%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET647+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 08:57:13 AM UTC 2026
% Result : Theorem 209.06s 209.37s
% Output : Proof 209.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 197 ( 96 unt; 0 def)
% Number of atoms : 556 ( 9 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 616 ( 257 ~; 247 |; 76 &)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 219 ( 11 sgn 154 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('theBenchmark.p',p2) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,C)
=> ( subset(cross_product(D,B),cross_product(D,C))
& subset(cross_product(B,D),cross_product(C,D)) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,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',p4) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p10) ).
fof(p12,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',p12) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p13) ).
fof(p15,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',p15) ).
fof(p20,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',p20) ).
fof(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p21) ).
fof(p22,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',p22) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_9,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
file('theBenchmark.p',prove_relset_1_9) ).
fof(f_2_1,plain,
! [B] :
( subset(B,cross_product(domain_of(B),range_of(B)))
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_3] :
( subset(U_3,cross_product(domain_of(U_3),range_of(U_3)))
| ~ ilf_type(U_3,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3] :
( subset(U_3,cross_product(domain_of(U_3),range_of(U_3)))
| ~ ilf_type(U_3,binary_relation_type) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_3,cross_product(domain_of(U_3),range_of(U_3)))
| ~ ilf_type(U_3,binary_relation_type) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(cross_product(D,B),cross_product(D,C))
& subset(cross_product(B,D),cross_product(C,D)) )
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p3]) ).
fof(f_3_2,plain,
! [U_6] :
( ! [U_5] :
( ! [U_4] :
( ( subset(cross_product(U_4,U_6),cross_product(U_4,U_5))
& subset(cross_product(U_6,U_4),cross_product(U_5,U_4)) )
| ~ subset(U_6,U_5)
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) )
| ~ ilf_type(U_6,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_6,U_4,U_5] :
( subset(cross_product(U_4,U_6),cross_product(U_4,U_5))
| ~ sP0(U_6,U_4,U_5) )
& ! [U_6,U_4,U_5] :
( subset(cross_product(U_6,U_4),cross_product(U_5,U_4))
| ~ sP0(U_6,U_4,U_5) )
& ! [U_6,U_4,U_5] :
( sP0(U_6,U_4,U_5)
| ~ subset(U_6,U_5)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type)
| ~ ilf_type(U_6,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_6,U_4,U_5)
| ~ subset(U_6,U_5)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type)
| ~ ilf_type(U_6,set_type) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(cross_product(U_6,U_4),cross_product(U_5,U_4))
| ~ sP0(U_6,U_4,U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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)],[p4]) ).
fof(f_4_2,plain,
! [U_10] :
( ! [U_9] :
( ( ! [U_8] :
( ilf_type(U_8,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_8,relation_type(U_10,U_9)) )
& ! [U_7] :
( ilf_type(U_7,relation_type(U_10,U_9))
| ~ ilf_type(U_7,subset_type(cross_product(U_10,U_9))) ) )
| ~ ilf_type(U_9,set_type) )
| ~ ilf_type(U_10,set_type) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_8,U_7,U_10,U_9] :
( ilf_type(U_8,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_8,relation_type(U_10,U_9))
| ~ sP1(U_8,U_7,U_10,U_9) )
& ! [U_8,U_7,U_10,U_9] :
( ilf_type(U_7,relation_type(U_10,U_9))
| ~ ilf_type(U_7,subset_type(cross_product(U_10,U_9)))
| ~ sP1(U_8,U_7,U_10,U_9) )
& ! [U_8,U_7,U_10,U_9] :
( sP1(U_8,U_7,U_10,U_9)
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP1(U_8,U_7,U_10,U_9)
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ilf_type(U_7,relation_type(U_10,U_9))
| ~ ilf_type(U_7,subset_type(cross_product(U_10,U_9)))
| ~ sP1(U_8,U_7,U_10,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_10_1,plain,
! [B] :
( ( ( ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ relation_like(B) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p10]) ).
fof(f_10_2,plain,
! [U_24] :
( ( ( ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type)
| ~ relation_like(U_24) )
& ( ( ilf_type(U_24,set_type)
& relation_like(U_24) )
| ~ ilf_type(U_24,binary_relation_type) ) )
| ~ ilf_type(U_24,set_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_24] :
( ilf_type(U_24,set_type)
| ~ sP6(U_24) )
& ! [U_24] :
( relation_like(U_24)
| ~ sP6(U_24) )
& ! [U_24] :
( ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type)
| ~ relation_like(U_24)
| ~ sP7(U_24) )
& ! [U_24] :
( sP6(U_24)
| ~ ilf_type(U_24,binary_relation_type)
| ~ sP7(U_24) )
& ! [U_24] :
( sP7(U_24)
| ~ ilf_type(U_24,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP7(U_24)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( sP6(U_24)
| ~ ilf_type(U_24,binary_relation_type)
| ~ sP7(U_24) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_8,plain,
( ilf_type(U_24,set_type)
| ~ sP6(U_24) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_12_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)],[p12]) ).
fof(f_12_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_12_1]) ).
fof(f_12_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_12_2]) ).
fof(f_12_4,plain,
( ! [U_29,U_28] :
( ~ member(sK5(U_29,U_28),U_28)
| ~ sP8(U_29,U_28) )
& ! [U_29,U_28] :
( member(sK5(U_29,U_28),U_29)
| ~ sP8(U_29,U_28) )
& ! [U_29,U_28] :
( ilf_type(sK5(U_29,U_28),set_type)
| ~ sP8(U_29,U_28) )
& ! [U_29,U_26,U_28] :
( subset(U_29,U_28)
| sP8(U_29,U_28)
| ~ sP9(U_29,U_26,U_28) )
& ! [U_29,U_26,U_28] :
( member(U_26,U_28)
| ~ member(U_26,U_29)
| ~ ilf_type(U_26,set_type)
| ~ subset(U_29,U_28)
| ~ sP9(U_29,U_26,U_28) )
& ! [U_29,U_26,U_28] :
( sP9(U_29,U_26,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9])],[f_12_3]) ).
cnf(f_12_5,plain,
( sP9(U_29,U_26,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( member(U_26,U_28)
| ~ member(U_26,U_29)
| ~ ilf_type(U_26,set_type)
| ~ subset(U_29,U_28)
| ~ sP9(U_29,U_26,U_28) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [B] :
( ! [C] :
( ilf_type(cross_product(B,C),set_type)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p13]) ).
fof(f_13_2,plain,
! [U_31] :
( ! [U_30] :
( ilf_type(cross_product(U_31,U_30),set_type)
| ~ ilf_type(U_30,set_type) )
| ~ ilf_type(U_31,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_31,U_30] :
( ilf_type(cross_product(U_31,U_30),set_type)
| ~ ilf_type(U_30,set_type)
| ~ ilf_type(U_31,set_type) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( ilf_type(cross_product(U_31,U_30),set_type)
| ~ ilf_type(U_30,set_type)
| ~ ilf_type(U_31,set_type) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_15_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)],[p15]) ).
fof(f_15_2,plain,
! [U_35] :
( ! [U_34] :
( ( ( ilf_type(U_34,subset_type(U_35))
| ~ ilf_type(U_34,member_type(power_set(U_35))) )
& ( ilf_type(U_34,member_type(power_set(U_35)))
| ~ ilf_type(U_34,subset_type(U_35)) ) )
| ~ ilf_type(U_34,set_type) )
| ~ ilf_type(U_35,set_type) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_34,U_35] :
( ilf_type(U_34,subset_type(U_35))
| ~ ilf_type(U_34,member_type(power_set(U_35)))
| ~ sP10(U_34,U_35) )
& ! [U_34,U_35] :
( ilf_type(U_34,member_type(power_set(U_35)))
| ~ ilf_type(U_34,subset_type(U_35))
| ~ sP10(U_34,U_35) )
& ! [U_34,U_35] :
( sP10(U_34,U_35)
| ~ ilf_type(U_34,set_type)
| ~ ilf_type(U_35,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP10(U_34,U_35)
| ~ ilf_type(U_34,set_type)
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( ilf_type(U_34,subset_type(U_35))
| ~ ilf_type(U_34,member_type(power_set(U_35)))
| ~ sP10(U_34,U_35) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_20_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)],[p20]) ).
fof(f_20_2,plain,
! [U_52] :
( ! [U_51] :
( ( ( member(U_52,power_set(U_51))
| ? [U_50] :
( ~ member(U_50,U_51)
& member(U_50,U_52)
& ilf_type(U_50,set_type) ) )
& ( ! [U_49] :
( member(U_49,U_51)
| ~ member(U_49,U_52)
| ~ ilf_type(U_49,set_type) )
| ~ member(U_52,power_set(U_51)) ) )
| ~ ilf_type(U_51,set_type) )
| ~ ilf_type(U_52,set_type) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_52] :
( ! [U_51] :
( ( ( member(U_52,power_set(U_51))
| ( ~ member(sK10(U_52,U_51),U_51)
& member(sK10(U_52,U_51),U_52)
& ilf_type(sK10(U_52,U_51),set_type) ) )
& ( ! [U_49] :
( member(U_49,U_51)
| ~ member(U_49,U_52)
| ~ ilf_type(U_49,set_type) )
| ~ member(U_52,power_set(U_51)) ) )
| ~ ilf_type(U_51,set_type) )
| ~ ilf_type(U_52,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10(U_52,U_51))],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_51,U_52] :
( ~ member(sK10(U_52,U_51),U_51)
| ~ sP14(U_51,U_52) )
& ! [U_51,U_52] :
( member(sK10(U_52,U_51),U_52)
| ~ sP14(U_51,U_52) )
& ! [U_51,U_52] :
( ilf_type(sK10(U_52,U_51),set_type)
| ~ sP14(U_51,U_52) )
& ! [U_51,U_49,U_52] :
( member(U_52,power_set(U_51))
| sP14(U_51,U_52)
| ~ sP15(U_51,U_49,U_52) )
& ! [U_51,U_49,U_52] :
( member(U_49,U_51)
| ~ member(U_49,U_52)
| ~ ilf_type(U_49,set_type)
| ~ member(U_52,power_set(U_51))
| ~ sP15(U_51,U_49,U_52) )
& ! [U_51,U_49,U_52] :
( sP15(U_51,U_49,U_52)
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_20_3]) ).
cnf(f_20_5,plain,
( sP15(U_51,U_49,U_52)
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( member(U_52,power_set(U_51))
| sP14(U_51,U_52)
| ~ sP15(U_51,U_49,U_52) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_9,plain,
( member(sK10(U_52,U_51),U_52)
| ~ sP14(U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_10,plain,
( ~ member(sK10(U_52,U_51),U_51)
| ~ sP14(U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p21]) ).
fof(f_21_2,plain,
! [U_53] :
( ( ilf_type(power_set(U_53),set_type)
& ~ empty(power_set(U_53)) )
| ~ ilf_type(U_53,set_type) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_53] :
( ilf_type(power_set(U_53),set_type)
| ~ sP16(U_53) )
& ! [U_53] :
( ~ empty(power_set(U_53))
| ~ sP16(U_53) )
& ! [U_53] :
( sP16(U_53)
| ~ ilf_type(U_53,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_21_2]) ).
cnf(f_21_4,plain,
( sP16(U_53)
| ~ ilf_type(U_53,set_type) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ empty(power_set(U_53))
| ~ sP16(U_53) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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)],[p22]) ).
fof(f_22_2,plain,
! [U_55] :
( ! [U_54] :
( ( ( ilf_type(U_55,member_type(U_54))
| ~ member(U_55,U_54) )
& ( member(U_55,U_54)
| ~ ilf_type(U_55,member_type(U_54)) ) )
| ~ ilf_type(U_54,set_type)
| empty(U_54) )
| ~ ilf_type(U_55,set_type) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_54,U_55] :
( ilf_type(U_55,member_type(U_54))
| ~ member(U_55,U_54)
| ~ sP17(U_54,U_55) )
& ! [U_54,U_55] :
( member(U_55,U_54)
| ~ ilf_type(U_55,member_type(U_54))
| ~ sP17(U_54,U_55) )
& ! [U_54,U_55] :
( sP17(U_54,U_55)
| ~ ilf_type(U_54,set_type)
| empty(U_54)
| ~ ilf_type(U_55,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP17(U_54,U_55)
| ~ ilf_type(U_54,set_type)
| empty(U_54)
| ~ ilf_type(U_55,set_type) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( ilf_type(U_55,member_type(U_54))
| ~ member(U_55,U_54)
| ~ sP17(U_54,U_55) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_26_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p26]) ).
fof(f_26_2,plain,
! [U_62] : ilf_type(U_62,set_type),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_62] : ilf_type(U_62,set_type),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
ilf_type(U_62,set_type),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_9]) ).
fof(f_27_2,negated_conjecture,
? [B] :
( ? [C] :
( ~ ilf_type(C,relation_type(B,range_of(C)))
& subset(domain_of(C),B)
& ilf_type(C,binary_relation_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_64] :
( ? [U_63] :
( ~ ilf_type(U_63,relation_type(U_64,range_of(U_63)))
& subset(domain_of(U_63),U_64)
& ilf_type(U_63,binary_relation_type) )
& ilf_type(U_64,set_type) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
( ? [U_63] :
( ~ ilf_type(U_63,relation_type(sK13,range_of(U_63)))
& subset(domain_of(U_63),sK13)
& ilf_type(U_63,binary_relation_type) )
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_64,sK13)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
( ~ ilf_type(sK14,relation_type(sK13,range_of(sK14)))
& subset(domain_of(sK14),sK13)
& ilf_type(sK14,binary_relation_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_63,sK14)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( ~ ilf_type(sK14,relation_type(sK13,range_of(sK14)))
& subset(domain_of(sK14),sK13)
& ilf_type(sK14,binary_relation_type)
& ilf_type(sK13,set_type) ),
inference(definitional_conversion,[status(esa)],[f_27_5]) ).
cnf(f_27_8,negated_conjecture,
ilf_type(sK14,binary_relation_type),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_9,negated_conjecture,
subset(domain_of(sK14),sK13),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_10,negated_conjecture,
~ ilf_type(sK14,relation_type(sK13,range_of(sK14))),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_27,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ ilf_type(sK14,relation_type(sK13,range_of(sK14))),
inference(start,[status(thm),parent(0:0)],[f_27_10]) ).
cnf(t2,plain,
( ~ ilf_type(sK14,subset_type(cross_product(sK13,range_of(sK14))))
| ~ sP1(U_8246,sK14,sK13,range_of(sK14))
| ilf_type(sK14,relation_type(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t1:1)],[f_4_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ ilf_type(sK13,set_type)
| ~ ilf_type(range_of(sK14),set_type)
| sP1(U_8246,sK14,sK13,range_of(sK14)) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t4:2)],[f_26_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
ilf_type(sK13,set_type),
inference(extension,[status(thm),parent(t4:3)],[f_26_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ sP10(sK14,cross_product(sK13,range_of(sK14)))
| ~ ilf_type(sK14,member_type(power_set(cross_product(sK13,range_of(sK14)))))
| ilf_type(sK14,subset_type(cross_product(sK13,range_of(sK14)))) ),
inference(extension,[status(thm),parent(t2:3)],[f_15_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ member(sK14,power_set(cross_product(sK13,range_of(sK14))))
| ~ sP17(power_set(cross_product(sK13,range_of(sK14))),sK14)
| ilf_type(sK14,member_type(power_set(cross_product(sK13,range_of(sK14))))) ),
inference(extension,[status(thm),parent(t10:2)],[f_22_6]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ ilf_type(power_set(cross_product(sK13,range_of(sK14))),set_type)
| empty(power_set(cross_product(sK13,range_of(sK14))))
| ~ ilf_type(sK14,set_type)
| sP17(power_set(cross_product(sK13,range_of(sK14))),sK14) ),
inference(extension,[status(thm),parent(t12:2)],[f_22_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ sP6(sK14)
| ilf_type(sK14,set_type) ),
inference(extension,[status(thm),parent(t14:2)],[f_10_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ sP7(sK14)
| ~ ilf_type(sK14,binary_relation_type)
| sP6(sK14) ),
inference(extension,[status(thm),parent(t16:2)],[f_10_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
ilf_type(sK14,binary_relation_type),
inference(extension,[status(thm),parent(t18:2)],[f_27_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( sK14 != sK14
| ~ sP7(sK14)
| sP7(sK14) ),
inference(extension,[status(thm),parent(t18:3)],[equality_35]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( ~ ilf_type(sK14,set_type)
| sP7(sK14) ),
inference(extension,[status(thm),parent(t22:2)],[f_10_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t24:2)],[f_26_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
sK14 = sK14,
inference(extension,[status(thm),parent(t22:3)],[equality_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
( power_set(cross_product(sK13,range_of(sK14))) != power_set(cross_product(sK13,range_of(sK14)))
| empty(power_set(cross_product(sK13,range_of(sK14))))
| ~ empty(power_set(cross_product(sK13,range_of(sK14)))) ),
inference(extension,[status(thm),parent(t14:3)],[equality_27]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t14:3]) ).
cnf(t32,plain,
( power_set(cross_product(sK13,range_of(sK14))) != power_set(cross_product(sK13,range_of(sK14)))
| empty(power_set(cross_product(sK13,range_of(sK14))))
| ~ empty(power_set(cross_product(sK13,range_of(sK14)))) ),
inference(extension,[status(thm),parent(t30:2)],[equality_27]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( ~ sP16(cross_product(sK13,range_of(sK14)))
| ~ empty(power_set(cross_product(sK13,range_of(sK14)))) ),
inference(extension,[status(thm),parent(t32:2)],[f_21_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( ~ ilf_type(cross_product(sK13,range_of(sK14)),set_type)
| sP16(cross_product(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t34:2)],[f_21_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
ilf_type(cross_product(sK13,range_of(sK14)),set_type),
inference(extension,[status(thm),parent(t36:2)],[f_26_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
power_set(cross_product(sK13,range_of(sK14))) = power_set(cross_product(sK13,range_of(sK14))),
inference(extension,[status(thm),parent(t32:3)],[equality_1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t32:3]) ).
cnf(t42,plain,
power_set(cross_product(sK13,range_of(sK14))) = power_set(cross_product(sK13,range_of(sK14))),
inference(extension,[status(thm),parent(t30:3)],[equality_1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t30:3]) ).
cnf(t44,plain,
ilf_type(power_set(cross_product(sK13,range_of(sK14))),set_type),
inference(extension,[status(thm),parent(t14:4)],[f_26_4]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t14:4]) ).
cnf(t46,plain,
( sP14(cross_product(sK13,range_of(sK14)),sK14)
| ~ sP15(cross_product(sK13,range_of(sK14)),U_8278,sK14)
| member(sK14,power_set(cross_product(sK13,range_of(sK14)))) ),
inference(extension,[status(thm),parent(t12:3)],[f_20_7]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t12:3]) ).
cnf(t48,plain,
( ~ ilf_type(cross_product(sK13,range_of(sK14)),set_type)
| ~ ilf_type(sK14,set_type)
| sP15(cross_product(sK13,range_of(sK14)),U_8278,sK14) ),
inference(extension,[status(thm),parent(t46:2)],[f_20_5]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t48:2)],[f_26_4]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( ~ ilf_type(sK13,set_type)
| ~ ilf_type(range_of(sK14),set_type)
| ilf_type(cross_product(sK13,range_of(sK14)),set_type) ),
inference(extension,[status(thm),parent(t48:3)],[f_13_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t52:2)],[f_26_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
ilf_type(sK13,set_type),
inference(extension,[status(thm),parent(t52:3)],[f_26_4]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
( ~ member(sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(sK13,range_of(sK14)))
| ~ sP14(cross_product(sK13,range_of(sK14)),sK14) ),
inference(extension,[status(thm),parent(t46:3)],[f_20_10]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t46:3]) ).
cnf(t60,plain,
( ~ ilf_type(sK10(sK14,cross_product(sK13,range_of(sK14))),set_type)
| ~ sP9(cross_product(domain_of(sK14),range_of(sK14)),sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(sK13,range_of(sK14)))
| ~ member(sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(domain_of(sK14),range_of(sK14)))
| ~ subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,range_of(sK14)))
| member(sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t58:2)],[f_12_6]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( ~ sP0(domain_of(sK14),range_of(sK14),sK13)
| subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t60:2)],[f_3_5]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( ~ ilf_type(sK13,set_type)
| ~ subset(domain_of(sK14),sK13)
| ~ ilf_type(domain_of(sK14),set_type)
| ~ ilf_type(range_of(sK14),set_type)
| sP0(domain_of(sK14),range_of(sK14),sK13) ),
inference(extension,[status(thm),parent(t62:2)],[f_3_4]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t64:2)],[f_26_4]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
ilf_type(domain_of(sK14),set_type),
inference(extension,[status(thm),parent(t64:3)],[f_26_4]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
subset(domain_of(sK14),sK13),
inference(extension,[status(thm),parent(t64:4)],[f_27_9]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t64:4]) ).
cnf(t72,plain,
ilf_type(sK13,set_type),
inference(extension,[status(thm),parent(t64:5)],[f_26_4]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t64:5]) ).
cnf(t74,plain,
( ~ ilf_type(sK10(sK14,cross_product(sK13,range_of(sK14))),set_type)
| ~ sP9(sK14,sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(domain_of(sK14),range_of(sK14)))
| ~ member(sK10(sK14,cross_product(sK13,range_of(sK14))),sK14)
| ~ subset(sK14,cross_product(domain_of(sK14),range_of(sK14)))
| member(sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(domain_of(sK14),range_of(sK14))) ),
inference(extension,[status(thm),parent(t60:3)],[f_12_6]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t60:3]) ).
cnf(t76,plain,
( ~ ilf_type(sK14,binary_relation_type)
| subset(sK14,cross_product(domain_of(sK14),range_of(sK14))) ),
inference(extension,[status(thm),parent(t74:2)],[f_2_4]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
ilf_type(sK14,binary_relation_type),
inference(extension,[status(thm),parent(t76:2)],[f_27_8]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
( ~ sP14(cross_product(sK13,range_of(sK14)),sK14)
| member(sK10(sK14,cross_product(sK13,range_of(sK14))),sK14) ),
inference(extension,[status(thm),parent(t74:3)],[f_20_9]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t74:3]) ).
cnf(t82,plain,
$false,
inference(reduction,[status(thm),parent(t80:2)],[t80:2,t46:3]) ).
cnf(t83,plain,
( ~ ilf_type(cross_product(domain_of(sK14),range_of(sK14)),set_type)
| ~ ilf_type(sK14,set_type)
| sP9(sK14,sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(domain_of(sK14),range_of(sK14))) ),
inference(extension,[status(thm),parent(t74:4)],[f_12_5]) ).
cnf(t84,plain,
$false,
inference(connection,[status(thm),parent(t83:1)],[t83:1,t74:4]) ).
cnf(t85,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t83:2)],[f_26_4]) ).
cnf(t86,plain,
$false,
inference(connection,[status(thm),parent(t85:1)],[t85:1,t83:2]) ).
cnf(t87,plain,
ilf_type(cross_product(domain_of(sK14),range_of(sK14)),set_type),
inference(extension,[status(thm),parent(t83:3)],[f_26_4]) ).
cnf(t88,plain,
$false,
inference(connection,[status(thm),parent(t87:1)],[t87:1,t83:3]) ).
cnf(t89,plain,
ilf_type(sK10(sK14,cross_product(sK13,range_of(sK14))),set_type),
inference(extension,[status(thm),parent(t74:5)],[f_26_4]) ).
cnf(t90,plain,
$false,
inference(connection,[status(thm),parent(t89:1)],[t89:1,t74:5]) ).
cnf(t91,plain,
( ~ ilf_type(cross_product(sK13,range_of(sK14)),set_type)
| ~ ilf_type(cross_product(domain_of(sK14),range_of(sK14)),set_type)
| sP9(cross_product(domain_of(sK14),range_of(sK14)),sK10(sK14,cross_product(sK13,range_of(sK14))),cross_product(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t60:4)],[f_12_5]) ).
cnf(t92,plain,
$false,
inference(connection,[status(thm),parent(t91:1)],[t91:1,t60:4]) ).
cnf(t93,plain,
( ~ ilf_type(domain_of(sK14),set_type)
| ~ ilf_type(range_of(sK14),set_type)
| ilf_type(cross_product(domain_of(sK14),range_of(sK14)),set_type) ),
inference(extension,[status(thm),parent(t91:2)],[f_13_4]) ).
cnf(t94,plain,
$false,
inference(connection,[status(thm),parent(t93:1)],[t93:1,t91:2]) ).
cnf(t95,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t93:2)],[f_26_4]) ).
cnf(t96,plain,
$false,
inference(connection,[status(thm),parent(t95:1)],[t95:1,t93:2]) ).
cnf(t97,plain,
ilf_type(domain_of(sK14),set_type),
inference(extension,[status(thm),parent(t93:3)],[f_26_4]) ).
cnf(t98,plain,
$false,
inference(connection,[status(thm),parent(t97:1)],[t97:1,t93:3]) ).
cnf(t99,plain,
( ~ ilf_type(sK13,set_type)
| ~ ilf_type(range_of(sK14),set_type)
| ilf_type(cross_product(sK13,range_of(sK14)),set_type) ),
inference(extension,[status(thm),parent(t91:3)],[f_13_4]) ).
cnf(t100,plain,
$false,
inference(connection,[status(thm),parent(t99:1)],[t99:1,t91:3]) ).
cnf(t101,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t99:2)],[f_26_4]) ).
cnf(t102,plain,
$false,
inference(connection,[status(thm),parent(t101:1)],[t101:1,t99:2]) ).
cnf(t103,plain,
ilf_type(sK13,set_type),
inference(extension,[status(thm),parent(t99:3)],[f_26_4]) ).
cnf(t104,plain,
$false,
inference(connection,[status(thm),parent(t103:1)],[t103:1,t99:3]) ).
cnf(t105,plain,
ilf_type(sK10(sK14,cross_product(sK13,range_of(sK14))),set_type),
inference(extension,[status(thm),parent(t60:5)],[f_26_4]) ).
cnf(t106,plain,
$false,
inference(connection,[status(thm),parent(t105:1)],[t105:1,t60:5]) ).
cnf(t107,plain,
( ~ ilf_type(sK14,set_type)
| ~ ilf_type(cross_product(sK13,range_of(sK14)),set_type)
| sP10(sK14,cross_product(sK13,range_of(sK14))) ),
inference(extension,[status(thm),parent(t10:3)],[f_15_4]) ).
cnf(t108,plain,
$false,
inference(connection,[status(thm),parent(t107:1)],[t107:1,t10:3]) ).
cnf(t109,plain,
( ~ ilf_type(sK13,set_type)
| ~ ilf_type(range_of(sK14),set_type)
| ilf_type(cross_product(sK13,range_of(sK14)),set_type) ),
inference(extension,[status(thm),parent(t107:2)],[f_13_4]) ).
cnf(t110,plain,
$false,
inference(connection,[status(thm),parent(t109:1)],[t109:1,t107:2]) ).
cnf(t111,plain,
ilf_type(range_of(sK14),set_type),
inference(extension,[status(thm),parent(t109:2)],[f_26_4]) ).
cnf(t112,plain,
$false,
inference(connection,[status(thm),parent(t111:1)],[t111:1,t109:2]) ).
cnf(t113,plain,
ilf_type(sK13,set_type),
inference(extension,[status(thm),parent(t109:3)],[f_26_4]) ).
cnf(t114,plain,
$false,
inference(connection,[status(thm),parent(t113:1)],[t113:1,t109:3]) ).
cnf(t115,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t107:3)],[f_26_4]) ).
cnf(t116,plain,
$false,
inference(connection,[status(thm),parent(t115:1)],[t115:1,t107:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET647+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 22:44:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 209.06/209.37 % SZS status Theorem for theBenchmark
% 209.06/209.37 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------