%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET648+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 : n001.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 276.15s 276.46s
% Output : Proof 277.88s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('theBenchmark.p',p1) ).
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(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ? [D] : ilf_type(D,relation_type(C,B)) ) ),
file('theBenchmark.p',p5) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,domain_of(B))
<=> ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) ) ) ) ),
file('theBenchmark.p',p6) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(domain_of(B),set_type) ),
file('theBenchmark.p',p7) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,range_of(B))
<=> ? [D] :
( member(ordered_pair(D,C),B)
& ilf_type(D,set_type) ) ) ) ),
file('theBenchmark.p',p8) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(range_of(B),set_type) ),
file('theBenchmark.p',p9) ).
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(p11,axiom,
? [B] : ilf_type(B,binary_relation_type),
file('theBenchmark.p',p11) ).
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(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p14) ).
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(p16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ? [C] : ilf_type(C,subset_type(B)) ),
file('theBenchmark.p',p16) ).
fof(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( relation_like(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
=> ? [D] :
( ? [E] :
( C = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) ) ) ) ) ),
file('theBenchmark.p',p18) ).
fof(p19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('theBenchmark.p',p19) ).
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(p23,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('theBenchmark.p',p23) ).
fof(p24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p24) ).
fof(p25,axiom,
! [B] :
( ( ilf_type(B,set_type)
& empty(B) )
=> relation_like(B) ),
file('theBenchmark.p',p25) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_10,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> ilf_type(C,relation_type(domain_of(C),B)) ) ) ),
file('theBenchmark.p',prove_relset_1_10) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(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)],[p1]) ).
fof(f_1_2,plain,
! [U_2] :
( ! [U_1] :
( ! [U_0] :
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1)
| ~ ilf_type(U_0,set_type) )
| ~ ilf_type(U_1,set_type) )
| ~ ilf_type(U_2,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1)
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type)
| ~ ilf_type(U_2,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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]) ).
cnf(f_2_3,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_2]) ).
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]) ).
cnf(f_3_3,plain,
( 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(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(cross_product(U_4,U_6),cross_product(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_2]) ).
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]) ).
cnf(f_4_3,plain,
( 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(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ilf_type(U_8,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_8,relation_type(U_10,U_9))
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [B] :
( ! [C] :
( ? [D] : ilf_type(D,relation_type(C,B))
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p5]) ).
fof(f_5_2,plain,
! [U_13] :
( ! [U_12] :
( ? [U_11] : ilf_type(U_11,relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_13] :
( ! [U_12] :
( ilf_type(sK1(U_13,U_12),relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_13,U_12))],[f_5_2]) ).
cnf(f_5_4,plain,
( ilf_type(sK1(U_13,U_12),relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B] :
( ! [C] :
( ( ( member(C,domain_of(B))
| ! [D] :
( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type) ) )
& ( ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p6]) ).
fof(f_6_2,plain,
! [U_17] :
( ! [U_16] :
( ( ( member(U_16,domain_of(U_17))
| ! [U_15] :
( ~ member(ordered_pair(U_16,U_15),U_17)
| ~ ilf_type(U_15,set_type) ) )
& ( ? [U_14] :
( member(ordered_pair(U_16,U_14),U_17)
& ilf_type(U_14,set_type) )
| ~ member(U_16,domain_of(U_17)) ) )
| ~ ilf_type(U_16,set_type) )
| ~ ilf_type(U_17,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_17] :
( ! [U_16] :
( ( ( member(U_16,domain_of(U_17))
| ! [U_15] :
( ~ member(ordered_pair(U_16,U_15),U_17)
| ~ ilf_type(U_15,set_type) ) )
& ( ( member(ordered_pair(U_16,sK2(U_17,U_16)),U_17)
& ilf_type(sK2(U_17,U_16),set_type) )
| ~ member(U_16,domain_of(U_17)) ) )
| ~ ilf_type(U_16,set_type) )
| ~ ilf_type(U_17,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_17,U_16))],[f_6_2]) ).
cnf(f_6_4,plain,
( ilf_type(sK2(U_17,U_16),set_type)
| ~ member(U_16,domain_of(U_17))
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,binary_relation_type) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( member(ordered_pair(U_16,sK2(U_17,U_16)),U_17)
| ~ member(U_16,domain_of(U_17))
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,binary_relation_type) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( member(U_16,domain_of(U_17))
| ~ member(ordered_pair(U_16,U_15),U_17)
| ~ ilf_type(U_15,set_type)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,binary_relation_type) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [B] :
( ilf_type(domain_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p7]) ).
fof(f_7_2,plain,
! [U_18] :
( ilf_type(domain_of(U_18),set_type)
| ~ ilf_type(U_18,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ilf_type(domain_of(U_18),set_type)
| ~ ilf_type(U_18,binary_relation_type) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B] :
( ! [C] :
( ( ( member(C,range_of(B))
| ! [D] :
( ~ member(ordered_pair(D,C),B)
| ~ ilf_type(D,set_type) ) )
& ( ? [D] :
( member(ordered_pair(D,C),B)
& ilf_type(D,set_type) )
| ~ member(C,range_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p8]) ).
fof(f_8_2,plain,
! [U_22] :
( ! [U_21] :
( ( ( member(U_21,range_of(U_22))
| ! [U_20] :
( ~ member(ordered_pair(U_20,U_21),U_22)
| ~ ilf_type(U_20,set_type) ) )
& ( ? [U_19] :
( member(ordered_pair(U_19,U_21),U_22)
& ilf_type(U_19,set_type) )
| ~ member(U_21,range_of(U_22)) ) )
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_22] :
( ! [U_21] :
( ( ( member(U_21,range_of(U_22))
| ! [U_20] :
( ~ member(ordered_pair(U_20,U_21),U_22)
| ~ ilf_type(U_20,set_type) ) )
& ( ( member(ordered_pair(sK3(U_22,U_21),U_21),U_22)
& ilf_type(sK3(U_22,U_21),set_type) )
| ~ member(U_21,range_of(U_22)) ) )
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_22,U_21))],[f_8_2]) ).
cnf(f_8_4,plain,
( ilf_type(sK3(U_22,U_21),set_type)
| ~ member(U_21,range_of(U_22))
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( member(ordered_pair(sK3(U_22,U_21),U_21),U_22)
| ~ member(U_21,range_of(U_22))
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( member(U_21,range_of(U_22))
| ~ member(ordered_pair(U_20,U_21),U_22)
| ~ ilf_type(U_20,set_type)
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B] :
( ilf_type(range_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_9_2,plain,
! [U_23] :
( ilf_type(range_of(U_23),set_type)
| ~ ilf_type(U_23,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ilf_type(range_of(U_23),set_type)
| ~ ilf_type(U_23,binary_relation_type) ),
inference(clausify,[status(thm)],[f_9_2]) ).
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]) ).
cnf(f_10_3,plain,
( relation_like(U_24)
| ~ ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( ilf_type(U_24,set_type)
| ~ ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type)
| ~ relation_like(U_24)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
? [B] : ilf_type(B,binary_relation_type),
inference(fof_nnf,[status(thm)],[p11]) ).
fof(f_11_2,plain,
? [U_25] : ilf_type(U_25,binary_relation_type),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
ilf_type(sK4,binary_relation_type),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4)],[f_11_2]) ).
cnf(f_11_4,plain,
ilf_type(sK4,binary_relation_type),
inference(clausify,[status(thm)],[f_11_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]) ).
cnf(f_12_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_12_3]) ).
cnf(f_12_5,plain,
( ilf_type(sK5(U_29,U_28),set_type)
| subset(U_29,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( member(sK5(U_29,U_28),U_29)
| subset(U_29,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( ~ member(sK5(U_29,U_28),U_28)
| subset(U_29,U_28)
| ~ ilf_type(U_28,set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
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]) ).
cnf(f_13_3,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_2]) ).
fof(f_14_1,plain,
! [B] :
( ! [C] :
( ilf_type(ordered_pair(B,C),set_type)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_14_2,plain,
! [U_33] :
( ! [U_32] :
( ilf_type(ordered_pair(U_33,U_32),set_type)
| ~ ilf_type(U_32,set_type) )
| ~ ilf_type(U_33,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ilf_type(ordered_pair(U_33,U_32),set_type)
| ~ ilf_type(U_32,set_type)
| ~ ilf_type(U_33,set_type) ),
inference(clausify,[status(thm)],[f_14_2]) ).
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]) ).
cnf(f_15_3,plain,
( 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(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( ilf_type(U_34,subset_type(U_35))
| ~ ilf_type(U_34,member_type(power_set(U_35)))
| ~ ilf_type(U_34,set_type)
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p16]) ).
fof(f_16_2,plain,
! [U_37] :
( ? [U_36] : ilf_type(U_36,subset_type(U_37))
| ~ ilf_type(U_37,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_37] :
( ilf_type(sK6(U_37),subset_type(U_37))
| ~ ilf_type(U_37,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6(U_37))],[f_16_2]) ).
cnf(f_16_4,plain,
( ilf_type(sK6(U_37),subset_type(U_37))
| ~ ilf_type(U_37,set_type) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_17_2,plain,
! [U_38] :
( subset(U_38,U_38)
| ~ ilf_type(U_38,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( subset(U_38,U_38)
| ~ ilf_type(U_38,set_type) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [B] :
( ( ( relation_like(B)
| ? [C] :
( ! [D] :
( ! [E] :
( C != ordered_pair(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
& member(C,B)
& ilf_type(C,set_type) ) )
& ( ! [C] :
( ? [D] :
( ? [E] :
( C = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
| ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(f_18_2,plain,
! [U_45] :
( ( ( relation_like(U_45)
| ? [U_44] :
( ! [U_43] :
( ! [U_42] :
( U_44 != ordered_pair(U_43,U_42)
| ~ ilf_type(U_42,set_type) )
| ~ ilf_type(U_43,set_type) )
& member(U_44,U_45)
& ilf_type(U_44,set_type) ) )
& ( ! [U_41] :
( ? [U_40] :
( ? [U_39] :
( U_41 = ordered_pair(U_40,U_39)
& ilf_type(U_39,set_type) )
& ilf_type(U_40,set_type) )
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type) )
| ~ relation_like(U_45) ) )
| ~ ilf_type(U_45,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_45] :
( ( ( relation_like(U_45)
| ? [U_44] :
( ! [U_43] :
( ! [U_42] :
( U_44 != ordered_pair(U_43,U_42)
| ~ ilf_type(U_42,set_type) )
| ~ ilf_type(U_43,set_type) )
& member(U_44,U_45)
& ilf_type(U_44,set_type) ) )
& ( ! [U_41] :
( ( ? [U_39] :
( U_41 = ordered_pair(sK7(U_45,U_41),U_39)
& ilf_type(U_39,set_type) )
& ilf_type(sK7(U_45,U_41),set_type) )
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type) )
| ~ relation_like(U_45) ) )
| ~ ilf_type(U_45,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7(U_45,U_41))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_45] :
( ( ( relation_like(U_45)
| ? [U_44] :
( ! [U_43] :
( ! [U_42] :
( U_44 != ordered_pair(U_43,U_42)
| ~ ilf_type(U_42,set_type) )
| ~ ilf_type(U_43,set_type) )
& member(U_44,U_45)
& ilf_type(U_44,set_type) ) )
& ( ! [U_41] :
( ( U_41 = ordered_pair(sK7(U_45,U_41),sK8(U_45,U_41))
& ilf_type(sK8(U_45,U_41),set_type)
& ilf_type(sK7(U_45,U_41),set_type) )
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type) )
| ~ relation_like(U_45) ) )
| ~ ilf_type(U_45,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_39,sK8(U_45,U_41))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_45] :
( ( ( relation_like(U_45)
| ( ! [U_43] :
( ! [U_42] :
( sK9(U_45) != ordered_pair(U_43,U_42)
| ~ ilf_type(U_42,set_type) )
| ~ ilf_type(U_43,set_type) )
& member(sK9(U_45),U_45)
& ilf_type(sK9(U_45),set_type) ) )
& ( ! [U_41] :
( ( U_41 = ordered_pair(sK7(U_45,U_41),sK8(U_45,U_41))
& ilf_type(sK8(U_45,U_41),set_type)
& ilf_type(sK7(U_45,U_41),set_type) )
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type) )
| ~ relation_like(U_45) ) )
| ~ ilf_type(U_45,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_44,sK9(U_45))],[f_18_4]) ).
cnf(f_18_6,plain,
( ilf_type(sK7(U_45,U_41),set_type)
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type)
| ~ relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( ilf_type(sK8(U_45,U_41),set_type)
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type)
| ~ relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_8,plain,
( U_41 = ordered_pair(sK7(U_45,U_41),sK8(U_45,U_41))
| ~ member(U_41,U_45)
| ~ ilf_type(U_41,set_type)
| ~ relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_9,plain,
( ilf_type(sK9(U_45),set_type)
| relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_10,plain,
( member(sK9(U_45),U_45)
| relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_11,plain,
( sK9(U_45) != ordered_pair(U_43,U_42)
| ~ ilf_type(U_42,set_type)
| ~ ilf_type(U_43,set_type)
| relation_like(U_45)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(f_19_2,plain,
! [U_48] :
( ! [U_47] :
( ! [U_46] :
( relation_like(U_46)
| ~ ilf_type(U_46,subset_type(cross_product(U_48,U_47))) )
| ~ ilf_type(U_47,set_type) )
| ~ ilf_type(U_48,set_type) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( relation_like(U_46)
| ~ ilf_type(U_46,subset_type(cross_product(U_48,U_47)))
| ~ ilf_type(U_47,set_type)
| ~ ilf_type(U_48,set_type) ),
inference(clausify,[status(thm)],[f_19_2]) ).
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]) ).
cnf(f_20_4,plain,
( 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(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ilf_type(sK10(U_52,U_51),set_type)
| member(U_52,power_set(U_51))
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( member(sK10(U_52,U_51),U_52)
| member(U_52,power_set(U_51))
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( ~ member(sK10(U_52,U_51),U_51)
| member(U_52,power_set(U_51))
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
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]) ).
cnf(f_21_3,plain,
( ~ empty(power_set(U_53))
| ~ ilf_type(U_53,set_type) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ilf_type(power_set(U_53),set_type)
| ~ ilf_type(U_53,set_type) ),
inference(clausify,[status(thm)],[f_21_2]) ).
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]) ).
cnf(f_22_3,plain,
( 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(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ilf_type(U_55,member_type(U_54))
| ~ member(U_55,U_54)
| ~ ilf_type(U_54,set_type)
| empty(U_54)
| ~ ilf_type(U_55,set_type) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(fof_nnf,[status(thm)],[p23]) ).
fof(f_23_2,plain,
! [U_57] :
( ? [U_56] : ilf_type(U_56,member_type(U_57))
| ~ ilf_type(U_57,set_type)
| empty(U_57) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_57] :
( ilf_type(sK11(U_57),member_type(U_57))
| ~ ilf_type(U_57,set_type)
| empty(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_56,sK11(U_57))],[f_23_2]) ).
cnf(f_23_4,plain,
( ilf_type(sK11(U_57),member_type(U_57))
| ~ ilf_type(U_57,set_type)
| empty(U_57) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [B] :
( ( ( empty(B)
| ? [C] :
( member(C,B)
& ilf_type(C,set_type) ) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p24]) ).
fof(f_24_2,plain,
! [U_60] :
( ( ( empty(U_60)
| ? [U_59] :
( member(U_59,U_60)
& ilf_type(U_59,set_type) ) )
& ( ! [U_58] :
( ~ member(U_58,U_60)
| ~ ilf_type(U_58,set_type) )
| ~ empty(U_60) ) )
| ~ ilf_type(U_60,set_type) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_60] :
( ( ( empty(U_60)
| ( member(sK12(U_60),U_60)
& ilf_type(sK12(U_60),set_type) ) )
& ( ! [U_58] :
( ~ member(U_58,U_60)
| ~ ilf_type(U_58,set_type) )
| ~ empty(U_60) ) )
| ~ ilf_type(U_60,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_59,sK12(U_60))],[f_24_2]) ).
cnf(f_24_4,plain,
( ~ member(U_58,U_60)
| ~ ilf_type(U_58,set_type)
| ~ empty(U_60)
| ~ ilf_type(U_60,set_type) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( ilf_type(sK12(U_60),set_type)
| empty(U_60)
| ~ ilf_type(U_60,set_type) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( member(sK12(U_60),U_60)
| empty(U_60)
| ~ ilf_type(U_60,set_type) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p25]) ).
fof(f_25_2,plain,
! [U_61] :
( relation_like(U_61)
| ~ ilf_type(U_61,set_type)
| ~ empty(U_61) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( relation_like(U_61)
| ~ ilf_type(U_61,set_type)
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_25_2]) ).
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]) ).
cnf(f_26_3,plain,
ilf_type(U_62,set_type),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> ilf_type(C,relation_type(domain_of(C),B)) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_10]) ).
fof(f_27_2,negated_conjecture,
? [B] :
( ? [C] :
( ~ ilf_type(C,relation_type(domain_of(C),B))
& subset(range_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(domain_of(U_63),U_64))
& subset(range_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(domain_of(U_63),sK13))
& subset(range_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(domain_of(sK14),sK13))
& subset(range_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]) ).
cnf(f_27_6,negated_conjecture,
ilf_type(sK13,set_type),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_7,negated_conjecture,
ilf_type(sK14,binary_relation_type),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_8,negated_conjecture,
subset(range_of(sK14),sK13),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_9,negated_conjecture,
~ ilf_type(sK14,relation_type(domain_of(sK14),sK13)),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_10_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_4]) ).
cnf(f_10_5_simplified,plain,
( ilf_type(U_24,binary_relation_type)
| ~ ilf_type(U_24,set_type)
| ~ relation_like(U_24) ),
inference(simplify_clause,[status(thm)],[f_10_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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,
( domain_of(Eq_x_0) = domain_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( range_of(Eq_x_0) = range_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( cross_product(Eq_x_0,Eq_x_1) = cross_product(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( subset_type(Eq_x_0) = subset_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_type(Eq_x_0,Eq_x_1) = relation_type(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( member_type(Eq_x_0) = member_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( ilf_type(Eq_y_0,Eq_y_1)
| ~ ilf_type(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,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(equality_25,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET648+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
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 22:50:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 276.15/276.46 % SZS status Theorem for theBenchmark
% 276.15/276.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------