%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET668+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 : n019.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 166.73s 167.09s
% Output : Proof 168.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ( subset(C,B)
& subset(B,C) )
=> B = C ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
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)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( C = D
& member(C,B) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('theBenchmark.p',p4) ).
fof(p5,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',p5) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ? [D] : ilf_type(D,relation_type(C,B)) ) ),
file('theBenchmark.p',p6) ).
fof(p7,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',p7) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(D,E),B)
=> member(ordered_pair(D,E),C) ) ) ) ) ) ),
file('theBenchmark.p',p8) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(C,B)
& subset(B,C) ) ) ) ),
file('theBenchmark.p',p9) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(domain_of(B),set_type) ),
file('theBenchmark.p',p10) ).
fof(p11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p11) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(range_of(B),set_type) ),
file('theBenchmark.p',p12) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p14) ).
fof(p15,axiom,
? [B] : ilf_type(B,binary_relation_type),
file('theBenchmark.p',p15) ).
fof(p16,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',p16) ).
fof(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ? [C] : ilf_type(C,subset_type(B)) ),
file('theBenchmark.p',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p18) ).
fof(p19,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,B) ),
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)
=> ( 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',p24) ).
fof(p25,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',p25) ).
fof(p26,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p26) ).
fof(p27,axiom,
! [B] :
( ( ilf_type(B,set_type)
& empty(B) )
=> relation_like(B) ),
file('theBenchmark.p',p27) ).
fof(p28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('theBenchmark.p',p28) ).
fof(p29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('theBenchmark.p',p29) ).
fof(p30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('theBenchmark.p',p30) ).
fof(p31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('theBenchmark.p',p31) ).
fof(p32,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p32) ).
fof(prove_relset_1_31,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_31) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( B = C
| ~ subset(C,B)
| ~ subset(B,C)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_1] :
( ! [U_0] :
( U_1 = U_0
| ~ subset(U_0,U_1)
| ~ subset(U_1,U_0)
| ~ ilf_type(U_0,set_type) )
| ~ ilf_type(U_1,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( U_1 = U_0
| ~ subset(U_0,U_1)
| ~ subset(U_1,U_0)
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) )
| ~ subset(identity_relation_of(D),E)
| ~ ilf_type(E,relation_type(B,C)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_5] :
( ! [U_4] :
( ! [U_3] :
( ! [U_2] :
( ( subset(U_3,range(U_5,U_4,U_2))
& subset(U_3,domain(U_5,U_4,U_2)) )
| ~ subset(identity_relation_of(U_3),U_2)
| ~ ilf_type(U_2,relation_type(U_5,U_4)) )
| ~ ilf_type(U_3,set_type) )
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( subset(U_3,domain(U_5,U_4,U_2))
| ~ subset(identity_relation_of(U_3),U_2)
| ~ ilf_type(U_2,relation_type(U_5,U_4))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_3,range(U_5,U_4,U_2))
| ~ subset(identity_relation_of(U_3),U_2)
| ~ ilf_type(U_2,relation_type(U_5,U_4))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( member(ordered_pair(C,D),identity_relation_of(B))
| C != D
| ~ member(C,B) )
& ( ( C = D
& member(C,B) )
| ~ member(ordered_pair(C,D),identity_relation_of(B)) ) )
| ~ 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_8] :
( ! [U_7] :
( ! [U_6] :
( ( ( member(ordered_pair(U_7,U_6),identity_relation_of(U_8))
| U_7 != U_6
| ~ member(U_7,U_8) )
& ( ( U_7 = U_6
& member(U_7,U_8) )
| ~ member(ordered_pair(U_7,U_6),identity_relation_of(U_8)) ) )
| ~ ilf_type(U_6,set_type) )
| ~ ilf_type(U_7,set_type) )
| ~ ilf_type(U_8,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( member(U_7,U_8)
| ~ member(ordered_pair(U_7,U_6),identity_relation_of(U_8))
| ~ ilf_type(U_6,set_type)
| ~ ilf_type(U_7,set_type)
| ~ ilf_type(U_8,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( U_7 = U_6
| ~ member(ordered_pair(U_7,U_6),identity_relation_of(U_8))
| ~ ilf_type(U_6,set_type)
| ~ ilf_type(U_7,set_type)
| ~ ilf_type(U_8,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( member(ordered_pair(U_7,U_6),identity_relation_of(U_8))
| U_7 != U_6
| ~ member(U_7,U_8)
| ~ ilf_type(U_6,set_type)
| ~ ilf_type(U_7,set_type)
| ~ ilf_type(U_8,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [B] :
( ilf_type(identity_relation_of(B),binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(f_4_2,plain,
! [U_9] :
( ilf_type(identity_relation_of(U_9),binary_relation_type)
| ~ ilf_type(U_9,set_type) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ilf_type(identity_relation_of(U_9),binary_relation_type)
| ~ ilf_type(U_9,set_type) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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)],[p5]) ).
fof(f_5_2,plain,
! [U_13] :
( ! [U_12] :
( ( ! [U_11] :
( ilf_type(U_11,subset_type(cross_product(U_13,U_12)))
| ~ ilf_type(U_11,relation_type(U_13,U_12)) )
& ! [U_10] :
( ilf_type(U_10,relation_type(U_13,U_12))
| ~ ilf_type(U_10,subset_type(cross_product(U_13,U_12))) ) )
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ilf_type(U_10,relation_type(U_13,U_12))
| ~ ilf_type(U_10,subset_type(cross_product(U_13,U_12)))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( ilf_type(U_11,subset_type(cross_product(U_13,U_12)))
| ~ ilf_type(U_11,relation_type(U_13,U_12))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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)],[p6]) ).
fof(f_6_2,plain,
! [U_16] :
( ! [U_15] :
( ? [U_14] : ilf_type(U_14,relation_type(U_15,U_16))
| ~ ilf_type(U_15,set_type) )
| ~ ilf_type(U_16,set_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_16] :
( ! [U_15] :
( ilf_type(sK1(U_16,U_15),relation_type(U_15,U_16))
| ~ ilf_type(U_15,set_type) )
| ~ ilf_type(U_16,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_14,sK1(U_16,U_15))],[f_6_2]) ).
cnf(f_6_4,plain,
( ilf_type(sK1(U_16,U_15),relation_type(U_15,U_16))
| ~ ilf_type(U_15,set_type)
| ~ ilf_type(U_16,set_type) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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)],[p7]) ).
fof(f_7_2,plain,
! [U_20] :
( ! [U_19] :
( ( ( subset(U_20,U_19)
| ? [U_18] :
( ~ member(U_18,U_19)
& member(U_18,U_20)
& ilf_type(U_18,set_type) ) )
& ( ! [U_17] :
( member(U_17,U_19)
| ~ member(U_17,U_20)
| ~ ilf_type(U_17,set_type) )
| ~ subset(U_20,U_19) ) )
| ~ ilf_type(U_19,set_type) )
| ~ ilf_type(U_20,set_type) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_20] :
( ! [U_19] :
( ( ( subset(U_20,U_19)
| ( ~ member(sK2(U_20,U_19),U_19)
& member(sK2(U_20,U_19),U_20)
& ilf_type(sK2(U_20,U_19),set_type) ) )
& ( ! [U_17] :
( member(U_17,U_19)
| ~ member(U_17,U_20)
| ~ ilf_type(U_17,set_type) )
| ~ subset(U_20,U_19) ) )
| ~ ilf_type(U_19,set_type) )
| ~ ilf_type(U_20,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2(U_20,U_19))],[f_7_2]) ).
cnf(f_7_4,plain,
( member(U_17,U_19)
| ~ member(U_17,U_20)
| ~ ilf_type(U_17,set_type)
| ~ subset(U_20,U_19)
| ~ ilf_type(U_19,set_type)
| ~ ilf_type(U_20,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ilf_type(sK2(U_20,U_19),set_type)
| subset(U_20,U_19)
| ~ ilf_type(U_19,set_type)
| ~ ilf_type(U_20,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( member(sK2(U_20,U_19),U_20)
| subset(U_20,U_19)
| ~ ilf_type(U_19,set_type)
| ~ ilf_type(U_20,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( ~ member(sK2(U_20,U_19),U_19)
| subset(U_20,U_19)
| ~ ilf_type(U_19,set_type)
| ~ ilf_type(U_20,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [B] :
( ! [C] :
( ( ( subset(B,C)
| ? [D] :
( ? [E] :
( ~ member(ordered_pair(D,E),C)
& member(ordered_pair(D,E),B)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) ) )
& ( ! [D] :
( ! [E] :
( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p8]) ).
fof(f_8_2,plain,
! [U_26] :
( ! [U_25] :
( ( ( subset(U_26,U_25)
| ? [U_24] :
( ? [U_23] :
( ~ member(ordered_pair(U_24,U_23),U_25)
& member(ordered_pair(U_24,U_23),U_26)
& ilf_type(U_23,set_type) )
& ilf_type(U_24,set_type) ) )
& ( ! [U_22] :
( ! [U_21] :
( member(ordered_pair(U_22,U_21),U_25)
| ~ member(ordered_pair(U_22,U_21),U_26)
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,set_type) )
| ~ subset(U_26,U_25) ) )
| ~ ilf_type(U_25,binary_relation_type) )
| ~ ilf_type(U_26,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_26] :
( ! [U_25] :
( ( ( subset(U_26,U_25)
| ( ? [U_23] :
( ~ member(ordered_pair(sK3(U_26,U_25),U_23),U_25)
& member(ordered_pair(sK3(U_26,U_25),U_23),U_26)
& ilf_type(U_23,set_type) )
& ilf_type(sK3(U_26,U_25),set_type) ) )
& ( ! [U_22] :
( ! [U_21] :
( member(ordered_pair(U_22,U_21),U_25)
| ~ member(ordered_pair(U_22,U_21),U_26)
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,set_type) )
| ~ subset(U_26,U_25) ) )
| ~ ilf_type(U_25,binary_relation_type) )
| ~ ilf_type(U_26,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_26,U_25))],[f_8_2]) ).
fof(f_8_4,plain,
! [U_26] :
( ! [U_25] :
( ( ( subset(U_26,U_25)
| ( ~ member(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
& member(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_26)
& ilf_type(sK4(U_26,U_25),set_type)
& ilf_type(sK3(U_26,U_25),set_type) ) )
& ( ! [U_22] :
( ! [U_21] :
( member(ordered_pair(U_22,U_21),U_25)
| ~ member(ordered_pair(U_22,U_21),U_26)
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,set_type) )
| ~ subset(U_26,U_25) ) )
| ~ ilf_type(U_25,binary_relation_type) )
| ~ ilf_type(U_26,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_23,sK4(U_26,U_25))],[f_8_3]) ).
cnf(f_8_5,plain,
( member(ordered_pair(U_22,U_21),U_25)
| ~ member(ordered_pair(U_22,U_21),U_26)
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,set_type)
| ~ subset(U_26,U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_26,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( ilf_type(sK3(U_26,U_25),set_type)
| subset(U_26,U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_26,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ilf_type(sK4(U_26,U_25),set_type)
| subset(U_26,U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_26,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( member(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_26)
| subset(U_26,U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_26,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_9,plain,
( ~ member(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
| subset(U_26,U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_26,binary_relation_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [B] :
( ! [C] :
( ( ( B = C
| ~ subset(C,B)
| ~ subset(B,C) )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_9_2,plain,
! [U_28] :
( ! [U_27] :
( ( ( U_28 = U_27
| ~ subset(U_27,U_28)
| ~ subset(U_28,U_27) )
& ( ( subset(U_27,U_28)
& subset(U_28,U_27) )
| U_28 != U_27 ) )
| ~ ilf_type(U_27,set_type) )
| ~ ilf_type(U_28,set_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( subset(U_28,U_27)
| U_28 != U_27
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( subset(U_27,U_28)
| U_28 != U_27
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( U_28 = U_27
| ~ subset(U_27,U_28)
| ~ subset(U_28,U_27)
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [B] :
( ilf_type(domain_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p10]) ).
fof(f_10_2,plain,
! [U_29] :
( ilf_type(domain_of(U_29),set_type)
| ~ ilf_type(U_29,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ilf_type(domain_of(U_29),set_type)
| ~ ilf_type(U_29,binary_relation_type) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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)],[p11]) ).
fof(f_11_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_11_1]) ).
cnf(f_11_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_11_2]) ).
fof(f_12_1,plain,
! [B] :
( ilf_type(range_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p12]) ).
fof(f_12_2,plain,
! [U_32] :
( ilf_type(range_of(U_32),set_type)
| ~ ilf_type(U_32,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ilf_type(range_of(U_32),set_type)
| ~ ilf_type(U_32,binary_relation_type) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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)],[p13]) ).
fof(f_13_2,plain,
! [U_34] :
( ! [U_33] :
( ilf_type(ordered_pair(U_34,U_33),set_type)
| ~ ilf_type(U_33,set_type) )
| ~ ilf_type(U_34,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ilf_type(ordered_pair(U_34,U_33),set_type)
| ~ ilf_type(U_33,set_type)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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)],[p14]) ).
fof(f_14_2,plain,
! [U_35] :
( ( ( ilf_type(U_35,binary_relation_type)
| ~ ilf_type(U_35,set_type)
| ~ relation_like(U_35) )
& ( ( ilf_type(U_35,set_type)
& relation_like(U_35) )
| ~ ilf_type(U_35,binary_relation_type) ) )
| ~ ilf_type(U_35,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( relation_like(U_35)
| ~ ilf_type(U_35,binary_relation_type)
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( ilf_type(U_35,set_type)
| ~ ilf_type(U_35,binary_relation_type)
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( ilf_type(U_35,binary_relation_type)
| ~ ilf_type(U_35,set_type)
| ~ relation_like(U_35)
| ~ ilf_type(U_35,set_type) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
? [B] : ilf_type(B,binary_relation_type),
inference(fof_nnf,[status(thm)],[p15]) ).
fof(f_15_2,plain,
? [U_36] : ilf_type(U_36,binary_relation_type),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
ilf_type(sK5,binary_relation_type),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5)],[f_15_2]) ).
cnf(f_15_4,plain,
ilf_type(sK5,binary_relation_type),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_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)],[p16]) ).
fof(f_16_2,plain,
! [U_38] :
( ! [U_37] :
( ( ( ilf_type(U_37,subset_type(U_38))
| ~ ilf_type(U_37,member_type(power_set(U_38))) )
& ( ilf_type(U_37,member_type(power_set(U_38)))
| ~ ilf_type(U_37,subset_type(U_38)) ) )
| ~ ilf_type(U_37,set_type) )
| ~ ilf_type(U_38,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ilf_type(U_37,member_type(power_set(U_38)))
| ~ ilf_type(U_37,subset_type(U_38))
| ~ ilf_type(U_37,set_type)
| ~ ilf_type(U_38,set_type) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( ilf_type(U_37,subset_type(U_38))
| ~ ilf_type(U_37,member_type(power_set(U_38)))
| ~ ilf_type(U_37,set_type)
| ~ ilf_type(U_38,set_type) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_17_2,plain,
! [U_40] :
( ? [U_39] : ilf_type(U_39,subset_type(U_40))
| ~ ilf_type(U_40,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_40] :
( ilf_type(sK6(U_40),subset_type(U_40))
| ~ ilf_type(U_40,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6(U_40))],[f_17_2]) ).
cnf(f_17_4,plain,
( ilf_type(sK6(U_40),subset_type(U_40))
| ~ ilf_type(U_40,set_type) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(f_18_2,plain,
! [U_41] :
( subset(U_41,U_41)
| ~ ilf_type(U_41,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( subset(U_41,U_41)
| ~ ilf_type(U_41,set_type) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(f_19_2,plain,
! [U_42] :
( subset(U_42,U_42)
| ~ ilf_type(U_42,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( subset(U_42,U_42)
| ~ ilf_type(U_42,binary_relation_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_46] :
( ! [U_45] :
( ( ( member(U_46,power_set(U_45))
| ? [U_44] :
( ~ member(U_44,U_45)
& member(U_44,U_46)
& ilf_type(U_44,set_type) ) )
& ( ! [U_43] :
( member(U_43,U_45)
| ~ member(U_43,U_46)
| ~ ilf_type(U_43,set_type) )
| ~ member(U_46,power_set(U_45)) ) )
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_46] :
( ! [U_45] :
( ( ( member(U_46,power_set(U_45))
| ( ~ member(sK7(U_46,U_45),U_45)
& member(sK7(U_46,U_45),U_46)
& ilf_type(sK7(U_46,U_45),set_type) ) )
& ( ! [U_43] :
( member(U_43,U_45)
| ~ member(U_43,U_46)
| ~ ilf_type(U_43,set_type) )
| ~ member(U_46,power_set(U_45)) ) )
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_44,sK7(U_46,U_45))],[f_20_2]) ).
cnf(f_20_4,plain,
( member(U_43,U_45)
| ~ member(U_43,U_46)
| ~ ilf_type(U_43,set_type)
| ~ member(U_46,power_set(U_45))
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ilf_type(sK7(U_46,U_45),set_type)
| member(U_46,power_set(U_45))
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( member(sK7(U_46,U_45),U_46)
| member(U_46,power_set(U_45))
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,set_type) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( ~ member(sK7(U_46,U_45),U_45)
| member(U_46,power_set(U_45))
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,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_47] :
( ( ilf_type(power_set(U_47),set_type)
& ~ empty(power_set(U_47)) )
| ~ ilf_type(U_47,set_type) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ empty(power_set(U_47))
| ~ ilf_type(U_47,set_type) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ilf_type(power_set(U_47),set_type)
| ~ ilf_type(U_47,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_49] :
( ! [U_48] :
( ( ( ilf_type(U_49,member_type(U_48))
| ~ member(U_49,U_48) )
& ( member(U_49,U_48)
| ~ ilf_type(U_49,member_type(U_48)) ) )
| ~ ilf_type(U_48,set_type)
| empty(U_48) )
| ~ ilf_type(U_49,set_type) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( member(U_49,U_48)
| ~ ilf_type(U_49,member_type(U_48))
| ~ ilf_type(U_48,set_type)
| empty(U_48)
| ~ ilf_type(U_49,set_type) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ilf_type(U_49,member_type(U_48))
| ~ member(U_49,U_48)
| ~ ilf_type(U_48,set_type)
| empty(U_48)
| ~ ilf_type(U_49,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_51] :
( ? [U_50] : ilf_type(U_50,member_type(U_51))
| ~ ilf_type(U_51,set_type)
| empty(U_51) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_51] :
( ilf_type(sK8(U_51),member_type(U_51))
| ~ ilf_type(U_51,set_type)
| empty(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_50,sK8(U_51))],[f_23_2]) ).
cnf(f_23_4,plain,
( ilf_type(sK8(U_51),member_type(U_51))
| ~ ilf_type(U_51,set_type)
| empty(U_51) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_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)],[p24]) ).
fof(f_24_2,plain,
! [U_58] :
( ( ( relation_like(U_58)
| ? [U_57] :
( ! [U_56] :
( ! [U_55] :
( U_57 != ordered_pair(U_56,U_55)
| ~ ilf_type(U_55,set_type) )
| ~ ilf_type(U_56,set_type) )
& member(U_57,U_58)
& ilf_type(U_57,set_type) ) )
& ( ! [U_54] :
( ? [U_53] :
( ? [U_52] :
( U_54 = ordered_pair(U_53,U_52)
& ilf_type(U_52,set_type) )
& ilf_type(U_53,set_type) )
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type) )
| ~ relation_like(U_58) ) )
| ~ ilf_type(U_58,set_type) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_58] :
( ( ( relation_like(U_58)
| ? [U_57] :
( ! [U_56] :
( ! [U_55] :
( U_57 != ordered_pair(U_56,U_55)
| ~ ilf_type(U_55,set_type) )
| ~ ilf_type(U_56,set_type) )
& member(U_57,U_58)
& ilf_type(U_57,set_type) ) )
& ( ! [U_54] :
( ( ? [U_52] :
( U_54 = ordered_pair(sK9(U_58,U_54),U_52)
& ilf_type(U_52,set_type) )
& ilf_type(sK9(U_58,U_54),set_type) )
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type) )
| ~ relation_like(U_58) ) )
| ~ ilf_type(U_58,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_53,sK9(U_58,U_54))],[f_24_2]) ).
fof(f_24_4,plain,
! [U_58] :
( ( ( relation_like(U_58)
| ? [U_57] :
( ! [U_56] :
( ! [U_55] :
( U_57 != ordered_pair(U_56,U_55)
| ~ ilf_type(U_55,set_type) )
| ~ ilf_type(U_56,set_type) )
& member(U_57,U_58)
& ilf_type(U_57,set_type) ) )
& ( ! [U_54] :
( ( U_54 = ordered_pair(sK9(U_58,U_54),sK10(U_58,U_54))
& ilf_type(sK10(U_58,U_54),set_type)
& ilf_type(sK9(U_58,U_54),set_type) )
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type) )
| ~ relation_like(U_58) ) )
| ~ ilf_type(U_58,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_52,sK10(U_58,U_54))],[f_24_3]) ).
fof(f_24_5,plain,
! [U_58] :
( ( ( relation_like(U_58)
| ( ! [U_56] :
( ! [U_55] :
( sK11(U_58) != ordered_pair(U_56,U_55)
| ~ ilf_type(U_55,set_type) )
| ~ ilf_type(U_56,set_type) )
& member(sK11(U_58),U_58)
& ilf_type(sK11(U_58),set_type) ) )
& ( ! [U_54] :
( ( U_54 = ordered_pair(sK9(U_58,U_54),sK10(U_58,U_54))
& ilf_type(sK10(U_58,U_54),set_type)
& ilf_type(sK9(U_58,U_54),set_type) )
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type) )
| ~ relation_like(U_58) ) )
| ~ ilf_type(U_58,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_57,sK11(U_58))],[f_24_4]) ).
cnf(f_24_6,plain,
( ilf_type(sK9(U_58,U_54),set_type)
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type)
| ~ relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,plain,
( ilf_type(sK10(U_58,U_54),set_type)
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type)
| ~ relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,plain,
( U_54 = ordered_pair(sK9(U_58,U_54),sK10(U_58,U_54))
| ~ member(U_54,U_58)
| ~ ilf_type(U_54,set_type)
| ~ relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_9,plain,
( ilf_type(sK11(U_58),set_type)
| relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_10,plain,
( member(sK11(U_58),U_58)
| relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_11,plain,
( sK11(U_58) != ordered_pair(U_56,U_55)
| ~ ilf_type(U_55,set_type)
| ~ ilf_type(U_56,set_type)
| relation_like(U_58)
| ~ ilf_type(U_58,set_type) ),
inference(clausify,[status(thm)],[f_24_5]) ).
fof(f_25_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)],[p25]) ).
fof(f_25_2,plain,
! [U_61] :
( ! [U_60] :
( ! [U_59] :
( relation_like(U_59)
| ~ ilf_type(U_59,subset_type(cross_product(U_61,U_60))) )
| ~ ilf_type(U_60,set_type) )
| ~ ilf_type(U_61,set_type) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( relation_like(U_59)
| ~ ilf_type(U_59,subset_type(cross_product(U_61,U_60)))
| ~ ilf_type(U_60,set_type)
| ~ ilf_type(U_61,set_type) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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)],[p26]) ).
fof(f_26_2,plain,
! [U_64] :
( ( ( empty(U_64)
| ? [U_63] :
( member(U_63,U_64)
& ilf_type(U_63,set_type) ) )
& ( ! [U_62] :
( ~ member(U_62,U_64)
| ~ ilf_type(U_62,set_type) )
| ~ empty(U_64) ) )
| ~ ilf_type(U_64,set_type) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_64] :
( ( ( empty(U_64)
| ( member(sK12(U_64),U_64)
& ilf_type(sK12(U_64),set_type) ) )
& ( ! [U_62] :
( ~ member(U_62,U_64)
| ~ ilf_type(U_62,set_type) )
| ~ empty(U_64) ) )
| ~ ilf_type(U_64,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_63,sK12(U_64))],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ member(U_62,U_64)
| ~ ilf_type(U_62,set_type)
| ~ empty(U_64)
| ~ ilf_type(U_64,set_type) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( ilf_type(sK12(U_64),set_type)
| empty(U_64)
| ~ ilf_type(U_64,set_type) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( member(sK12(U_64),U_64)
| empty(U_64)
| ~ ilf_type(U_64,set_type) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p27]) ).
fof(f_27_2,plain,
! [U_65] :
( relation_like(U_65)
| ~ ilf_type(U_65,set_type)
| ~ empty(U_65) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( relation_like(U_65)
| ~ ilf_type(U_65,set_type)
| ~ empty(U_65) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p28]) ).
fof(f_28_2,plain,
! [U_68] :
( ! [U_67] :
( ! [U_66] :
( domain(U_68,U_67,U_66) = domain_of(U_66)
| ~ ilf_type(U_66,relation_type(U_68,U_67)) )
| ~ ilf_type(U_67,set_type) )
| ~ ilf_type(U_68,set_type) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( domain(U_68,U_67,U_66) = domain_of(U_66)
| ~ ilf_type(U_66,relation_type(U_68,U_67))
| ~ ilf_type(U_67,set_type)
| ~ ilf_type(U_68,set_type) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p29]) ).
fof(f_29_2,plain,
! [U_71] :
( ! [U_70] :
( ! [U_69] :
( ilf_type(domain(U_71,U_70,U_69),subset_type(U_71))
| ~ ilf_type(U_69,relation_type(U_71,U_70)) )
| ~ ilf_type(U_70,set_type) )
| ~ ilf_type(U_71,set_type) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( ilf_type(domain(U_71,U_70,U_69),subset_type(U_71))
| ~ ilf_type(U_69,relation_type(U_71,U_70))
| ~ ilf_type(U_70,set_type)
| ~ ilf_type(U_71,set_type) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p30]) ).
fof(f_30_2,plain,
! [U_74] :
( ! [U_73] :
( ! [U_72] :
( range(U_74,U_73,U_72) = range_of(U_72)
| ~ ilf_type(U_72,relation_type(U_74,U_73)) )
| ~ ilf_type(U_73,set_type) )
| ~ ilf_type(U_74,set_type) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( range(U_74,U_73,U_72) = range_of(U_72)
| ~ ilf_type(U_72,relation_type(U_74,U_73))
| ~ ilf_type(U_73,set_type)
| ~ ilf_type(U_74,set_type) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(range(B,C,D),subset_type(C))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p31]) ).
fof(f_31_2,plain,
! [U_77] :
( ! [U_76] :
( ! [U_75] :
( ilf_type(range(U_77,U_76,U_75),subset_type(U_76))
| ~ ilf_type(U_75,relation_type(U_77,U_76)) )
| ~ ilf_type(U_76,set_type) )
| ~ ilf_type(U_77,set_type) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ilf_type(range(U_77,U_76,U_75),subset_type(U_76))
| ~ ilf_type(U_75,relation_type(U_77,U_76))
| ~ ilf_type(U_76,set_type)
| ~ ilf_type(U_77,set_type) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p32]) ).
fof(f_32_2,plain,
! [U_78] : ilf_type(U_78,set_type),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
ilf_type(U_78,set_type),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_31]) ).
fof(f_33_2,negated_conjecture,
? [B] :
( ? [C] :
( ? [D] :
( ( ~ subset(C,range(C,B,D))
| C != domain(C,B,D) )
& subset(identity_relation_of(C),D)
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_81] :
( ? [U_80] :
( ? [U_79] :
( ( ~ subset(U_80,range(U_80,U_81,U_79))
| U_80 != domain(U_80,U_81,U_79) )
& subset(identity_relation_of(U_80),U_79)
& ilf_type(U_79,relation_type(U_80,U_81)) )
& ilf_type(U_80,set_type) )
& ilf_type(U_81,set_type) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
( ? [U_80] :
( ? [U_79] :
( ( ~ subset(U_80,range(U_80,sK13,U_79))
| U_80 != domain(U_80,sK13,U_79) )
& subset(identity_relation_of(U_80),U_79)
& ilf_type(U_79,relation_type(U_80,sK13)) )
& ilf_type(U_80,set_type) )
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_81,sK13)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( ? [U_79] :
( ( ~ subset(sK14,range(sK14,sK13,U_79))
| sK14 != domain(sK14,sK13,U_79) )
& subset(identity_relation_of(sK14),U_79)
& ilf_type(U_79,relation_type(sK14,sK13)) )
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_80,sK14)],[f_33_4]) ).
fof(f_33_6,negated_conjecture,
( ( ~ subset(sK14,range(sK14,sK13,sK15))
| sK14 != domain(sK14,sK13,sK15) )
& subset(identity_relation_of(sK14),sK15)
& ilf_type(sK15,relation_type(sK14,sK13))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_79,sK15)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
ilf_type(sK13,set_type),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,negated_conjecture,
ilf_type(sK14,set_type),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_9,negated_conjecture,
ilf_type(sK15,relation_type(sK14,sK13)),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_10,negated_conjecture,
subset(identity_relation_of(sK14),sK15),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_11,negated_conjecture,
( ~ subset(sK14,range(sK14,sK13,sK15))
| sK14 != domain(sK14,sK13,sK15) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_14_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_4]) ).
cnf(f_14_5_simplified,plain,
( ilf_type(U_35,binary_relation_type)
| ~ ilf_type(U_35,set_type)
| ~ relation_like(U_35) ),
inference(simplify_clause,[status(thm)],[f_14_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,
( 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_5,axiom,
( identity_relation_of(Eq_x_0) = identity_relation_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( domain(Eq_x_0,Eq_x_1,Eq_x_2) = domain(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( range(Eq_x_0,Eq_x_1,Eq_x_2) = range(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,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_10,axiom,
( subset_type(Eq_x_0) = subset_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( domain_of(Eq_x_0) = domain_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( range_of(Eq_x_0) = range_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( member_type(Eq_x_0) = member_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,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_17,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_18,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,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_29,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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
% 0.00/0.02 % Problem : SET668+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
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 22:45:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 166.73/167.09 % SZS status Theorem for theBenchmark
% 166.73/167.09 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------