%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET640+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 : n026.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 08:57:12 AM UTC 2026
% Result : Theorem 216.09s 216.47s
% Output : Proof 217.60s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,cross_product(B,C))
<=> ? [E] :
( ? [F] :
( D = ordered_pair(E,F)
& member(F,C)
& member(E,B)
& ilf_type(F,set_type) )
& ilf_type(E,set_type) ) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',p4) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ? [D] : ilf_type(D,relation_type(C,B)) ) ),
file('theBenchmark.p',p5) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,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',p6) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p7) ).
fof(p8,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',p8) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ? [C] : ilf_type(C,subset_type(B)) ),
file('theBenchmark.p',p9) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p10) ).
fof(p11,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',p11) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p12) ).
fof(p13,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',p13) ).
fof(p14,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('theBenchmark.p',p14) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p15) ).
fof(p16,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',p16) ).
fof(p17,axiom,
! [B] :
( ( ilf_type(B,set_type)
& empty(B) )
=> relation_like(B) ),
file('theBenchmark.p',p17) ).
fof(p18,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',p18) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p19) ).
fof(prove_relset_1_2,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_2) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_2] :
( ! [U_1] :
( ! [U_0] :
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1)
| ~ ilf_type(U_0,set_type) )
| ~ ilf_type(U_1,set_type) )
| ~ ilf_type(U_2,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_2,U_0] :
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1)
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type)
| ~ ilf_type(U_2,set_type) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1)
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type)
| ~ ilf_type(U_2,set_type) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( member(D,cross_product(B,C))
| ! [E] :
( ! [F] :
( D != ordered_pair(E,F)
| ~ member(F,C)
| ~ member(E,B)
| ~ ilf_type(F,set_type) )
| ~ ilf_type(E,set_type) ) )
& ( ? [E] :
( ? [F] :
( D = ordered_pair(E,F)
& member(F,C)
& member(E,B)
& ilf_type(F,set_type) )
& ilf_type(E,set_type) )
| ~ member(D,cross_product(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_9] :
( ! [U_8] :
( ! [U_7] :
( ( ( member(U_7,cross_product(U_9,U_8))
| ! [U_6] :
( ! [U_5] :
( U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ member(U_6,U_9)
| ~ ilf_type(U_5,set_type) )
| ~ ilf_type(U_6,set_type) ) )
& ( ? [U_4] :
( ? [U_3] :
( U_7 = ordered_pair(U_4,U_3)
& member(U_3,U_8)
& member(U_4,U_9)
& ilf_type(U_3,set_type) )
& ilf_type(U_4,set_type) )
| ~ member(U_7,cross_product(U_9,U_8)) ) )
| ~ ilf_type(U_7,set_type) )
| ~ ilf_type(U_8,set_type) )
| ~ ilf_type(U_9,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_9] :
( ! [U_8] :
( ! [U_7] :
( ( ( member(U_7,cross_product(U_9,U_8))
| ! [U_6] :
( ! [U_5] :
( U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ ilf_type(U_5,set_type) )
| ~ member(U_6,U_9)
| ~ ilf_type(U_6,set_type) ) )
& ( ? [U_4] :
( ? [U_3] :
( U_7 = ordered_pair(U_4,U_3)
& member(U_3,U_8)
& ilf_type(U_3,set_type) )
& member(U_4,U_9)
& ilf_type(U_4,set_type) )
| ~ member(U_7,cross_product(U_9,U_8)) ) )
| ~ ilf_type(U_7,set_type) )
| ~ ilf_type(U_8,set_type) )
| ~ ilf_type(U_9,set_type) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
! [U_9] :
( ! [U_8] :
( ! [U_7] :
( ( ( member(U_7,cross_product(U_9,U_8))
| ! [U_6] :
( ! [U_5] :
( U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ ilf_type(U_5,set_type) )
| ~ member(U_6,U_9)
| ~ ilf_type(U_6,set_type) ) )
& ( ( ? [U_3] :
( U_7 = ordered_pair(sK1(U_9,U_8,U_7),U_3)
& member(U_3,U_8)
& ilf_type(U_3,set_type) )
& member(sK1(U_9,U_8,U_7),U_9)
& ilf_type(sK1(U_9,U_8,U_7),set_type) )
| ~ member(U_7,cross_product(U_9,U_8)) ) )
| ~ ilf_type(U_7,set_type) )
| ~ ilf_type(U_8,set_type) )
| ~ ilf_type(U_9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1(U_9,U_8,U_7))],[f_2_3]) ).
fof(f_2_5,plain,
! [U_9] :
( ! [U_8] :
( ! [U_7] :
( ( ( member(U_7,cross_product(U_9,U_8))
| ! [U_6] :
( ! [U_5] :
( U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ ilf_type(U_5,set_type) )
| ~ member(U_6,U_9)
| ~ ilf_type(U_6,set_type) ) )
& ( ( U_7 = ordered_pair(sK1(U_9,U_8,U_7),sK2(U_9,U_8,U_7))
& member(sK2(U_9,U_8,U_7),U_8)
& ilf_type(sK2(U_9,U_8,U_7),set_type)
& member(sK1(U_9,U_8,U_7),U_9)
& ilf_type(sK1(U_9,U_8,U_7),set_type) )
| ~ member(U_7,cross_product(U_9,U_8)) ) )
| ~ ilf_type(U_7,set_type) )
| ~ ilf_type(U_8,set_type) )
| ~ ilf_type(U_9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2(U_9,U_8,U_7))],[f_2_4]) ).
fof(f_2_6,plain,
( ! [U_7,U_8,U_9] :
( U_7 = ordered_pair(sK1(U_9,U_8,U_7),sK2(U_9,U_8,U_7))
| ~ sP0(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( member(sK2(U_9,U_8,U_7),U_8)
| ~ sP0(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( ilf_type(sK2(U_9,U_8,U_7),set_type)
| ~ sP0(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( member(sK1(U_9,U_8,U_7),U_9)
| ~ sP0(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( ilf_type(sK1(U_9,U_8,U_7),set_type)
| ~ sP0(U_7,U_8,U_9) )
& ! [U_6,U_5,U_7,U_8,U_9] :
( member(U_7,cross_product(U_9,U_8))
| U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ ilf_type(U_5,set_type)
| ~ member(U_6,U_9)
| ~ ilf_type(U_6,set_type)
| ~ sP1(U_6,U_5,U_7,U_8,U_9) )
& ! [U_6,U_5,U_7,U_8,U_9] :
( sP0(U_7,U_8,U_9)
| ~ member(U_7,cross_product(U_9,U_8))
| ~ sP1(U_6,U_5,U_7,U_8,U_9) )
& ! [U_6,U_5,U_7,U_8,U_9] :
( sP1(U_6,U_5,U_7,U_8,U_9)
| ~ ilf_type(U_7,set_type)
| ~ ilf_type(U_8,set_type)
| ~ ilf_type(U_9,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_2_5]) ).
cnf(f_2_7,plain,
( sP1(U_6,U_5,U_7,U_8,U_9)
| ~ ilf_type(U_7,set_type)
| ~ ilf_type(U_8,set_type)
| ~ ilf_type(U_9,set_type) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_8,plain,
( sP0(U_7,U_8,U_9)
| ~ member(U_7,cross_product(U_9,U_8))
| ~ sP1(U_6,U_5,U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_9,plain,
( member(U_7,cross_product(U_9,U_8))
| U_7 != ordered_pair(U_6,U_5)
| ~ member(U_5,U_8)
| ~ ilf_type(U_5,set_type)
| ~ member(U_6,U_9)
| ~ ilf_type(U_6,set_type)
| ~ sP1(U_6,U_5,U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_10,plain,
( ilf_type(sK1(U_9,U_8,U_7),set_type)
| ~ sP0(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_11,plain,
( member(sK1(U_9,U_8,U_7),U_9)
| ~ sP0(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_12,plain,
( ilf_type(sK2(U_9,U_8,U_7),set_type)
| ~ sP0(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_13,plain,
( member(sK2(U_9,U_8,U_7),U_8)
| ~ sP0(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_14,plain,
( U_7 = ordered_pair(sK1(U_9,U_8,U_7),sK2(U_9,U_8,U_7))
| ~ sP0(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_2_6]) ).
fof(f_3_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)],[p3]) ).
fof(f_3_2,plain,
! [U_11] :
( ! [U_10] :
( ilf_type(cross_product(U_11,U_10),set_type)
| ~ ilf_type(U_10,set_type) )
| ~ ilf_type(U_11,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_11,U_10] :
( ilf_type(cross_product(U_11,U_10),set_type)
| ~ ilf_type(U_10,set_type)
| ~ ilf_type(U_11,set_type) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( ilf_type(cross_product(U_11,U_10),set_type)
| ~ ilf_type(U_10,set_type)
| ~ ilf_type(U_11,set_type) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(f_4_2,plain,
! [U_15] :
( ! [U_14] :
( ( ! [U_13] :
( ilf_type(U_13,subset_type(cross_product(U_15,U_14)))
| ~ ilf_type(U_13,relation_type(U_15,U_14)) )
& ! [U_12] :
( ilf_type(U_12,relation_type(U_15,U_14))
| ~ ilf_type(U_12,subset_type(cross_product(U_15,U_14))) ) )
| ~ ilf_type(U_14,set_type) )
| ~ ilf_type(U_15,set_type) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_12,U_13,U_14,U_15] :
( ilf_type(U_13,subset_type(cross_product(U_15,U_14)))
| ~ ilf_type(U_13,relation_type(U_15,U_14))
| ~ sP2(U_12,U_13,U_14,U_15) )
& ! [U_12,U_13,U_14,U_15] :
( ilf_type(U_12,relation_type(U_15,U_14))
| ~ ilf_type(U_12,subset_type(cross_product(U_15,U_14)))
| ~ sP2(U_12,U_13,U_14,U_15) )
& ! [U_12,U_13,U_14,U_15] :
( sP2(U_12,U_13,U_14,U_15)
| ~ ilf_type(U_14,set_type)
| ~ ilf_type(U_15,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP2(U_12,U_13,U_14,U_15)
| ~ ilf_type(U_14,set_type)
| ~ ilf_type(U_15,set_type) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ilf_type(U_12,relation_type(U_15,U_14))
| ~ ilf_type(U_12,subset_type(cross_product(U_15,U_14)))
| ~ sP2(U_12,U_13,U_14,U_15) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( ilf_type(U_13,subset_type(cross_product(U_15,U_14)))
| ~ ilf_type(U_13,relation_type(U_15,U_14))
| ~ sP2(U_12,U_13,U_14,U_15) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B] :
( ! [C] :
( ? [D] : ilf_type(D,relation_type(C,B))
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p5]) ).
fof(f_5_2,plain,
! [U_18] :
( ! [U_17] :
( ? [U_16] : ilf_type(U_16,relation_type(U_17,U_18))
| ~ ilf_type(U_17,set_type) )
| ~ ilf_type(U_18,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_18] :
( ! [U_17] :
( ilf_type(sK3(U_18,U_17),relation_type(U_17,U_18))
| ~ ilf_type(U_17,set_type) )
| ~ ilf_type(U_18,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_18,U_17))],[f_5_2]) ).
fof(f_5_4,plain,
! [U_18,U_17] :
( ilf_type(sK3(U_18,U_17),relation_type(U_17,U_18))
| ~ ilf_type(U_17,set_type)
| ~ ilf_type(U_18,set_type) ),
inference(definitional_conversion,[status(esa)],[f_5_3]) ).
cnf(f_5_5,plain,
( ilf_type(sK3(U_18,U_17),relation_type(U_17,U_18))
| ~ ilf_type(U_17,set_type)
| ~ ilf_type(U_18,set_type) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_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)],[p6]) ).
fof(f_6_2,plain,
! [U_22] :
( ! [U_21] :
( ( ( subset(U_22,U_21)
| ? [U_20] :
( ~ member(U_20,U_21)
& member(U_20,U_22)
& ilf_type(U_20,set_type) ) )
& ( ! [U_19] :
( member(U_19,U_21)
| ~ member(U_19,U_22)
| ~ ilf_type(U_19,set_type) )
| ~ subset(U_22,U_21) ) )
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,set_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_22] :
( ! [U_21] :
( ( ( subset(U_22,U_21)
| ( ~ member(sK4(U_22,U_21),U_21)
& member(sK4(U_22,U_21),U_22)
& ilf_type(sK4(U_22,U_21),set_type) ) )
& ( ! [U_19] :
( member(U_19,U_21)
| ~ member(U_19,U_22)
| ~ ilf_type(U_19,set_type) )
| ~ subset(U_22,U_21) ) )
| ~ ilf_type(U_21,set_type) )
| ~ ilf_type(U_22,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4(U_22,U_21))],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_21,U_22] :
( ~ member(sK4(U_22,U_21),U_21)
| ~ sP3(U_21,U_22) )
& ! [U_21,U_22] :
( member(sK4(U_22,U_21),U_22)
| ~ sP3(U_21,U_22) )
& ! [U_21,U_22] :
( ilf_type(sK4(U_22,U_21),set_type)
| ~ sP3(U_21,U_22) )
& ! [U_21,U_22,U_19] :
( subset(U_22,U_21)
| sP3(U_21,U_22)
| ~ sP4(U_21,U_22,U_19) )
& ! [U_21,U_22,U_19] :
( member(U_19,U_21)
| ~ member(U_19,U_22)
| ~ ilf_type(U_19,set_type)
| ~ subset(U_22,U_21)
| ~ sP4(U_21,U_22,U_19) )
& ! [U_21,U_22,U_19] :
( sP4(U_21,U_22,U_19)
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_6_3]) ).
cnf(f_6_5,plain,
( sP4(U_21,U_22,U_19)
| ~ ilf_type(U_21,set_type)
| ~ ilf_type(U_22,set_type) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( member(U_19,U_21)
| ~ member(U_19,U_22)
| ~ ilf_type(U_19,set_type)
| ~ subset(U_22,U_21)
| ~ sP4(U_21,U_22,U_19) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( subset(U_22,U_21)
| sP3(U_21,U_22)
| ~ sP4(U_21,U_22,U_19) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_8,plain,
( ilf_type(sK4(U_22,U_21),set_type)
| ~ sP3(U_21,U_22) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_9,plain,
( member(sK4(U_22,U_21),U_22)
| ~ sP3(U_21,U_22) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_10,plain,
( ~ member(sK4(U_22,U_21),U_21)
| ~ sP3(U_21,U_22) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_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)],[p7]) ).
fof(f_7_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_7_1]) ).
fof(f_7_3,plain,
! [U_23,U_24] :
( 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_7_2]) ).
cnf(f_7_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_7_3]) ).
fof(f_8_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)],[p8]) ).
fof(f_8_2,plain,
! [U_26] :
( ! [U_25] :
( ( ( ilf_type(U_25,subset_type(U_26))
| ~ ilf_type(U_25,member_type(power_set(U_26))) )
& ( ilf_type(U_25,member_type(power_set(U_26)))
| ~ ilf_type(U_25,subset_type(U_26)) ) )
| ~ ilf_type(U_25,set_type) )
| ~ ilf_type(U_26,set_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_26,U_25] :
( ilf_type(U_25,subset_type(U_26))
| ~ ilf_type(U_25,member_type(power_set(U_26)))
| ~ sP5(U_26,U_25) )
& ! [U_26,U_25] :
( ilf_type(U_25,member_type(power_set(U_26)))
| ~ ilf_type(U_25,subset_type(U_26))
| ~ sP5(U_26,U_25) )
& ! [U_26,U_25] :
( sP5(U_26,U_25)
| ~ ilf_type(U_25,set_type)
| ~ ilf_type(U_26,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP5(U_26,U_25)
| ~ ilf_type(U_25,set_type)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( ilf_type(U_25,member_type(power_set(U_26)))
| ~ ilf_type(U_25,subset_type(U_26))
| ~ sP5(U_26,U_25) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( ilf_type(U_25,subset_type(U_26))
| ~ ilf_type(U_25,member_type(power_set(U_26)))
| ~ sP5(U_26,U_25) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_9_2,plain,
! [U_28] :
( ? [U_27] : ilf_type(U_27,subset_type(U_28))
| ~ ilf_type(U_28,set_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_28] :
( ilf_type(sK5(U_28),subset_type(U_28))
| ~ ilf_type(U_28,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5(U_28))],[f_9_2]) ).
fof(f_9_4,plain,
! [U_28] :
( ilf_type(sK5(U_28),subset_type(U_28))
| ~ ilf_type(U_28,set_type) ),
inference(definitional_conversion,[status(esa)],[f_9_3]) ).
cnf(f_9_5,plain,
( ilf_type(sK5(U_28),subset_type(U_28))
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p10]) ).
fof(f_10_2,plain,
! [U_29] :
( subset(U_29,U_29)
| ~ ilf_type(U_29,set_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_29] :
( subset(U_29,U_29)
| ~ ilf_type(U_29,set_type) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( subset(U_29,U_29)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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)],[p11]) ).
fof(f_11_2,plain,
! [U_33] :
( ! [U_32] :
( ( ( member(U_33,power_set(U_32))
| ? [U_31] :
( ~ member(U_31,U_32)
& member(U_31,U_33)
& ilf_type(U_31,set_type) ) )
& ( ! [U_30] :
( member(U_30,U_32)
| ~ member(U_30,U_33)
| ~ ilf_type(U_30,set_type) )
| ~ member(U_33,power_set(U_32)) ) )
| ~ ilf_type(U_32,set_type) )
| ~ ilf_type(U_33,set_type) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_33] :
( ! [U_32] :
( ( ( member(U_33,power_set(U_32))
| ( ~ member(sK6(U_33,U_32),U_32)
& member(sK6(U_33,U_32),U_33)
& ilf_type(sK6(U_33,U_32),set_type) ) )
& ( ! [U_30] :
( member(U_30,U_32)
| ~ member(U_30,U_33)
| ~ ilf_type(U_30,set_type) )
| ~ member(U_33,power_set(U_32)) ) )
| ~ ilf_type(U_32,set_type) )
| ~ ilf_type(U_33,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6(U_33,U_32))],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_32,U_33] :
( ~ member(sK6(U_33,U_32),U_32)
| ~ sP6(U_32,U_33) )
& ! [U_32,U_33] :
( member(sK6(U_33,U_32),U_33)
| ~ sP6(U_32,U_33) )
& ! [U_32,U_33] :
( ilf_type(sK6(U_33,U_32),set_type)
| ~ sP6(U_32,U_33) )
& ! [U_32,U_33,U_30] :
( member(U_33,power_set(U_32))
| sP6(U_32,U_33)
| ~ sP7(U_32,U_33,U_30) )
& ! [U_32,U_33,U_30] :
( member(U_30,U_32)
| ~ member(U_30,U_33)
| ~ ilf_type(U_30,set_type)
| ~ member(U_33,power_set(U_32))
| ~ sP7(U_32,U_33,U_30) )
& ! [U_32,U_33,U_30] :
( sP7(U_32,U_33,U_30)
| ~ ilf_type(U_32,set_type)
| ~ ilf_type(U_33,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7])],[f_11_3]) ).
cnf(f_11_5,plain,
( sP7(U_32,U_33,U_30)
| ~ ilf_type(U_32,set_type)
| ~ ilf_type(U_33,set_type) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( member(U_30,U_32)
| ~ member(U_30,U_33)
| ~ ilf_type(U_30,set_type)
| ~ member(U_33,power_set(U_32))
| ~ sP7(U_32,U_33,U_30) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_7,plain,
( member(U_33,power_set(U_32))
| sP6(U_32,U_33)
| ~ sP7(U_32,U_33,U_30) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_8,plain,
( ilf_type(sK6(U_33,U_32),set_type)
| ~ sP6(U_32,U_33) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_9,plain,
( member(sK6(U_33,U_32),U_33)
| ~ sP6(U_32,U_33) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_10,plain,
( ~ member(sK6(U_33,U_32),U_32)
| ~ sP6(U_32,U_33) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p12]) ).
fof(f_12_2,plain,
! [U_34] :
( ( ilf_type(power_set(U_34),set_type)
& ~ empty(power_set(U_34)) )
| ~ ilf_type(U_34,set_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_34] :
( ilf_type(power_set(U_34),set_type)
| ~ sP8(U_34) )
& ! [U_34] :
( ~ empty(power_set(U_34))
| ~ sP8(U_34) )
& ! [U_34] :
( sP8(U_34)
| ~ ilf_type(U_34,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP8(U_34)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( ~ empty(power_set(U_34))
| ~ sP8(U_34) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( ilf_type(power_set(U_34),set_type)
| ~ sP8(U_34) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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)],[p13]) ).
fof(f_13_2,plain,
! [U_36] :
( ! [U_35] :
( ( ( ilf_type(U_36,member_type(U_35))
| ~ member(U_36,U_35) )
& ( member(U_36,U_35)
| ~ ilf_type(U_36,member_type(U_35)) ) )
| ~ ilf_type(U_35,set_type)
| empty(U_35) )
| ~ ilf_type(U_36,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_36,U_35] :
( ilf_type(U_36,member_type(U_35))
| ~ member(U_36,U_35)
| ~ sP9(U_36,U_35) )
& ! [U_36,U_35] :
( member(U_36,U_35)
| ~ ilf_type(U_36,member_type(U_35))
| ~ sP9(U_36,U_35) )
& ! [U_36,U_35] :
( sP9(U_36,U_35)
| ~ ilf_type(U_35,set_type)
| empty(U_35)
| ~ ilf_type(U_36,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP9(U_36,U_35)
| ~ ilf_type(U_35,set_type)
| empty(U_35)
| ~ ilf_type(U_36,set_type) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( member(U_36,U_35)
| ~ ilf_type(U_36,member_type(U_35))
| ~ sP9(U_36,U_35) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( ilf_type(U_36,member_type(U_35))
| ~ member(U_36,U_35)
| ~ sP9(U_36,U_35) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_14_2,plain,
! [U_38] :
( ? [U_37] : ilf_type(U_37,member_type(U_38))
| ~ ilf_type(U_38,set_type)
| empty(U_38) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_38] :
( ilf_type(sK7(U_38),member_type(U_38))
| ~ ilf_type(U_38,set_type)
| empty(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7(U_38))],[f_14_2]) ).
fof(f_14_4,plain,
! [U_38] :
( ilf_type(sK7(U_38),member_type(U_38))
| ~ ilf_type(U_38,set_type)
| empty(U_38) ),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
( ilf_type(sK7(U_38),member_type(U_38))
| ~ ilf_type(U_38,set_type)
| empty(U_38) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_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)],[p15]) ).
fof(f_15_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_15_1]) ).
fof(f_15_3,plain,
! [U_41] :
( ( ( empty(U_41)
| ( member(sK8(U_41),U_41)
& ilf_type(sK8(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,[sK8]),skolemize(U_40,sK8(U_41))],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_41] :
( member(sK8(U_41),U_41)
| ~ sP10(U_41) )
& ! [U_41] :
( ilf_type(sK8(U_41),set_type)
| ~ sP10(U_41) )
& ! [U_41,U_39] :
( empty(U_41)
| sP10(U_41)
| ~ sP11(U_41,U_39) )
& ! [U_41,U_39] :
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type)
| ~ empty(U_41)
| ~ sP11(U_41,U_39) )
& ! [U_41,U_39] :
( sP11(U_41,U_39)
| ~ ilf_type(U_41,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP11(U_41,U_39)
| ~ ilf_type(U_41,set_type) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( ~ member(U_39,U_41)
| ~ ilf_type(U_39,set_type)
| ~ empty(U_41)
| ~ sP11(U_41,U_39) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( empty(U_41)
| sP10(U_41)
| ~ sP11(U_41,U_39) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
( ilf_type(sK8(U_41),set_type)
| ~ sP10(U_41) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_9,plain,
( member(sK8(U_41),U_41)
| ~ sP10(U_41) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_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)],[p16]) ).
fof(f_16_2,plain,
! [U_48] :
( ( ( relation_like(U_48)
| ? [U_47] :
( ! [U_46] :
( ! [U_45] :
( U_47 != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) )
& member(U_47,U_48)
& ilf_type(U_47,set_type) ) )
& ( ! [U_44] :
( ? [U_43] :
( ? [U_42] :
( U_44 = ordered_pair(U_43,U_42)
& ilf_type(U_42,set_type) )
& ilf_type(U_43,set_type) )
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type) )
| ~ relation_like(U_48) ) )
| ~ ilf_type(U_48,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_48] :
( ( ( relation_like(U_48)
| ? [U_47] :
( ! [U_46] :
( ! [U_45] :
( U_47 != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) )
& member(U_47,U_48)
& ilf_type(U_47,set_type) ) )
& ( ! [U_44] :
( ( ? [U_42] :
( U_44 = ordered_pair(sK9(U_48,U_44),U_42)
& ilf_type(U_42,set_type) )
& ilf_type(sK9(U_48,U_44),set_type) )
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type) )
| ~ relation_like(U_48) ) )
| ~ ilf_type(U_48,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_43,sK9(U_48,U_44))],[f_16_2]) ).
fof(f_16_4,plain,
! [U_48] :
( ( ( relation_like(U_48)
| ? [U_47] :
( ! [U_46] :
( ! [U_45] :
( U_47 != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) )
& member(U_47,U_48)
& ilf_type(U_47,set_type) ) )
& ( ! [U_44] :
( ( U_44 = ordered_pair(sK9(U_48,U_44),sK10(U_48,U_44))
& ilf_type(sK10(U_48,U_44),set_type)
& ilf_type(sK9(U_48,U_44),set_type) )
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type) )
| ~ relation_like(U_48) ) )
| ~ ilf_type(U_48,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_42,sK10(U_48,U_44))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_48] :
( ( ( relation_like(U_48)
| ( ! [U_46] :
( ! [U_45] :
( sK11(U_48) != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type) )
| ~ ilf_type(U_46,set_type) )
& member(sK11(U_48),U_48)
& ilf_type(sK11(U_48),set_type) ) )
& ( ! [U_44] :
( ( U_44 = ordered_pair(sK9(U_48,U_44),sK10(U_48,U_44))
& ilf_type(sK10(U_48,U_44),set_type)
& ilf_type(sK9(U_48,U_44),set_type) )
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type) )
| ~ relation_like(U_48) ) )
| ~ ilf_type(U_48,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11(U_48))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_45,U_46,U_48] :
( sK11(U_48) != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,set_type)
| ~ sP13(U_45,U_46,U_48) )
& ! [U_45,U_46,U_48] :
( member(sK11(U_48),U_48)
| ~ sP13(U_45,U_46,U_48) )
& ! [U_45,U_46,U_48] :
( ilf_type(sK11(U_48),set_type)
| ~ sP13(U_45,U_46,U_48) )
& ! [U_44,U_48] :
( U_44 = ordered_pair(sK9(U_48,U_44),sK10(U_48,U_44))
| ~ sP12(U_44,U_48) )
& ! [U_44,U_48] :
( ilf_type(sK10(U_48,U_44),set_type)
| ~ sP12(U_44,U_48) )
& ! [U_44,U_48] :
( ilf_type(sK9(U_48,U_44),set_type)
| ~ sP12(U_44,U_48) )
& ! [U_44,U_45,U_46,U_48] :
( relation_like(U_48)
| sP13(U_45,U_46,U_48)
| ~ sP14(U_44,U_45,U_46,U_48) )
& ! [U_44,U_45,U_46,U_48] :
( sP12(U_44,U_48)
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type)
| ~ relation_like(U_48)
| ~ sP14(U_44,U_45,U_46,U_48) )
& ! [U_44,U_45,U_46,U_48] :
( sP14(U_44,U_45,U_46,U_48)
| ~ ilf_type(U_48,set_type) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13,sP14])],[f_16_5]) ).
cnf(f_16_7,plain,
( sP14(U_44,U_45,U_46,U_48)
| ~ ilf_type(U_48,set_type) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_8,plain,
( sP12(U_44,U_48)
| ~ member(U_44,U_48)
| ~ ilf_type(U_44,set_type)
| ~ relation_like(U_48)
| ~ sP14(U_44,U_45,U_46,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_9,plain,
( relation_like(U_48)
| sP13(U_45,U_46,U_48)
| ~ sP14(U_44,U_45,U_46,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_10,plain,
( ilf_type(sK9(U_48,U_44),set_type)
| ~ sP12(U_44,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_11,plain,
( ilf_type(sK10(U_48,U_44),set_type)
| ~ sP12(U_44,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_12,plain,
( U_44 = ordered_pair(sK9(U_48,U_44),sK10(U_48,U_44))
| ~ sP12(U_44,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_13,plain,
( ilf_type(sK11(U_48),set_type)
| ~ sP13(U_45,U_46,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_14,plain,
( member(sK11(U_48),U_48)
| ~ sP13(U_45,U_46,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_15,plain,
( sK11(U_48) != ordered_pair(U_46,U_45)
| ~ ilf_type(U_45,set_type)
| ~ ilf_type(U_46,set_type)
| ~ sP13(U_45,U_46,U_48) ),
inference(clausify,[status(thm)],[f_16_6]) ).
fof(f_17_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_17_2,plain,
! [U_49] :
( relation_like(U_49)
| ~ ilf_type(U_49,set_type)
| ~ empty(U_49) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_49] :
( relation_like(U_49)
| ~ ilf_type(U_49,set_type)
| ~ empty(U_49) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( relation_like(U_49)
| ~ ilf_type(U_49,set_type)
| ~ empty(U_49) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_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)],[p18]) ).
fof(f_18_2,plain,
! [U_52] :
( ! [U_51] :
( ! [U_50] :
( relation_like(U_50)
| ~ ilf_type(U_50,subset_type(cross_product(U_52,U_51))) )
| ~ ilf_type(U_51,set_type) )
| ~ ilf_type(U_52,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_52,U_51,U_50] :
( relation_like(U_50)
| ~ ilf_type(U_50,subset_type(cross_product(U_52,U_51)))
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( relation_like(U_50)
| ~ ilf_type(U_50,subset_type(cross_product(U_52,U_51)))
| ~ ilf_type(U_51,set_type)
| ~ ilf_type(U_52,set_type) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(f_19_2,plain,
! [U_53] : ilf_type(U_53,set_type),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_53] : ilf_type(U_53,set_type),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
ilf_type(U_53,set_type),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_2]) ).
fof(f_20_2,negated_conjecture,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ subset(B,cross_product(C,D))
& subset(B,E)
& ilf_type(E,relation_type(C,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_20_1]) ).
fof(f_20_3,negated_conjecture,
? [U_57] :
( ? [U_56] :
( ? [U_55] :
( ? [U_54] :
( ~ subset(U_57,cross_product(U_56,U_55))
& subset(U_57,U_54)
& ilf_type(U_54,relation_type(U_56,U_55)) )
& ilf_type(U_55,set_type) )
& ilf_type(U_56,set_type) )
& ilf_type(U_57,set_type) ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( ? [U_56] :
( ? [U_55] :
( ? [U_54] :
( ~ subset(sK12,cross_product(U_56,U_55))
& subset(sK12,U_54)
& ilf_type(U_54,relation_type(U_56,U_55)) )
& ilf_type(U_55,set_type) )
& ilf_type(U_56,set_type) )
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_57,sK12)],[f_20_3]) ).
fof(f_20_5,negated_conjecture,
( ? [U_55] :
( ? [U_54] :
( ~ subset(sK12,cross_product(sK13,U_55))
& subset(sK12,U_54)
& ilf_type(U_54,relation_type(sK13,U_55)) )
& ilf_type(U_55,set_type) )
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_56,sK13)],[f_20_4]) ).
fof(f_20_6,negated_conjecture,
( ? [U_54] :
( ~ subset(sK12,cross_product(sK13,sK14))
& subset(sK12,U_54)
& ilf_type(U_54,relation_type(sK13,sK14)) )
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_55,sK14)],[f_20_5]) ).
fof(f_20_7,negated_conjecture,
( ~ subset(sK12,cross_product(sK13,sK14))
& subset(sK12,sK15)
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_54,sK15)],[f_20_6]) ).
fof(f_20_8,negated_conjecture,
( ~ subset(sK12,cross_product(sK13,sK14))
& subset(sK12,sK15)
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(definitional_conversion,[status(esa)],[f_20_7]) ).
cnf(f_20_9,negated_conjecture,
ilf_type(sK12,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_10,negated_conjecture,
ilf_type(sK13,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_11,negated_conjecture,
ilf_type(sK14,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_12,negated_conjecture,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_13,negated_conjecture,
subset(sK12,sK15),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_14,negated_conjecture,
~ subset(sK12,cross_product(sK13,sK14)),
inference(clausify,[status(thm)],[f_20_8]) ).
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,
( 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_5,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_6,axiom,
( subset_type(Eq_x_0) = subset_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( member_type(Eq_x_0) = member_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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_11,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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_12,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_13,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_14,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,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_20,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,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_23,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_24,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(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_27,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_28,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_29,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(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,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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_31,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_32,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_33,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_34,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(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,
( sP10(Eq_y_0)
| ~ sP10(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,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_38,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(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_40,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP14(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
% 0.00/0.02 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 22:47:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 216.09/216.47 % SZS status Theorem for theBenchmark
% 216.09/216.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------