%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET663+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 : n016.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 63.15s 68.44s
% Output : Proof 63.68s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( range_of(B) = empty_set
| domain_of(B) = empty_set )
=> B = empty_set ) ),
file('theBenchmark.p',p2) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('theBenchmark.p',p4) ).
fof(p5a,axiom,
empty(empty_set),
file('theBenchmark.p',p5a) ).
fof(p5b,axiom,
type(empty_set,set_type),
file('theBenchmark.p',p5b) ).
fof(p6,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',p6) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ? [D] : ilf_type(D,relation_type(C,B)) ) ),
file('theBenchmark.p',p7) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( 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,binary_relation_type)
=> ilf_type(domain_of(B),set_type) ),
file('theBenchmark.p',p9) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p10) ).
fof(p11,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(range_of(B),set_type) ),
file('theBenchmark.p',p11) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p12) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
? [B] : ilf_type(B,binary_relation_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,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( B = C
=> C = B ) ) ),
file('theBenchmark.p',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> B = B ),
file('theBenchmark.p',p18) ).
fof(p19,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',p19) ).
fof(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p20) ).
fof(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p21) ).
fof(p22,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',p22) ).
fof(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p23) ).
fof(p24,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',p24) ).
fof(p25,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('theBenchmark.p',p25) ).
fof(p26,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',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,subset_type(cross_product(B,C)))
=> relation_like(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))
=> domain(B,C,D) = domain_of(D) ) ) ),
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))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
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))
=> range(B,C,D) = range_of(D) ) ) ),
file('theBenchmark.p',p31) ).
fof(p32,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',p32) ).
fof(p33,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p33) ).
fof(prove_relset_1_26,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
file('theBenchmark.p',prove_relset_1_26) ).
fof(f_1_1,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_0] :
( U_0 = empty_set
| ~ subset(U_0,empty_set)
| ~ ilf_type(U_0,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0] :
( U_0 = empty_set
| ~ subset(U_0,empty_set)
| ~ ilf_type(U_0,set_type) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( U_0 = empty_set
| ~ subset(U_0,empty_set)
| ~ ilf_type(U_0,set_type) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B] :
( B = empty_set
| ( range_of(B) != empty_set
& domain_of(B) != empty_set )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_1] :
( U_1 = empty_set
| ( range_of(U_1) != empty_set
& domain_of(U_1) != empty_set )
| ~ ilf_type(U_1,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_1] :
( range_of(U_1) != empty_set
| ~ sP0(U_1) )
& ! [U_1] :
( domain_of(U_1) != empty_set
| ~ sP0(U_1) )
& ! [U_1] :
( U_1 = empty_set
| sP0(U_1)
| ~ ilf_type(U_1,binary_relation_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_2_2]) ).
cnf(f_2_4,plain,
( U_1 = empty_set
| sP0(U_1)
| ~ ilf_type(U_1,binary_relation_type) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( domain_of(U_1) != empty_set
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( range_of(U_1) != empty_set
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p3]) ).
fof(f_3_2,plain,
! [U_4] :
( ! [U_3] :
( ! [U_2] :
( ( subset(range_of(U_2),U_3)
& subset(domain_of(U_2),U_4) )
| ~ ilf_type(U_2,relation_type(U_4,U_3)) )
| ~ ilf_type(U_3,set_type) )
| ~ ilf_type(U_4,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3,U_2,U_4] :
( subset(range_of(U_2),U_3)
| ~ sP1(U_3,U_2,U_4) )
& ! [U_3,U_2,U_4] :
( subset(domain_of(U_2),U_4)
| ~ sP1(U_3,U_2,U_4) )
& ! [U_3,U_2,U_4] :
( sP1(U_3,U_2,U_4)
| ~ ilf_type(U_2,relation_type(U_4,U_3))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP1(U_3,U_2,U_4)
| ~ ilf_type(U_2,relation_type(U_4,U_3))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(domain_of(U_2),U_4)
| ~ sP1(U_3,U_2,U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( subset(range_of(U_2),U_3)
| ~ sP1(U_3,U_2,U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(f_4_2,plain,
! [U_5] :
( ~ member(U_5,empty_set)
| ~ ilf_type(U_5,set_type) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5] :
( ~ member(U_5,empty_set)
| ~ ilf_type(U_5,set_type) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ member(U_5,empty_set)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[p5a]) ).
fof(f_5_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
type(empty_set,set_type),
inference(fof_nnf,[status(thm)],[p5b]) ).
fof(f_6_2,plain,
type(empty_set,set_type),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
type(empty_set,set_type),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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)],[p6]) ).
fof(f_7_2,plain,
! [U_9] :
( ! [U_8] :
( ( ! [U_7] :
( ilf_type(U_7,subset_type(cross_product(U_9,U_8)))
| ~ ilf_type(U_7,relation_type(U_9,U_8)) )
& ! [U_6] :
( ilf_type(U_6,relation_type(U_9,U_8))
| ~ ilf_type(U_6,subset_type(cross_product(U_9,U_8))) ) )
| ~ ilf_type(U_8,set_type) )
| ~ ilf_type(U_9,set_type) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_8,U_6,U_7,U_9] :
( ilf_type(U_7,subset_type(cross_product(U_9,U_8)))
| ~ ilf_type(U_7,relation_type(U_9,U_8))
| ~ sP2(U_8,U_6,U_7,U_9) )
& ! [U_8,U_6,U_7,U_9] :
( ilf_type(U_6,relation_type(U_9,U_8))
| ~ ilf_type(U_6,subset_type(cross_product(U_9,U_8)))
| ~ sP2(U_8,U_6,U_7,U_9) )
& ! [U_8,U_6,U_7,U_9] :
( sP2(U_8,U_6,U_7,U_9)
| ~ ilf_type(U_8,set_type)
| ~ ilf_type(U_9,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_8,U_6,U_7,U_9)
| ~ ilf_type(U_8,set_type)
| ~ ilf_type(U_9,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ilf_type(U_6,relation_type(U_9,U_8))
| ~ ilf_type(U_6,subset_type(cross_product(U_9,U_8)))
| ~ sP2(U_8,U_6,U_7,U_9) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( ilf_type(U_7,subset_type(cross_product(U_9,U_8)))
| ~ ilf_type(U_7,relation_type(U_9,U_8))
| ~ sP2(U_8,U_6,U_7,U_9) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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)],[p7]) ).
fof(f_8_2,plain,
! [U_12] :
( ! [U_11] :
( ? [U_10] : ilf_type(U_10,relation_type(U_11,U_12))
| ~ ilf_type(U_11,set_type) )
| ~ ilf_type(U_12,set_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_12] :
( ! [U_11] :
( ilf_type(sK1(U_12,U_11),relation_type(U_11,U_12))
| ~ ilf_type(U_11,set_type) )
| ~ ilf_type(U_12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_12,U_11))],[f_8_2]) ).
fof(f_8_4,plain,
! [U_12,U_11] :
( ilf_type(sK1(U_12,U_11),relation_type(U_11,U_12))
| ~ ilf_type(U_11,set_type)
| ~ ilf_type(U_12,set_type) ),
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
( ilf_type(sK1(U_12,U_11),relation_type(U_11,U_12))
| ~ ilf_type(U_11,set_type)
| ~ ilf_type(U_12,set_type) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [B] :
( ! [C] :
( ( ( B = C
| ? [D] :
( ? [E] :
( ( ( ~ member(ordered_pair(D,E),B)
& member(ordered_pair(D,E),C) )
| ( ~ 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),B)
| ~ member(ordered_pair(D,E),C) )
& ( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B) ) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| B != C ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p8]) ).
fof(f_9_2,plain,
! [U_18] :
( ! [U_17] :
( ( ( U_18 = U_17
| ? [U_16] :
( ? [U_15] :
( ( ( ~ member(ordered_pair(U_16,U_15),U_18)
& member(ordered_pair(U_16,U_15),U_17) )
| ( ~ member(ordered_pair(U_16,U_15),U_17)
& member(ordered_pair(U_16,U_15),U_18) ) )
& ilf_type(U_15,set_type) )
& ilf_type(U_16,set_type) ) )
& ( ! [U_14] :
( ! [U_13] :
( ( ( member(ordered_pair(U_14,U_13),U_18)
| ~ member(ordered_pair(U_14,U_13),U_17) )
& ( member(ordered_pair(U_14,U_13),U_17)
| ~ member(ordered_pair(U_14,U_13),U_18) ) )
| ~ ilf_type(U_13,set_type) )
| ~ ilf_type(U_14,set_type) )
| U_18 != U_17 ) )
| ~ ilf_type(U_17,binary_relation_type) )
| ~ ilf_type(U_18,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_18] :
( ! [U_17] :
( ( ( U_18 = U_17
| ( ? [U_15] :
( ( ( ~ member(ordered_pair(sK2(U_18,U_17),U_15),U_18)
& member(ordered_pair(sK2(U_18,U_17),U_15),U_17) )
| ( ~ member(ordered_pair(sK2(U_18,U_17),U_15),U_17)
& member(ordered_pair(sK2(U_18,U_17),U_15),U_18) ) )
& ilf_type(U_15,set_type) )
& ilf_type(sK2(U_18,U_17),set_type) ) )
& ( ! [U_14] :
( ! [U_13] :
( ( ( member(ordered_pair(U_14,U_13),U_18)
| ~ member(ordered_pair(U_14,U_13),U_17) )
& ( member(ordered_pair(U_14,U_13),U_17)
| ~ member(ordered_pair(U_14,U_13),U_18) ) )
| ~ ilf_type(U_13,set_type) )
| ~ ilf_type(U_14,set_type) )
| U_18 != U_17 ) )
| ~ ilf_type(U_17,binary_relation_type) )
| ~ ilf_type(U_18,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_18,U_17))],[f_9_2]) ).
fof(f_9_4,plain,
! [U_18] :
( ! [U_17] :
( ( ( U_18 = U_17
| ( ( ( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18)
& member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17) )
| ( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17)
& member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18) ) )
& ilf_type(sK3(U_18,U_17),set_type)
& ilf_type(sK2(U_18,U_17),set_type) ) )
& ( ! [U_14] :
( ! [U_13] :
( ( ( member(ordered_pair(U_14,U_13),U_18)
| ~ member(ordered_pair(U_14,U_13),U_17) )
& ( member(ordered_pair(U_14,U_13),U_17)
| ~ member(ordered_pair(U_14,U_13),U_18) ) )
| ~ ilf_type(U_13,set_type) )
| ~ ilf_type(U_14,set_type) )
| U_18 != U_17 ) )
| ~ ilf_type(U_17,binary_relation_type) )
| ~ ilf_type(U_18,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3(U_18,U_17))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_17,U_18] :
( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18)
| ~ sP5(U_17,U_18) )
& ! [U_17,U_18] :
( member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17)
| ~ sP5(U_17,U_18) )
& ! [U_17,U_18] :
( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17)
| ~ sP4(U_17,U_18) )
& ! [U_17,U_18] :
( member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18)
| ~ sP4(U_17,U_18) )
& ! [U_17,U_18] :
( sP5(U_17,U_18)
| sP4(U_17,U_18)
| ~ sP6(U_17,U_18) )
& ! [U_17,U_18] :
( ilf_type(sK3(U_18,U_17),set_type)
| ~ sP6(U_17,U_18) )
& ! [U_17,U_18] :
( ilf_type(sK2(U_18,U_17),set_type)
| ~ sP6(U_17,U_18) )
& ! [U_17,U_13,U_14,U_18] :
( member(ordered_pair(U_14,U_13),U_18)
| ~ member(ordered_pair(U_14,U_13),U_17)
| ~ sP3(U_17,U_13,U_14,U_18) )
& ! [U_17,U_13,U_14,U_18] :
( member(ordered_pair(U_14,U_13),U_17)
| ~ member(ordered_pair(U_14,U_13),U_18)
| ~ sP3(U_17,U_13,U_14,U_18) )
& ! [U_17,U_13,U_14,U_18] :
( U_18 = U_17
| sP6(U_17,U_18)
| ~ sP7(U_17,U_13,U_14,U_18) )
& ! [U_17,U_13,U_14,U_18] :
( sP3(U_17,U_13,U_14,U_18)
| ~ ilf_type(U_13,set_type)
| ~ ilf_type(U_14,set_type)
| U_18 != U_17
| ~ sP7(U_17,U_13,U_14,U_18) )
& ! [U_17,U_13,U_14,U_18] :
( sP7(U_17,U_13,U_14,U_18)
| ~ ilf_type(U_17,binary_relation_type)
| ~ ilf_type(U_18,binary_relation_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5,sP6,sP7])],[f_9_4]) ).
cnf(f_9_6,plain,
( sP7(U_17,U_13,U_14,U_18)
| ~ ilf_type(U_17,binary_relation_type)
| ~ ilf_type(U_18,binary_relation_type) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( sP3(U_17,U_13,U_14,U_18)
| ~ ilf_type(U_13,set_type)
| ~ ilf_type(U_14,set_type)
| U_18 != U_17
| ~ sP7(U_17,U_13,U_14,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( U_18 = U_17
| sP6(U_17,U_18)
| ~ sP7(U_17,U_13,U_14,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( member(ordered_pair(U_14,U_13),U_17)
| ~ member(ordered_pair(U_14,U_13),U_18)
| ~ sP3(U_17,U_13,U_14,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( member(ordered_pair(U_14,U_13),U_18)
| ~ member(ordered_pair(U_14,U_13),U_17)
| ~ sP3(U_17,U_13,U_14,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ilf_type(sK2(U_18,U_17),set_type)
| ~ sP6(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_12,plain,
( ilf_type(sK3(U_18,U_17),set_type)
| ~ sP6(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_13,plain,
( sP5(U_17,U_18)
| sP4(U_17,U_18)
| ~ sP6(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_14,plain,
( member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18)
| ~ sP4(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_15,plain,
( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17)
| ~ sP4(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_16,plain,
( member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_17)
| ~ sP5(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_17,plain,
( ~ member(ordered_pair(sK2(U_18,U_17),sK3(U_18,U_17)),U_18)
| ~ sP5(U_17,U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [B] :
( ilf_type(domain_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_10_2,plain,
! [U_19] :
( ilf_type(domain_of(U_19),set_type)
| ~ ilf_type(U_19,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_19] :
( ilf_type(domain_of(U_19),set_type)
| ~ ilf_type(U_19,binary_relation_type) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( ilf_type(domain_of(U_19),set_type)
| ~ ilf_type(U_19,binary_relation_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
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)],[p10]) ).
fof(f_11_2,plain,
! [U_21] :
( ! [U_20] :
( ilf_type(cross_product(U_21,U_20),set_type)
| ~ ilf_type(U_20,set_type) )
| ~ ilf_type(U_21,set_type) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_21,U_20] :
( ilf_type(cross_product(U_21,U_20),set_type)
| ~ ilf_type(U_20,set_type)
| ~ ilf_type(U_21,set_type) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( ilf_type(cross_product(U_21,U_20),set_type)
| ~ ilf_type(U_20,set_type)
| ~ ilf_type(U_21,set_type) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [B] :
( ilf_type(range_of(B),set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p11]) ).
fof(f_12_2,plain,
! [U_22] :
( ilf_type(range_of(U_22),set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_22] :
( ilf_type(range_of(U_22),set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( ilf_type(range_of(U_22),set_type)
| ~ ilf_type(U_22,binary_relation_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
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)],[p12]) ).
fof(f_13_2,plain,
! [U_24] :
( ! [U_23] :
( ilf_type(ordered_pair(U_24,U_23),set_type)
| ~ ilf_type(U_23,set_type) )
| ~ ilf_type(U_24,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_24,U_23] :
( ilf_type(ordered_pair(U_24,U_23),set_type)
| ~ ilf_type(U_23,set_type)
| ~ ilf_type(U_24,set_type) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( ilf_type(ordered_pair(U_24,U_23),set_type)
| ~ ilf_type(U_23,set_type)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_13_3]) ).
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)],[p13]) ).
fof(f_14_2,plain,
! [U_25] :
( ( ( ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_25,set_type)
| ~ relation_like(U_25) )
& ( ( ilf_type(U_25,set_type)
& relation_like(U_25) )
| ~ ilf_type(U_25,binary_relation_type) ) )
| ~ ilf_type(U_25,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_25] :
( ilf_type(U_25,set_type)
| ~ sP8(U_25) )
& ! [U_25] :
( relation_like(U_25)
| ~ sP8(U_25) )
& ! [U_25] :
( ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_25,set_type)
| ~ relation_like(U_25)
| ~ sP9(U_25) )
& ! [U_25] :
( sP8(U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ sP9(U_25) )
& ! [U_25] :
( sP9(U_25)
| ~ ilf_type(U_25,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP9(U_25)
| ~ ilf_type(U_25,set_type) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( sP8(U_25)
| ~ ilf_type(U_25,binary_relation_type)
| ~ sP9(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( ilf_type(U_25,binary_relation_type)
| ~ ilf_type(U_25,set_type)
| ~ relation_like(U_25)
| ~ sP9(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_7,plain,
( relation_like(U_25)
| ~ sP8(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_8,plain,
( ilf_type(U_25,set_type)
| ~ sP8(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [B] : ilf_type(B,binary_relation_type),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_15_2,plain,
? [U_26] : ilf_type(U_26,binary_relation_type),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
ilf_type(sK4,binary_relation_type),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_15_2]) ).
fof(f_15_4,plain,
ilf_type(sK4,binary_relation_type),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
ilf_type(sK4,binary_relation_type),
inference(clausify,[status(thm)],[f_15_4]) ).
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)],[p15]) ).
fof(f_16_2,plain,
! [U_28] :
( ! [U_27] :
( ( ( ilf_type(U_27,subset_type(U_28))
| ~ ilf_type(U_27,member_type(power_set(U_28))) )
& ( ilf_type(U_27,member_type(power_set(U_28)))
| ~ ilf_type(U_27,subset_type(U_28)) ) )
| ~ ilf_type(U_27,set_type) )
| ~ ilf_type(U_28,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_27,U_28] :
( ilf_type(U_27,subset_type(U_28))
| ~ ilf_type(U_27,member_type(power_set(U_28)))
| ~ sP10(U_27,U_28) )
& ! [U_27,U_28] :
( ilf_type(U_27,member_type(power_set(U_28)))
| ~ ilf_type(U_27,subset_type(U_28))
| ~ sP10(U_27,U_28) )
& ! [U_27,U_28] :
( sP10(U_27,U_28)
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_16_2]) ).
cnf(f_16_4,plain,
( sP10(U_27,U_28)
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( ilf_type(U_27,member_type(power_set(U_28)))
| ~ ilf_type(U_27,subset_type(U_28))
| ~ sP10(U_27,U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( ilf_type(U_27,subset_type(U_28))
| ~ ilf_type(U_27,member_type(power_set(U_28)))
| ~ sP10(U_27,U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p16]) ).
fof(f_17_2,plain,
! [U_30] :
( ? [U_29] : ilf_type(U_29,subset_type(U_30))
| ~ ilf_type(U_30,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_30] :
( ilf_type(sK5(U_30),subset_type(U_30))
| ~ ilf_type(U_30,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_30))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_30] :
( ilf_type(sK5(U_30),subset_type(U_30))
| ~ ilf_type(U_30,set_type) ),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
( ilf_type(sK5(U_30),subset_type(U_30))
| ~ ilf_type(U_30,set_type) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [B] :
( ! [C] :
( C = B
| B != C
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_18_2,plain,
! [U_32] :
( ! [U_31] :
( U_31 = U_32
| U_32 != U_31
| ~ ilf_type(U_31,binary_relation_type) )
| ~ ilf_type(U_32,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_31,U_32] :
( U_31 = U_32
| U_32 != U_31
| ~ ilf_type(U_31,binary_relation_type)
| ~ ilf_type(U_32,binary_relation_type) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( U_31 = U_32
| U_32 != U_31
| ~ ilf_type(U_31,binary_relation_type)
| ~ ilf_type(U_32,binary_relation_type) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [B] :
( B = B
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(f_19_2,plain,
! [U_33] :
( U_33 = U_33
| ~ ilf_type(U_33,binary_relation_type) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_33] :
( U_33 = U_33
| ~ ilf_type(U_33,binary_relation_type) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( U_33 = U_33
| ~ ilf_type(U_33,binary_relation_type) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_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)],[p19]) ).
fof(f_20_2,plain,
! [U_37] :
( ! [U_36] :
( ( ( subset(U_37,U_36)
| ? [U_35] :
( ~ member(U_35,U_36)
& member(U_35,U_37)
& ilf_type(U_35,set_type) ) )
& ( ! [U_34] :
( member(U_34,U_36)
| ~ member(U_34,U_37)
| ~ ilf_type(U_34,set_type) )
| ~ subset(U_37,U_36) ) )
| ~ ilf_type(U_36,set_type) )
| ~ ilf_type(U_37,set_type) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_37] :
( ! [U_36] :
( ( ( subset(U_37,U_36)
| ( ~ member(sK6(U_37,U_36),U_36)
& member(sK6(U_37,U_36),U_37)
& ilf_type(sK6(U_37,U_36),set_type) ) )
& ( ! [U_34] :
( member(U_34,U_36)
| ~ member(U_34,U_37)
| ~ ilf_type(U_34,set_type) )
| ~ subset(U_37,U_36) ) )
| ~ ilf_type(U_36,set_type) )
| ~ ilf_type(U_37,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6(U_37,U_36))],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_36,U_37] :
( ~ member(sK6(U_37,U_36),U_36)
| ~ sP11(U_36,U_37) )
& ! [U_36,U_37] :
( member(sK6(U_37,U_36),U_37)
| ~ sP11(U_36,U_37) )
& ! [U_36,U_37] :
( ilf_type(sK6(U_37,U_36),set_type)
| ~ sP11(U_36,U_37) )
& ! [U_34,U_36,U_37] :
( subset(U_37,U_36)
| sP11(U_36,U_37)
| ~ sP12(U_34,U_36,U_37) )
& ! [U_34,U_36,U_37] :
( member(U_34,U_36)
| ~ member(U_34,U_37)
| ~ ilf_type(U_34,set_type)
| ~ subset(U_37,U_36)
| ~ sP12(U_34,U_36,U_37) )
& ! [U_34,U_36,U_37] :
( sP12(U_34,U_36,U_37)
| ~ ilf_type(U_36,set_type)
| ~ ilf_type(U_37,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12])],[f_20_3]) ).
cnf(f_20_5,plain,
( sP12(U_34,U_36,U_37)
| ~ ilf_type(U_36,set_type)
| ~ ilf_type(U_37,set_type) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( member(U_34,U_36)
| ~ member(U_34,U_37)
| ~ ilf_type(U_34,set_type)
| ~ subset(U_37,U_36)
| ~ sP12(U_34,U_36,U_37) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( subset(U_37,U_36)
| sP11(U_36,U_37)
| ~ sP12(U_34,U_36,U_37) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_8,plain,
( ilf_type(sK6(U_37,U_36),set_type)
| ~ sP11(U_36,U_37) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_9,plain,
( member(sK6(U_37,U_36),U_37)
| ~ sP11(U_36,U_37) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_10,plain,
( ~ member(sK6(U_37,U_36),U_36)
| ~ sP11(U_36,U_37) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p20]) ).
fof(f_21_2,plain,
! [U_38] :
( subset(U_38,U_38)
| ~ ilf_type(U_38,set_type) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_38] :
( subset(U_38,U_38)
| ~ ilf_type(U_38,set_type) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( subset(U_38,U_38)
| ~ ilf_type(U_38,set_type) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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)],[p21]) ).
fof(f_22_2,plain,
! [U_41] :
( ( ( empty(U_41)
| ? [U_40] :
( member(U_40,U_41)
& ilf_type(U_40,set_type) ) )
& ( ! [U_39] :
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type) )
| ~ empty(U_41) ) )
| ~ ilf_type(U_41,set_type) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_41] :
( ( ( empty(U_41)
| ( member(sK7(U_41),U_41)
& ilf_type(sK7(U_41),set_type) ) )
& ( ! [U_39] :
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type) )
| ~ empty(U_41) ) )
| ~ ilf_type(U_41,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7(U_41))],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_41] :
( member(sK7(U_41),U_41)
| ~ sP13(U_41) )
& ! [U_41] :
( ilf_type(sK7(U_41),set_type)
| ~ sP13(U_41) )
& ! [U_41,U_39] :
( empty(U_41)
| sP13(U_41)
| ~ sP14(U_41,U_39) )
& ! [U_41,U_39] :
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type)
| ~ empty(U_41)
| ~ sP14(U_41,U_39) )
& ! [U_41,U_39] :
( sP14(U_41,U_39)
| ~ ilf_type(U_41,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14])],[f_22_3]) ).
cnf(f_22_5,plain,
( sP14(U_41,U_39)
| ~ ilf_type(U_41,set_type) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type)
| ~ empty(U_41)
| ~ sP14(U_41,U_39) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
( empty(U_41)
| sP13(U_41)
| ~ sP14(U_41,U_39) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_8,plain,
( ilf_type(sK7(U_41),set_type)
| ~ sP13(U_41) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_9,plain,
( member(sK7(U_41),U_41)
| ~ sP13(U_41) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_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)],[p22]) ).
fof(f_23_2,plain,
! [U_45] :
( ! [U_44] :
( ( ( member(U_45,power_set(U_44))
| ? [U_43] :
( ~ member(U_43,U_44)
& member(U_43,U_45)
& ilf_type(U_43,set_type) ) )
& ( ! [U_42] :
( member(U_42,U_44)
| ~ member(U_42,U_45)
| ~ ilf_type(U_42,set_type) )
| ~ member(U_45,power_set(U_44)) ) )
| ~ ilf_type(U_44,set_type) )
| ~ ilf_type(U_45,set_type) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_45] :
( ! [U_44] :
( ( ( member(U_45,power_set(U_44))
| ( ~ member(sK8(U_45,U_44),U_44)
& member(sK8(U_45,U_44),U_45)
& ilf_type(sK8(U_45,U_44),set_type) ) )
& ( ! [U_42] :
( member(U_42,U_44)
| ~ member(U_42,U_45)
| ~ ilf_type(U_42,set_type) )
| ~ member(U_45,power_set(U_44)) ) )
| ~ ilf_type(U_44,set_type) )
| ~ ilf_type(U_45,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_45,U_44))],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_45,U_44] :
( ~ member(sK8(U_45,U_44),U_44)
| ~ sP15(U_45,U_44) )
& ! [U_45,U_44] :
( member(sK8(U_45,U_44),U_45)
| ~ sP15(U_45,U_44) )
& ! [U_45,U_44] :
( ilf_type(sK8(U_45,U_44),set_type)
| ~ sP15(U_45,U_44) )
& ! [U_45,U_42,U_44] :
( member(U_45,power_set(U_44))
| sP15(U_45,U_44)
| ~ sP16(U_45,U_42,U_44) )
& ! [U_45,U_42,U_44] :
( member(U_42,U_44)
| ~ member(U_42,U_45)
| ~ ilf_type(U_42,set_type)
| ~ member(U_45,power_set(U_44))
| ~ sP16(U_45,U_42,U_44) )
& ! [U_45,U_42,U_44] :
( sP16(U_45,U_42,U_44)
| ~ ilf_type(U_44,set_type)
| ~ ilf_type(U_45,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15,sP16])],[f_23_3]) ).
cnf(f_23_5,plain,
( sP16(U_45,U_42,U_44)
| ~ ilf_type(U_44,set_type)
| ~ ilf_type(U_45,set_type) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( member(U_42,U_44)
| ~ member(U_42,U_45)
| ~ ilf_type(U_42,set_type)
| ~ member(U_45,power_set(U_44))
| ~ sP16(U_45,U_42,U_44) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( member(U_45,power_set(U_44))
| sP15(U_45,U_44)
| ~ sP16(U_45,U_42,U_44) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_8,plain,
( ilf_type(sK8(U_45,U_44),set_type)
| ~ sP15(U_45,U_44) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_9,plain,
( member(sK8(U_45,U_44),U_45)
| ~ sP15(U_45,U_44) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_10,plain,
( ~ member(sK8(U_45,U_44),U_44)
| ~ sP15(U_45,U_44) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p23]) ).
fof(f_24_2,plain,
! [U_46] :
( ( ilf_type(power_set(U_46),set_type)
& ~ empty(power_set(U_46)) )
| ~ ilf_type(U_46,set_type) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_46] :
( ilf_type(power_set(U_46),set_type)
| ~ sP17(U_46) )
& ! [U_46] :
( ~ empty(power_set(U_46))
| ~ sP17(U_46) )
& ! [U_46] :
( sP17(U_46)
| ~ ilf_type(U_46,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP17(U_46)
| ~ ilf_type(U_46,set_type) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ empty(power_set(U_46))
| ~ sP17(U_46) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( ilf_type(power_set(U_46),set_type)
| ~ sP17(U_46) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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)],[p24]) ).
fof(f_25_2,plain,
! [U_48] :
( ! [U_47] :
( ( ( ilf_type(U_48,member_type(U_47))
| ~ member(U_48,U_47) )
& ( member(U_48,U_47)
| ~ ilf_type(U_48,member_type(U_47)) ) )
| ~ ilf_type(U_47,set_type)
| empty(U_47) )
| ~ ilf_type(U_48,set_type) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_48,U_47] :
( ilf_type(U_48,member_type(U_47))
| ~ member(U_48,U_47)
| ~ sP18(U_48,U_47) )
& ! [U_48,U_47] :
( member(U_48,U_47)
| ~ ilf_type(U_48,member_type(U_47))
| ~ sP18(U_48,U_47) )
& ! [U_48,U_47] :
( sP18(U_48,U_47)
| ~ ilf_type(U_47,set_type)
| empty(U_47)
| ~ ilf_type(U_48,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP18(U_48,U_47)
| ~ ilf_type(U_47,set_type)
| empty(U_47)
| ~ ilf_type(U_48,set_type) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( member(U_48,U_47)
| ~ ilf_type(U_48,member_type(U_47))
| ~ sP18(U_48,U_47) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( ilf_type(U_48,member_type(U_47))
| ~ member(U_48,U_47)
| ~ sP18(U_48,U_47) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(fof_nnf,[status(thm)],[p25]) ).
fof(f_26_2,plain,
! [U_50] :
( ? [U_49] : ilf_type(U_49,member_type(U_50))
| ~ ilf_type(U_50,set_type)
| empty(U_50) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_50] :
( ilf_type(sK9(U_50),member_type(U_50))
| ~ ilf_type(U_50,set_type)
| empty(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_49,sK9(U_50))],[f_26_2]) ).
fof(f_26_4,plain,
! [U_50] :
( ilf_type(sK9(U_50),member_type(U_50))
| ~ ilf_type(U_50,set_type)
| empty(U_50) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
( ilf_type(sK9(U_50),member_type(U_50))
| ~ ilf_type(U_50,set_type)
| empty(U_50) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_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)],[p26]) ).
fof(f_27_2,plain,
! [U_57] :
( ( ( relation_like(U_57)
| ? [U_56] :
( ! [U_55] :
( ! [U_54] :
( U_56 != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type) )
| ~ ilf_type(U_55,set_type) )
& member(U_56,U_57)
& ilf_type(U_56,set_type) ) )
& ( ! [U_53] :
( ? [U_52] :
( ? [U_51] :
( U_53 = ordered_pair(U_52,U_51)
& ilf_type(U_51,set_type) )
& ilf_type(U_52,set_type) )
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type) )
| ~ relation_like(U_57) ) )
| ~ ilf_type(U_57,set_type) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_57] :
( ( ( relation_like(U_57)
| ? [U_56] :
( ! [U_55] :
( ! [U_54] :
( U_56 != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type) )
| ~ ilf_type(U_55,set_type) )
& member(U_56,U_57)
& ilf_type(U_56,set_type) ) )
& ( ! [U_53] :
( ( ? [U_51] :
( U_53 = ordered_pair(sK10(U_57,U_53),U_51)
& ilf_type(U_51,set_type) )
& ilf_type(sK10(U_57,U_53),set_type) )
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type) )
| ~ relation_like(U_57) ) )
| ~ ilf_type(U_57,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_52,sK10(U_57,U_53))],[f_27_2]) ).
fof(f_27_4,plain,
! [U_57] :
( ( ( relation_like(U_57)
| ? [U_56] :
( ! [U_55] :
( ! [U_54] :
( U_56 != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type) )
| ~ ilf_type(U_55,set_type) )
& member(U_56,U_57)
& ilf_type(U_56,set_type) ) )
& ( ! [U_53] :
( ( U_53 = ordered_pair(sK10(U_57,U_53),sK11(U_57,U_53))
& ilf_type(sK11(U_57,U_53),set_type)
& ilf_type(sK10(U_57,U_53),set_type) )
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type) )
| ~ relation_like(U_57) ) )
| ~ ilf_type(U_57,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11(U_57,U_53))],[f_27_3]) ).
fof(f_27_5,plain,
! [U_57] :
( ( ( relation_like(U_57)
| ( ! [U_55] :
( ! [U_54] :
( sK12(U_57) != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type) )
| ~ ilf_type(U_55,set_type) )
& member(sK12(U_57),U_57)
& ilf_type(sK12(U_57),set_type) ) )
& ( ! [U_53] :
( ( U_53 = ordered_pair(sK10(U_57,U_53),sK11(U_57,U_53))
& ilf_type(sK11(U_57,U_53),set_type)
& ilf_type(sK10(U_57,U_53),set_type) )
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type) )
| ~ relation_like(U_57) ) )
| ~ ilf_type(U_57,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12(U_57))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_57,U_54,U_55] :
( sK12(U_57) != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type)
| ~ ilf_type(U_55,set_type)
| ~ sP20(U_57,U_54,U_55) )
& ! [U_57,U_54,U_55] :
( member(sK12(U_57),U_57)
| ~ sP20(U_57,U_54,U_55) )
& ! [U_57,U_54,U_55] :
( ilf_type(sK12(U_57),set_type)
| ~ sP20(U_57,U_54,U_55) )
& ! [U_57,U_53] :
( U_53 = ordered_pair(sK10(U_57,U_53),sK11(U_57,U_53))
| ~ sP19(U_57,U_53) )
& ! [U_57,U_53] :
( ilf_type(sK11(U_57,U_53),set_type)
| ~ sP19(U_57,U_53) )
& ! [U_57,U_53] :
( ilf_type(sK10(U_57,U_53),set_type)
| ~ sP19(U_57,U_53) )
& ! [U_57,U_54,U_53,U_55] :
( relation_like(U_57)
| sP20(U_57,U_54,U_55)
| ~ sP21(U_57,U_54,U_53,U_55) )
& ! [U_57,U_54,U_53,U_55] :
( sP19(U_57,U_53)
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type)
| ~ relation_like(U_57)
| ~ sP21(U_57,U_54,U_53,U_55) )
& ! [U_57,U_54,U_53,U_55] :
( sP21(U_57,U_54,U_53,U_55)
| ~ ilf_type(U_57,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20,sP21])],[f_27_5]) ).
cnf(f_27_7,plain,
( sP21(U_57,U_54,U_53,U_55)
| ~ ilf_type(U_57,set_type) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,plain,
( sP19(U_57,U_53)
| ~ member(U_53,U_57)
| ~ ilf_type(U_53,set_type)
| ~ relation_like(U_57)
| ~ sP21(U_57,U_54,U_53,U_55) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_9,plain,
( relation_like(U_57)
| sP20(U_57,U_54,U_55)
| ~ sP21(U_57,U_54,U_53,U_55) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_10,plain,
( ilf_type(sK10(U_57,U_53),set_type)
| ~ sP19(U_57,U_53) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_11,plain,
( ilf_type(sK11(U_57,U_53),set_type)
| ~ sP19(U_57,U_53) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_12,plain,
( U_53 = ordered_pair(sK10(U_57,U_53),sK11(U_57,U_53))
| ~ sP19(U_57,U_53) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_13,plain,
( ilf_type(sK12(U_57),set_type)
| ~ sP20(U_57,U_54,U_55) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_14,plain,
( member(sK12(U_57),U_57)
| ~ sP20(U_57,U_54,U_55) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_15,plain,
( sK12(U_57) != ordered_pair(U_55,U_54)
| ~ ilf_type(U_54,set_type)
| ~ ilf_type(U_55,set_type)
| ~ sP20(U_57,U_54,U_55) ),
inference(clausify,[status(thm)],[f_27_6]) ).
fof(f_28_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p27]) ).
fof(f_28_2,plain,
! [U_58] :
( relation_like(U_58)
| ~ ilf_type(U_58,set_type)
| ~ empty(U_58) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_58] :
( relation_like(U_58)
| ~ ilf_type(U_58,set_type)
| ~ empty(U_58) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( relation_like(U_58)
| ~ ilf_type(U_58,set_type)
| ~ empty(U_58) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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)],[p28]) ).
fof(f_29_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_29_1]) ).
fof(f_29_3,plain,
! [U_60,U_59,U_61] :
( 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(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,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_29_3]) ).
fof(f_30_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)],[p29]) ).
fof(f_30_2,plain,
! [U_64] :
( ! [U_63] :
( ! [U_62] :
( domain(U_64,U_63,U_62) = domain_of(U_62)
| ~ ilf_type(U_62,relation_type(U_64,U_63)) )
| ~ ilf_type(U_63,set_type) )
| ~ ilf_type(U_64,set_type) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_63,U_64,U_62] :
( domain(U_64,U_63,U_62) = domain_of(U_62)
| ~ ilf_type(U_62,relation_type(U_64,U_63))
| ~ ilf_type(U_63,set_type)
| ~ ilf_type(U_64,set_type) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( domain(U_64,U_63,U_62) = domain_of(U_62)
| ~ ilf_type(U_62,relation_type(U_64,U_63))
| ~ ilf_type(U_63,set_type)
| ~ ilf_type(U_64,set_type) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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)],[p30]) ).
fof(f_31_2,plain,
! [U_67] :
( ! [U_66] :
( ! [U_65] :
( ilf_type(domain(U_67,U_66,U_65),subset_type(U_67))
| ~ ilf_type(U_65,relation_type(U_67,U_66)) )
| ~ ilf_type(U_66,set_type) )
| ~ ilf_type(U_67,set_type) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_66,U_65,U_67] :
( ilf_type(domain(U_67,U_66,U_65),subset_type(U_67))
| ~ ilf_type(U_65,relation_type(U_67,U_66))
| ~ ilf_type(U_66,set_type)
| ~ ilf_type(U_67,set_type) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( ilf_type(domain(U_67,U_66,U_65),subset_type(U_67))
| ~ ilf_type(U_65,relation_type(U_67,U_66))
| ~ ilf_type(U_66,set_type)
| ~ ilf_type(U_67,set_type) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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)],[p31]) ).
fof(f_32_2,plain,
! [U_70] :
( ! [U_69] :
( ! [U_68] :
( range(U_70,U_69,U_68) = range_of(U_68)
| ~ ilf_type(U_68,relation_type(U_70,U_69)) )
| ~ ilf_type(U_69,set_type) )
| ~ ilf_type(U_70,set_type) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_68,U_69,U_70] :
( range(U_70,U_69,U_68) = range_of(U_68)
| ~ ilf_type(U_68,relation_type(U_70,U_69))
| ~ ilf_type(U_69,set_type)
| ~ ilf_type(U_70,set_type) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( range(U_70,U_69,U_68) = range_of(U_68)
| ~ ilf_type(U_68,relation_type(U_70,U_69))
| ~ ilf_type(U_69,set_type)
| ~ ilf_type(U_70,set_type) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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)],[p32]) ).
fof(f_33_2,plain,
! [U_73] :
( ! [U_72] :
( ! [U_71] :
( ilf_type(range(U_73,U_72,U_71),subset_type(U_72))
| ~ ilf_type(U_71,relation_type(U_73,U_72)) )
| ~ ilf_type(U_72,set_type) )
| ~ ilf_type(U_73,set_type) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_71,U_72,U_73] :
( ilf_type(range(U_73,U_72,U_71),subset_type(U_72))
| ~ ilf_type(U_71,relation_type(U_73,U_72))
| ~ ilf_type(U_72,set_type)
| ~ ilf_type(U_73,set_type) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( ilf_type(range(U_73,U_72,U_71),subset_type(U_72))
| ~ ilf_type(U_71,relation_type(U_73,U_72))
| ~ ilf_type(U_72,set_type)
| ~ ilf_type(U_73,set_type) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p33]) ).
fof(f_34_2,plain,
! [U_74] : ilf_type(U_74,set_type),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_74] : ilf_type(U_74,set_type),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
ilf_type(U_74,set_type),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_26]) ).
fof(f_35_2,negated_conjecture,
? [B] :
( ? [C] :
( ? [D] :
( D != empty_set
& ilf_type(D,relation_type(empty_set,C))
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_77] :
( ? [U_76] :
( ? [U_75] :
( U_75 != empty_set
& ilf_type(U_75,relation_type(empty_set,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_35_2]) ).
fof(f_35_4,negated_conjecture,
( ? [U_76] :
( ? [U_75] :
( U_75 != empty_set
& ilf_type(U_75,relation_type(empty_set,U_76))
& ilf_type(U_75,relation_type(sK13,U_76)) )
& ilf_type(U_76,set_type) )
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_77,sK13)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
( ? [U_75] :
( U_75 != empty_set
& ilf_type(U_75,relation_type(empty_set,sK14))
& ilf_type(U_75,relation_type(sK13,sK14)) )
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_76,sK14)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( sK15 != empty_set
& ilf_type(sK15,relation_type(empty_set,sK14))
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_75,sK15)],[f_35_5]) ).
fof(f_35_7,negated_conjecture,
( sK15 != empty_set
& ilf_type(sK15,relation_type(empty_set,sK14))
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(definitional_conversion,[status(esa)],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
ilf_type(sK13,set_type),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,negated_conjecture,
ilf_type(sK14,set_type),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,negated_conjecture,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,negated_conjecture,
ilf_type(sK15,relation_type(empty_set,sK14)),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,negated_conjecture,
sK15 != empty_set,
inference(clausify,[status(thm)],[f_35_7]) ).
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,
( 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_7,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_8,axiom,
( subset_type(Eq_x_0) = subset_type(Eq_y_0)
| 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,
( 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_13,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_14,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_15,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_16,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_17,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(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,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(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,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,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_27,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_28,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( type(Eq_y_0,Eq_y_1)
| ~ 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_30,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP9(Eq_y_0)
| ~ sP9(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP13(Eq_y_0)
| ~ sP13(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP14(Eq_y_0,Eq_y_1)
| ~ sP14(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP15(Eq_y_0,Eq_y_1)
| ~ sP15(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP17(Eq_y_0)
| ~ sP17(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP18(Eq_y_0,Eq_y_1)
| ~ sP18(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP19(Eq_y_0,Eq_y_1)
| ~ sP19(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| 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 : SET663+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
% 0.09/5.36 % Computer : n016.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 22:50:13 UTC 2026
% 0.09/5.37 % CPUTime :
% 63.15/68.44 % SZS status Theorem for theBenchmark
% 63.15/68.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------