%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET642+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 : n007.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 0.12s 0.45s
% Output : Proof 0.12s
% 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)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,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)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p3,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',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ? [D] : ilf_type(D,relation_type(C,B)) ) ),
file('theBenchmark.p',p4) ).
fof(p5,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',p5) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p6) ).
fof(p7,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',p7) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ? [C] : ilf_type(C,subset_type(B)) ),
file('theBenchmark.p',p8) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('theBenchmark.p',p9) ).
fof(p10,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',p10) ).
fof(p11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p11) ).
fof(p12,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',p12) ).
fof(p13,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p14) ).
fof(p15,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',p15) ).
fof(p16,axiom,
! [B] :
( ( ilf_type(B,set_type)
& empty(B) )
=> relation_like(B) ),
file('theBenchmark.p',p16) ).
fof(p17,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',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p18) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p19) ).
fof(prove_relset_1_4,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)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_4) ).
fof(f_1_1,plain,
! [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)],[p1]) ).
fof(f_1_2,plain,
! [U_3] :
( ! [U_2] :
( ! [U_1] :
( ! [U_0] :
( subset(U_3,cross_product(U_2,U_1))
| ~ subset(U_3,U_0)
| ~ ilf_type(U_0,relation_type(U_2,U_1)) )
| ~ ilf_type(U_1,set_type) )
| ~ ilf_type(U_2,set_type) )
| ~ ilf_type(U_3,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( subset(U_3,cross_product(U_2,U_1))
| ~ subset(U_3,U_0)
| ~ ilf_type(U_0,relation_type(U_2,U_1))
| ~ ilf_type(U_1,set_type)
| ~ ilf_type(U_2,set_type)
| ~ ilf_type(U_3,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(B,relation_type(C,D))
| ~ subset(B,cross_product(C,D))
| ~ 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_6] :
( ! [U_5] :
( ! [U_4] :
( ilf_type(U_6,relation_type(U_5,U_4))
| ~ subset(U_6,cross_product(U_5,U_4))
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) )
| ~ ilf_type(U_6,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ilf_type(U_6,relation_type(U_5,U_4))
| ~ subset(U_6,cross_product(U_5,U_4))
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type)
| ~ ilf_type(U_6,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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)],[p3]) ).
fof(f_3_2,plain,
! [U_10] :
( ! [U_9] :
( ( ! [U_8] :
( ilf_type(U_8,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_8,relation_type(U_10,U_9)) )
& ! [U_7] :
( ilf_type(U_7,relation_type(U_10,U_9))
| ~ ilf_type(U_7,subset_type(cross_product(U_10,U_9))) ) )
| ~ ilf_type(U_9,set_type) )
| ~ ilf_type(U_10,set_type) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ilf_type(U_7,relation_type(U_10,U_9))
| ~ ilf_type(U_7,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( ilf_type(U_8,subset_type(cross_product(U_10,U_9)))
| ~ ilf_type(U_8,relation_type(U_10,U_9))
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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)],[p4]) ).
fof(f_4_2,plain,
! [U_13] :
( ! [U_12] :
( ? [U_11] : ilf_type(U_11,relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_13] :
( ! [U_12] :
( ilf_type(sK1(U_13,U_12),relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_13,U_12))],[f_4_2]) ).
cnf(f_4_4,plain,
( ilf_type(sK1(U_13,U_12),relation_type(U_12,U_13))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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)],[p5]) ).
fof(f_5_2,plain,
! [U_17] :
( ! [U_16] :
( ( ( subset(U_17,U_16)
| ? [U_15] :
( ~ member(U_15,U_16)
& member(U_15,U_17)
& ilf_type(U_15,set_type) ) )
& ( ! [U_14] :
( member(U_14,U_16)
| ~ member(U_14,U_17)
| ~ ilf_type(U_14,set_type) )
| ~ subset(U_17,U_16) ) )
| ~ ilf_type(U_16,set_type) )
| ~ ilf_type(U_17,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_17] :
( ! [U_16] :
( ( ( subset(U_17,U_16)
| ( ~ member(sK2(U_17,U_16),U_16)
& member(sK2(U_17,U_16),U_17)
& ilf_type(sK2(U_17,U_16),set_type) ) )
& ( ! [U_14] :
( member(U_14,U_16)
| ~ member(U_14,U_17)
| ~ ilf_type(U_14,set_type) )
| ~ subset(U_17,U_16) ) )
| ~ ilf_type(U_16,set_type) )
| ~ ilf_type(U_17,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_17,U_16))],[f_5_2]) ).
cnf(f_5_4,plain,
( member(U_14,U_16)
| ~ member(U_14,U_17)
| ~ ilf_type(U_14,set_type)
| ~ subset(U_17,U_16)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,set_type) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( ilf_type(sK2(U_17,U_16),set_type)
| subset(U_17,U_16)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,set_type) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( member(sK2(U_17,U_16),U_17)
| subset(U_17,U_16)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,set_type) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( ~ member(sK2(U_17,U_16),U_16)
| subset(U_17,U_16)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,set_type) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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)],[p6]) ).
fof(f_6_2,plain,
! [U_19] :
( ! [U_18] :
( ilf_type(cross_product(U_19,U_18),set_type)
| ~ ilf_type(U_18,set_type) )
| ~ ilf_type(U_19,set_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ilf_type(cross_product(U_19,U_18),set_type)
| ~ ilf_type(U_18,set_type)
| ~ ilf_type(U_19,set_type) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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)],[p7]) ).
fof(f_7_2,plain,
! [U_21] :
( ! [U_20] :
( ( ( ilf_type(U_20,subset_type(U_21))
| ~ ilf_type(U_20,member_type(power_set(U_21))) )
& ( ilf_type(U_20,member_type(power_set(U_21)))
| ~ ilf_type(U_20,subset_type(U_21)) ) )
| ~ ilf_type(U_20,set_type) )
| ~ ilf_type(U_21,set_type) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ilf_type(U_20,member_type(power_set(U_21)))
| ~ ilf_type(U_20,subset_type(U_21))
| ~ ilf_type(U_20,set_type)
| ~ ilf_type(U_21,set_type) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ilf_type(U_20,subset_type(U_21))
| ~ ilf_type(U_20,member_type(power_set(U_21)))
| ~ ilf_type(U_20,set_type)
| ~ ilf_type(U_21,set_type) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p8]) ).
fof(f_8_2,plain,
! [U_23] :
( ? [U_22] : ilf_type(U_22,subset_type(U_23))
| ~ ilf_type(U_23,set_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_23] :
( ilf_type(sK3(U_23),subset_type(U_23))
| ~ ilf_type(U_23,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3(U_23))],[f_8_2]) ).
cnf(f_8_4,plain,
( ilf_type(sK3(U_23),subset_type(U_23))
| ~ ilf_type(U_23,set_type) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_9_2,plain,
! [U_24] :
( subset(U_24,U_24)
| ~ ilf_type(U_24,set_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( subset(U_24,U_24)
| ~ ilf_type(U_24,set_type) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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)],[p10]) ).
fof(f_10_2,plain,
! [U_28] :
( ! [U_27] :
( ( ( member(U_28,power_set(U_27))
| ? [U_26] :
( ~ member(U_26,U_27)
& member(U_26,U_28)
& ilf_type(U_26,set_type) ) )
& ( ! [U_25] :
( member(U_25,U_27)
| ~ member(U_25,U_28)
| ~ ilf_type(U_25,set_type) )
| ~ member(U_28,power_set(U_27)) ) )
| ~ ilf_type(U_27,set_type) )
| ~ ilf_type(U_28,set_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_28] :
( ! [U_27] :
( ( ( member(U_28,power_set(U_27))
| ( ~ member(sK4(U_28,U_27),U_27)
& member(sK4(U_28,U_27),U_28)
& ilf_type(sK4(U_28,U_27),set_type) ) )
& ( ! [U_25] :
( member(U_25,U_27)
| ~ member(U_25,U_28)
| ~ ilf_type(U_25,set_type) )
| ~ member(U_28,power_set(U_27)) ) )
| ~ ilf_type(U_27,set_type) )
| ~ ilf_type(U_28,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4(U_28,U_27))],[f_10_2]) ).
cnf(f_10_4,plain,
( member(U_25,U_27)
| ~ member(U_25,U_28)
| ~ ilf_type(U_25,set_type)
| ~ member(U_28,power_set(U_27))
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( ilf_type(sK4(U_28,U_27),set_type)
| member(U_28,power_set(U_27))
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( member(sK4(U_28,U_27),U_28)
| member(U_28,power_set(U_27))
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( ~ member(sK4(U_28,U_27),U_27)
| member(U_28,power_set(U_27))
| ~ ilf_type(U_27,set_type)
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p11]) ).
fof(f_11_2,plain,
! [U_29] :
( ( ilf_type(power_set(U_29),set_type)
& ~ empty(power_set(U_29)) )
| ~ ilf_type(U_29,set_type) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( ~ empty(power_set(U_29))
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( ilf_type(power_set(U_29),set_type)
| ~ ilf_type(U_29,set_type) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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)],[p12]) ).
fof(f_12_2,plain,
! [U_31] :
( ! [U_30] :
( ( ( ilf_type(U_31,member_type(U_30))
| ~ member(U_31,U_30) )
& ( member(U_31,U_30)
| ~ ilf_type(U_31,member_type(U_30)) ) )
| ~ ilf_type(U_30,set_type)
| empty(U_30) )
| ~ ilf_type(U_31,set_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( member(U_31,U_30)
| ~ ilf_type(U_31,member_type(U_30))
| ~ ilf_type(U_30,set_type)
| empty(U_30)
| ~ ilf_type(U_31,set_type) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( ilf_type(U_31,member_type(U_30))
| ~ member(U_31,U_30)
| ~ ilf_type(U_30,set_type)
| empty(U_30)
| ~ ilf_type(U_31,set_type) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(fof_nnf,[status(thm)],[p13]) ).
fof(f_13_2,plain,
! [U_33] :
( ? [U_32] : ilf_type(U_32,member_type(U_33))
| ~ ilf_type(U_33,set_type)
| empty(U_33) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_33] :
( ilf_type(sK5(U_33),member_type(U_33))
| ~ ilf_type(U_33,set_type)
| empty(U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_32,sK5(U_33))],[f_13_2]) ).
cnf(f_13_4,plain,
( ilf_type(sK5(U_33),member_type(U_33))
| ~ ilf_type(U_33,set_type)
| empty(U_33) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_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)],[p14]) ).
fof(f_14_2,plain,
! [U_36] :
( ( ( empty(U_36)
| ? [U_35] :
( member(U_35,U_36)
& ilf_type(U_35,set_type) ) )
& ( ! [U_34] :
( ~ member(U_34,U_36)
| ~ ilf_type(U_34,set_type) )
| ~ empty(U_36) ) )
| ~ ilf_type(U_36,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_36] :
( ( ( empty(U_36)
| ( member(sK6(U_36),U_36)
& ilf_type(sK6(U_36),set_type) ) )
& ( ! [U_34] :
( ~ member(U_34,U_36)
| ~ ilf_type(U_34,set_type) )
| ~ empty(U_36) ) )
| ~ ilf_type(U_36,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6(U_36))],[f_14_2]) ).
cnf(f_14_4,plain,
( ~ member(U_34,U_36)
| ~ ilf_type(U_34,set_type)
| ~ empty(U_36)
| ~ ilf_type(U_36,set_type) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( ilf_type(sK6(U_36),set_type)
| empty(U_36)
| ~ ilf_type(U_36,set_type) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( member(sK6(U_36),U_36)
| empty(U_36)
| ~ ilf_type(U_36,set_type) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_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)],[p15]) ).
fof(f_15_2,plain,
! [U_43] :
( ( ( relation_like(U_43)
| ? [U_42] :
( ! [U_41] :
( ! [U_40] :
( U_42 != ordered_pair(U_41,U_40)
| ~ ilf_type(U_40,set_type) )
| ~ ilf_type(U_41,set_type) )
& member(U_42,U_43)
& ilf_type(U_42,set_type) ) )
& ( ! [U_39] :
( ? [U_38] :
( ? [U_37] :
( U_39 = ordered_pair(U_38,U_37)
& ilf_type(U_37,set_type) )
& ilf_type(U_38,set_type) )
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type) )
| ~ relation_like(U_43) ) )
| ~ ilf_type(U_43,set_type) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_43] :
( ( ( relation_like(U_43)
| ? [U_42] :
( ! [U_41] :
( ! [U_40] :
( U_42 != ordered_pair(U_41,U_40)
| ~ ilf_type(U_40,set_type) )
| ~ ilf_type(U_41,set_type) )
& member(U_42,U_43)
& ilf_type(U_42,set_type) ) )
& ( ! [U_39] :
( ( ? [U_37] :
( U_39 = ordered_pair(sK7(U_43,U_39),U_37)
& ilf_type(U_37,set_type) )
& ilf_type(sK7(U_43,U_39),set_type) )
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type) )
| ~ relation_like(U_43) ) )
| ~ ilf_type(U_43,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_38,sK7(U_43,U_39))],[f_15_2]) ).
fof(f_15_4,plain,
! [U_43] :
( ( ( relation_like(U_43)
| ? [U_42] :
( ! [U_41] :
( ! [U_40] :
( U_42 != ordered_pair(U_41,U_40)
| ~ ilf_type(U_40,set_type) )
| ~ ilf_type(U_41,set_type) )
& member(U_42,U_43)
& ilf_type(U_42,set_type) ) )
& ( ! [U_39] :
( ( U_39 = ordered_pair(sK7(U_43,U_39),sK8(U_43,U_39))
& ilf_type(sK8(U_43,U_39),set_type)
& ilf_type(sK7(U_43,U_39),set_type) )
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type) )
| ~ relation_like(U_43) ) )
| ~ ilf_type(U_43,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_37,sK8(U_43,U_39))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_43] :
( ( ( relation_like(U_43)
| ( ! [U_41] :
( ! [U_40] :
( sK9(U_43) != ordered_pair(U_41,U_40)
| ~ ilf_type(U_40,set_type) )
| ~ ilf_type(U_41,set_type) )
& member(sK9(U_43),U_43)
& ilf_type(sK9(U_43),set_type) ) )
& ( ! [U_39] :
( ( U_39 = ordered_pair(sK7(U_43,U_39),sK8(U_43,U_39))
& ilf_type(sK8(U_43,U_39),set_type)
& ilf_type(sK7(U_43,U_39),set_type) )
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type) )
| ~ relation_like(U_43) ) )
| ~ ilf_type(U_43,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_42,sK9(U_43))],[f_15_4]) ).
cnf(f_15_6,plain,
( ilf_type(sK7(U_43,U_39),set_type)
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type)
| ~ relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,plain,
( ilf_type(sK8(U_43,U_39),set_type)
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type)
| ~ relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,plain,
( U_39 = ordered_pair(sK7(U_43,U_39),sK8(U_43,U_39))
| ~ member(U_39,U_43)
| ~ ilf_type(U_39,set_type)
| ~ relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,plain,
( ilf_type(sK9(U_43),set_type)
| relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,plain,
( member(sK9(U_43),U_43)
| relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,plain,
( sK9(U_43) != ordered_pair(U_41,U_40)
| ~ ilf_type(U_40,set_type)
| ~ ilf_type(U_41,set_type)
| relation_like(U_43)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_15_5]) ).
fof(f_16_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p16]) ).
fof(f_16_2,plain,
! [U_44] :
( relation_like(U_44)
| ~ ilf_type(U_44,set_type)
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( relation_like(U_44)
| ~ ilf_type(U_44,set_type)
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_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)],[p17]) ).
fof(f_17_2,plain,
! [U_47] :
( ! [U_46] :
( ! [U_45] :
( relation_like(U_45)
| ~ ilf_type(U_45,subset_type(cross_product(U_47,U_46))) )
| ~ ilf_type(U_46,set_type) )
| ~ ilf_type(U_47,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( relation_like(U_45)
| ~ ilf_type(U_45,subset_type(cross_product(U_47,U_46)))
| ~ ilf_type(U_46,set_type)
| ~ ilf_type(U_47,set_type) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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)],[p18]) ).
fof(f_18_2,plain,
! [U_49] :
( ! [U_48] :
( ilf_type(ordered_pair(U_49,U_48),set_type)
| ~ ilf_type(U_48,set_type) )
| ~ ilf_type(U_49,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ilf_type(ordered_pair(U_49,U_48),set_type)
| ~ ilf_type(U_48,set_type)
| ~ ilf_type(U_49,set_type) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(f_19_2,plain,
! [U_50] : ilf_type(U_50,set_type),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
ilf_type(U_50,set_type),
inference(clausify,[status(thm)],[f_19_2]) ).
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)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_4]) ).
fof(f_20_2,negated_conjecture,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(B,relation_type(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_54] :
( ? [U_53] :
( ? [U_52] :
( ? [U_51] :
( ~ ilf_type(U_54,relation_type(U_53,U_52))
& subset(U_54,U_51)
& ilf_type(U_51,relation_type(U_53,U_52)) )
& ilf_type(U_52,set_type) )
& ilf_type(U_53,set_type) )
& ilf_type(U_54,set_type) ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( ? [U_53] :
( ? [U_52] :
( ? [U_51] :
( ~ ilf_type(sK10,relation_type(U_53,U_52))
& subset(sK10,U_51)
& ilf_type(U_51,relation_type(U_53,U_52)) )
& ilf_type(U_52,set_type) )
& ilf_type(U_53,set_type) )
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_54,sK10)],[f_20_3]) ).
fof(f_20_5,negated_conjecture,
( ? [U_52] :
( ? [U_51] :
( ~ ilf_type(sK10,relation_type(sK11,U_52))
& subset(sK10,U_51)
& ilf_type(U_51,relation_type(sK11,U_52)) )
& ilf_type(U_52,set_type) )
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_53,sK11)],[f_20_4]) ).
fof(f_20_6,negated_conjecture,
( ? [U_51] :
( ~ ilf_type(sK10,relation_type(sK11,sK12))
& subset(sK10,U_51)
& ilf_type(U_51,relation_type(sK11,sK12)) )
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_52,sK12)],[f_20_5]) ).
fof(f_20_7,negated_conjecture,
( ~ ilf_type(sK10,relation_type(sK11,sK12))
& subset(sK10,sK13)
& ilf_type(sK13,relation_type(sK11,sK12))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_51,sK13)],[f_20_6]) ).
fof(f_20_8,negated_conjecture,
( ~ ilf_type(sK10,relation_type(sK11,sK12))
& subset(sK10,sK13)
& ilf_type(sK13,relation_type(sK11,sK12))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(definitional_conversion,[status(esa)],[f_20_7]) ).
cnf(f_20_9,negated_conjecture,
ilf_type(sK10,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_10,negated_conjecture,
ilf_type(sK11,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_11,negated_conjecture,
ilf_type(sK12,set_type),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_12,negated_conjecture,
ilf_type(sK13,relation_type(sK11,sK12)),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_13,negated_conjecture,
subset(sK10,sK13),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_14,negated_conjecture,
~ ilf_type(sK10,relation_type(sK11,sK12)),
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,
( relation_type(Eq_x_0,Eq_x_1) = relation_type(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( 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_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,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( member_type(Eq_x_0) = member_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,
( 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_11,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_12,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| 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) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,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_21,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_22,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+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
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 22:42:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------