U_2] :
( ( ! [U_1] :
( ilf_type(U_1,subset_type(cross_product(U_3,U_2)))
| ~ ilf_type(U_1,relation_type(U_3,U_2)) )
& ! [U_0] :
( ilf_type(U_0,relation_type(U_3,U_2))
| ~ ilf_type(U_0,subset_type(cross_product(U_3,U_2))) ) )
| ~ ilf_type(U_2,set_type) )
| ~ ilf_type(U_3,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ilf_type(U_0,relation_type(U_3,U_2))
| ~ ilf_type(U_0,subset_type(cross_product(U_3,U_2)))
| ~ ilf_type(U_2,set_type)
| ~ ilf_type(U_3,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_3_1,plain,
! [B] :
( subset(identity_relation_of(B),cross_product(B,B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p3]) ).
fof(f_3_2,plain,
! [U_7] :
( subset(identity_relation_of(U_7),cross_product(U_7,U_7))
| ~ ilf_type(U_7,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( subset(identity_relation_of(U_7),cross_product(U_7,U_7))
| ~ ilf_type(U_7,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_6_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,relation_type(B,B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p6]) ).
fof(f_6_2,plain,
! [U_13] :
( ! [U_12] :
( ( ( ilf_type(U_12,identity_relation_of_type(U_13))
| ~ ilf_type(U_12,relation_type(U_13,U_13)) )
& ( ilf_type(U_12,relation_type(U_13,U_13))
| ~ ilf_type(U_12,identity_relation_of_type(U_13)) ) )
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_4,plain,
( ilf_type(U_12,identity_relation_of_type(U_13))
| ~ ilf_type(U_12,relation_type(U_13,U_13))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_12_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p12]) ).
fof(f_12_2,plain,
! [U_23] :
( ! [U_22] :
( ( ( ilf_type(U_22,subset_type(U_23))
| ~ ilf_type(U_22,member_type(power_set(U_23))) )
& ( ilf_type(U_22,member_type(power_set(U_23)))
| ~ ilf_type(U_22,subset_type(U_23)) ) )
| ~ ilf_type(U_22,set_type) )
| ~ ilf_type(U_23,set_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_4,plain,
( ilf_type(U_22,subset_type(U_23))
| ~ ilf_type(U_22,member_type(power_set(U_23)))
| ~ ilf_type(U_22,set_type)
| ~ ilf_type(U_23,set_type) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_14_1,plain,
! [B] :
( ! [C] :
( ( ( subset(B,C)
| ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_14_2,plain,
! [U_29] :
( ! [U_28] :
( ( ( subset(U_29,U_28)
| ? [U_27] :
( ~ member(U_27,U_28)
& member(U_27,U_29)
& ilf_type(U_27,set_type) ) )
& ( ! [U_26] :
( member(U_26,U_28)
| ~ member(U_26,U_29)
| ~ ilf_type(U_26,set_type) )
| ~ subset(U_29,U_28) ) )
| ~ ilf_type(U_28,set_type) )
| ~ ilf_type(U_29,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_29] :
( ! [U_28] :
( ( ( subset(U_29,U_28)
| ( ~ member(sK5(U_29,U_28),U_28)
& member(sK5(U_29,U_28),U_29)
& ilf_type(sK5(U_29,U_28),set_type) ) )
& ( ! [U_26] :
( member(U_26,U_28)
| ~ member(U_26,U_29)
| ~ ilf_type(U_26,set_type) )
| ~ subset(U_29,U_28) ) )
| ~ ilf_type(U_28,set_type) )
| ~ ilf_type(U_29,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5(U_29,U_28))],[f_14_2]) ).
cnf(f_14_4,plain,
( member(U_26,U_28)
| ~ member(U_26,U_29)
| ~ ilf_type(U_26,set_type)
| ~ subset(U_29,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_16_1,plain,
! [B] :
( ! [C] :
( ( ( member(B,power_set(C))
| ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p16]) ).
fof(f_16_2,plain,
! [U_34] :
( ! [U_33] :
( ( ( member(U_34,power_set(U_33))
| ? [U_32] :
( ~ member(U_32,U_33)
& member(U_32,U_34)
& ilf_type(U_32,set_type) ) )
& ( ! [U_31] :
( member(U_31,U_33)
| ~ member(U_31,U_34)
| ~ ilf_type(U_31,set_type) )
| ~ member(U_34,power_set(U_33)) ) )
| ~ ilf_type(U_33,set_type) )
| ~ ilf_type(U_34,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_34] :
( ! [U_33] :
( ( ( member(U_34,power_set(U_33))
| ( ~ member(sK6(U_34,U_33),U_33)
& member(sK6(U_34,U_33),U_34)
& ilf_type(sK6(U_34,U_33),set_type) ) )
& ( ! [U_31] :
( member(U_31,U_33)
| ~ member(U_31,U_34)
| ~ ilf_type(U_31,set_type) )
| ~ member(U_34,power_set(U_33)) ) )
| ~ ilf_type(U_33,set_type) )
| ~ ilf_type(U_34,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6(U_34,U_33))],[f_16_2]) ).
cnf(f_16_6,plain,
( member(sK6(U_34,U_33),U_34)
| member(U_34,power_set(U_33))
| ~ ilf_type(U_33,set_type)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_7,plain,
( ~ member(sK6(U_34,U_33),U_33)
| member(U_34,power_set(U_33))
| ~ ilf_type(U_33,set_type)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_17_2,plain,
! [U_35] :
( ( ilf_type(power_set(U_35),set_type)
& ~ empty(power_set(U_35)) )
| ~ ilf_type(U_35,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ empty(power_set(U_35))
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(B,member_type(C))
| ~ member(B,C) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(f_18_2,plain,
! [U_37] :
( ! [U_36] :
( ( ( ilf_type(U_37,member_type(U_36))
| ~ member(U_37,U_36) )
& ( member(U_37,U_36)
| ~ ilf_type(U_37,member_type(U_36)) ) )
| ~ ilf_type(U_36,set_type)
| empty(U_36) )
| ~ ilf_type(U_37,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_4,plain,
( ilf_type(U_37,member_type(U_36))
| ~ member(U_37,U_36)
| ~ ilf_type(U_36,set_type)
| empty(U_36)
| ~ ilf_type(U_37,set_type) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_24_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p24]) ).
fof(f_24_2,plain,
! [U_54] : ilf_type(U_54,set_type),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
ilf_type(U_54,set_type),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(negate,[status(cth)],[prove_relset_1_29]) ).
fof(f_25_2,negated_conjecture,
? [B] :
( ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_55] :
( ~ ilf_type(identity_relation_of(U_55),identity_relation_of_type(U_55))
& ilf_type(U_55,set_type) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
( ~ ilf_type(identity_relation_of(sK12),identity_relation_of_type(sK12))
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_55,sK12)],[f_25_3]) ).
cnf(f_25_5,negated_conjecture,
ilf_type(sK12,set_type),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,negated_conjecture,
~ ilf_type(identity_relation_of(sK12),identity_relation_of_type(sK12)),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(t1,plain,
~ ilf_type(identity_relation_of(sK12),identity_relation_of_type(sK12)),
inference(start,[status(thm),parent(0:0)],[f_25_6]) ).
cnf(t2,plain,
( ~ ilf_type(identity_relation_of(sK12),set_type)
| ~ ilf_type(identity_relation_of(sK12),relation_type(sK12,sK12))
| ~ ilf_type(sK12,set_type)
| ilf_type(identity_relation_of(sK12),identity_relation_of_type(sK12)) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
ilf_type(sK12,set_type),
inference(extension,[status(thm),parent(t2:2)],[f_25_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
ilf_type(sK12,set_type),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
( ~ ilf_type(sK12,set_type)
| ~ ilf_type(identity_relation_of(sK12),subset_type(cross_product(sK12,sK12)))
| ~ ilf_type(sK12,set_type)
| ilf_type(identity_relation_of(sK12),relation_type(sK12,sK12)) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
ilf_type(sK12,set_type),
inference(lemma_extension,[status(thm),parent(t6:2)],[l2:1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ ilf_type(identity_relation_of(sK12),set_type)
| ~ ilf_type(identity_relation_of(sK12),member_type(power_set(cross_product(sK12,sK12))))
| ~ ilf_type(cross_product(sK12,sK12),set_type)
| ilf_type(identity_relation_of(sK12),subset_type(cross_product(sK12,sK12))) ),
inference(extension,[status(thm),parent(t6:3)],[f_12_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
ilf_type(cross_product(sK12,sK12),set_type),
inference(extension,[status(thm),parent(t10:2)],[f_24_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l5,lemma,
ilf_type(cross_product(sK12,sK12),set_type),
inference(lemma,[status(cth),parent(t10:2),below(t6:3)],[t10:2]) ).
cnf(t14,plain,
( empty(power_set(cross_product(sK12,sK12)))
| ~ ilf_type(power_set(cross_product(sK12,sK12)),set_type)
| ~ member(identity_relation_of(sK12),power_set(cross_product(sK12,sK12)))
| ~ ilf_type(identity_relation_of(sK12),set_type)
| ilf_type(identity_relation_of(sK12),member_type(power_set(cross_product(sK12,sK12)))) ),
inference(extension,[status(thm),parent(t10:3)],[f_18_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(extension,[status(thm),parent(t14:2)],[f_24_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(l7,lemma,
ilf_type(identity_relation_of(sK12),set_type),
inference(lemma,[status(cth),parent(t14:2),below(t10:3)],[t14:2]) ).
cnf(t18,plain,
( ~ ilf_type(cross_product(sK12,sK12),set_type)
| member(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),identity_relation_of(sK12))
| ~ ilf_type(identity_relation_of(sK12),set_type)
| member(identity_relation_of(sK12),power_set(cross_product(sK12,sK12))) ),
inference(extension,[status(thm),parent(t14:3)],[f_16_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(lemma_extension,[status(thm),parent(t18:2)],[l7:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ ilf_type(cross_product(sK12,sK12),set_type)
| ~ subset(identity_relation_of(sK12),cross_product(sK12,sK12))
| ~ ilf_type(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),set_type)
| member(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),cross_product(sK12,sK12))
| ~ ilf_type(identity_relation_of(sK12),set_type)
| ~ member(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),identity_relation_of(sK12)) ),
inference(extension,[status(thm),parent(t18:3)],[f_14_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(lemma_extension,[status(thm),parent(t22:2)],[l7:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ ilf_type(cross_product(sK12,sK12),set_type)
| member(identity_relation_of(sK12),power_set(cross_product(sK12,sK12)))
| ~ ilf_type(identity_relation_of(sK12),set_type)
| ~ member(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),cross_product(sK12,sK12)) ),
inference(extension,[status(thm),parent(t22:3)],[f_16_7]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(lemma_extension,[status(thm),parent(t26:2)],[l7:1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
$false,
inference(reduction,[status(thm),parent(t26:3)],[t26:3,t14:3]) ).
cnf(t31,plain,
ilf_type(cross_product(sK12,sK12),set_type),
inference(lemma_extension,[status(thm),parent(t26:4)],[l5:1]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t26:4]) ).
cnf(t33,plain,
ilf_type(sK6(identity_relation_of(sK12),cross_product(sK12,sK12)),set_type),
inference(extension,[status(thm),parent(t22:4)],[f_24_3]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t22:4]) ).
cnf(t35,plain,
( ~ ilf_type(sK12,set_type)
| subset(identity_relation_of(sK12),cross_product(sK12,sK12)) ),
inference(extension,[status(thm),parent(t22:5)],[f_3_3]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t22:5]) ).
cnf(t37,plain,
ilf_type(sK12,set_type),
inference(lemma_extension,[status(thm),parent(t35:2)],[l2:1]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
ilf_type(cross_product(sK12,sK12),set_type),
inference(lemma_extension,[status(thm),parent(t22:6)],[l5:1]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t22:6]) ).
cnf(t41,plain,
ilf_type(cross_product(sK12,sK12),set_type),
inference(lemma_extension,[status(thm),parent(t18:4)],[l5:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t18:4]) ).
cnf(t43,plain,
ilf_type(power_set(cross_product(sK12,sK12)),set_type),
inference(extension,[status(thm),parent(t14:4)],[f_24_3]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t14:4]) ).
cnf(t45,plain,
( ~ ilf_type(cross_product(sK12,sK12),set_type)
| ~ empty(power_set(cross_product(sK12,sK12))) ),
inference(extension,[status(thm),parent(t14:5)],[f_17_3]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t14:5]) ).
cnf(t47,plain,
ilf_type(cross_product(sK12,sK12),set_type),
inference(lemma_extension,[status(thm),parent(t45:2)],[l5:1]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t45:2]) ).
cnf(t49,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(extension,[status(thm),parent(t10:4)],[f_24_3]) ).
cnf(t50,plain,
$false,
inference(connection,[status(thm),parent(t49:1)],[t49:1,t10:4]) ).
cnf(t51,plain,
ilf_type(sK12,set_type),
inference(lemma_extension,[status(thm),parent(t6:4)],[l2:1]) ).
cnf(t52,plain,
$false,
inference(connection,[status(thm),parent(t51:1)],[t51:1,t6:4]) ).
cnf(t53,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(extension,[status(thm),parent(t2:4)],[f_24_3]) ).
cnf(t54,plain,
$false,
inference(connection,[status(thm),parent(t53:1)],[t53:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n008.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sat Sep 19 22:46:23 UTC 2026
% 0.06/0.33 % CPUTime :
% 84.95/85.22 % SZS status Theorem for theBenchmark
% 84.95/85.22 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------