%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET636+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 : n011.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 08:57:11 AM UTC 2026
% Result : Theorem 263.01s 283.18s
% Output : Proof 263.64s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th118,conjecture,
! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
file('theBenchmark.p',prove_th118) ).
fof(f_1_1,plain,
! [B,C,D] :
( ( member(D,intersection(B,C))
| ~ member(D,C)
| ~ member(D,B) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(fof_nnf,[status(thm)],[intersection_defn]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,intersection(U_2,U_1))
| ~ member(U_0,U_1)
| ~ member(U_0,U_2) )
& ( ( member(U_0,U_1)
& member(U_0,U_2) )
| ~ member(U_0,intersection(U_2,U_1)) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_8,U_6,U_4] :
( member(U_4,intersection(U_8,U_6))
| ~ member(U_4,U_6)
| ~ member(U_4,U_8) )
& ! [U_7,U_5,U_3] :
( ( member(U_3,U_5)
& member(U_3,U_7) )
| ~ member(U_3,intersection(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_3,U_7)
| ~ member(U_3,intersection(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_3,U_5)
| ~ member(U_3,intersection(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( member(U_4,intersection(U_8,U_6))
| ~ member(U_4,U_6)
| ~ member(U_4,U_8) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B,C] :
( ( intersect(B,C)
| ! [D] :
( ~ member(D,C)
| ~ member(D,B) ) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11] :
( ( intersect(U_12,U_11)
| ! [U_10] :
( ~ member(U_10,U_11)
| ~ member(U_10,U_12) ) )
& ( ? [U_9] :
( member(U_9,U_11)
& member(U_9,U_12) )
| ~ intersect(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ? [U_9] :
( member(U_9,U_13)
& member(U_9,U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ( member(sK1(U_15,U_13),U_13)
& member(sK1(U_15,U_13),U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_15,U_13))],[f_2_3]) ).
cnf(f_2_5,plain,
( member(sK1(U_15,U_13),U_15)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(sK1(U_15,U_13),U_13)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( intersect(U_16,U_14)
| ~ member(U_10,U_14)
| ~ member(U_10,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_3_2,plain,
! [U_17] : ~ member(U_17,empty_set),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ member(U_17,empty_set),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [B,C] :
( ( disjoint(B,C)
| intersect(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[disjoint_defn]) ).
fof(f_4_2,plain,
! [U_19,U_18] :
( ( disjoint(U_19,U_18)
| intersect(U_19,U_18) )
& ( ~ intersect(U_19,U_18)
| ~ disjoint(U_19,U_18) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_23,U_21] :
( disjoint(U_23,U_21)
| intersect(U_23,U_21) )
& ! [U_22,U_20] :
( ~ intersect(U_22,U_20)
| ~ disjoint(U_22,U_20) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ intersect(U_22,U_20)
| ~ disjoint(U_22,U_20) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( disjoint(U_23,U_21)
| intersect(U_23,U_21) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C] :
( ( B = C
| ~ subset(C,B)
| ~ subset(B,C) )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_defn]) ).
fof(f_5_2,plain,
! [U_25,U_24] :
( ( U_25 = U_24
| ~ subset(U_24,U_25)
| ~ subset(U_25,U_24) )
& ( ( subset(U_24,U_25)
& subset(U_25,U_24) )
| U_25 != U_24 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_29,U_27] :
( U_29 = U_27
| ~ subset(U_27,U_29)
| ~ subset(U_29,U_27) )
& ! [U_28,U_26] :
( ( subset(U_26,U_28)
& subset(U_28,U_26) )
| U_28 != U_26 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_28,U_26)
| U_28 != U_26 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_26,U_28)
| U_28 != U_26 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_29 = U_27
| ~ subset(U_27,U_29)
| ~ subset(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_6_2,plain,
! [U_31,U_30] : intersection(U_31,U_30) = intersection(U_30,U_31),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
intersection(U_31,U_30) = intersection(U_30,U_31),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_7_2,plain,
! [U_33,U_32] :
( intersect(U_32,U_33)
| ~ intersect(U_33,U_32) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( intersect(U_32,U_33)
| ~ intersect(U_33,U_32) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B,C] :
( ( subset(B,C)
| ? [D] :
( ~ member(D,C)
& member(D,B) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(f_8_2,plain,
! [U_37,U_36] :
( ( subset(U_37,U_36)
| ? [U_35] :
( ~ member(U_35,U_36)
& member(U_35,U_37) ) )
& ( ! [U_34] :
( member(U_34,U_36)
| ~ member(U_34,U_37) )
| ~ subset(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_41,U_39] :
( subset(U_41,U_39)
| ? [U_35] :
( ~ member(U_35,U_39)
& member(U_35,U_41) ) )
& ! [U_40,U_38] :
( ! [U_34] :
( member(U_34,U_38)
| ~ member(U_34,U_40) )
| ~ subset(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_41,U_39] :
( subset(U_41,U_39)
| ( ~ member(sK2(U_41,U_39),U_39)
& member(sK2(U_41,U_39),U_41) ) )
& ! [U_40,U_38] :
( ! [U_34] :
( member(U_34,U_38)
| ~ member(U_34,U_40) )
| ~ subset(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_35,sK2(U_41,U_39))],[f_8_3]) ).
cnf(f_8_5,plain,
( member(U_34,U_38)
| ~ member(U_34,U_40)
| ~ subset(U_40,U_38) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( member(sK2(U_41,U_39),U_41)
| subset(U_41,U_39) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ member(sK2(U_41,U_39),U_39)
| subset(U_41,U_39) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_9_2,plain,
! [U_42] : subset(U_42,U_42),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
subset(U_42,U_42),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_10_2,plain,
! [U_45] :
( ( empty(U_45)
| ? [U_44] : member(U_44,U_45) )
& ( ! [U_43] : ~ member(U_43,U_45)
| ~ empty(U_45) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_47] :
( empty(U_47)
| ? [U_44] : member(U_44,U_47) )
& ! [U_46] :
( ! [U_43] : ~ member(U_43,U_46)
| ~ empty(U_46) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_47] :
( empty(U_47)
| member(sK3(U_47),U_47) )
& ! [U_46] :
( ! [U_43] : ~ member(U_43,U_46)
| ~ empty(U_46) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_44,sK3(U_47))],[f_10_3]) ).
cnf(f_10_5,plain,
( ~ member(U_43,U_46)
| ~ empty(U_46) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( empty(U_47)
| member(sK3(U_47),U_47) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [B,C] :
( ( B = C
| ? [D] :
( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) ) )
& ( ! [D] :
( ( member(D,B)
| ~ member(D,C) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(f_11_2,plain,
! [U_51,U_50] :
( ( U_51 = U_50
| ? [U_49] :
( ( ~ member(U_49,U_51)
& member(U_49,U_50) )
| ( ~ member(U_49,U_50)
& member(U_49,U_51) ) ) )
& ( ! [U_48] :
( ( member(U_48,U_51)
| ~ member(U_48,U_50) )
& ( member(U_48,U_50)
| ~ member(U_48,U_51) ) )
| U_51 != U_50 ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_59,U_57] :
( U_59 = U_57
| ? [U_55] :
( ~ member(U_55,U_59)
& member(U_55,U_57) )
| ? [U_54] :
( ~ member(U_54,U_57)
& member(U_54,U_59) ) )
& ! [U_58,U_56] :
( ( ! [U_53] :
( member(U_53,U_58)
| ~ member(U_53,U_56) )
& ! [U_52] :
( member(U_52,U_56)
| ~ member(U_52,U_58) ) )
| U_58 != U_56 ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_59,U_57] :
( U_59 = U_57
| ? [U_55] :
( ~ member(U_55,U_59)
& member(U_55,U_57) )
| ( ~ member(sK4(U_59,U_57),U_57)
& member(sK4(U_59,U_57),U_59) ) )
& ! [U_58,U_56] :
( ( ! [U_53] :
( member(U_53,U_58)
| ~ member(U_53,U_56) )
& ! [U_52] :
( member(U_52,U_56)
| ~ member(U_52,U_58) ) )
| U_58 != U_56 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_54,sK4(U_59,U_57))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_59,U_57] :
( U_59 = U_57
| ( ~ member(sK5(U_59,U_57),U_59)
& member(sK5(U_59,U_57),U_57) )
| ( ~ member(sK4(U_59,U_57),U_57)
& member(sK4(U_59,U_57),U_59) ) )
& ! [U_58,U_56] :
( ( ! [U_53] :
( member(U_53,U_58)
| ~ member(U_53,U_56) )
& ! [U_52] :
( member(U_52,U_56)
| ~ member(U_52,U_58) ) )
| U_58 != U_56 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_55,sK5(U_59,U_57))],[f_11_4]) ).
cnf(f_11_6,plain,
( member(U_52,U_56)
| ~ member(U_52,U_58)
| U_58 != U_56 ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( member(U_53,U_58)
| ~ member(U_53,U_56)
| U_58 != U_56 ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( member(sK5(U_59,U_57),U_57)
| member(sK4(U_59,U_57),U_59)
| U_59 = U_57 ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( ~ member(sK5(U_59,U_57),U_59)
| member(sK4(U_59,U_57),U_59)
| U_59 = U_57 ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_10,plain,
( member(sK5(U_59,U_57),U_57)
| ~ member(sK4(U_59,U_57),U_57)
| U_59 = U_57 ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_11,plain,
( ~ member(sK5(U_59,U_57),U_59)
| ~ member(sK4(U_59,U_57),U_57)
| U_59 = U_57 ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_1,negated_conjecture,
~ ! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
inference(negate,[status(cth)],[prove_th118]) ).
fof(f_12_2,negated_conjecture,
? [B,C] :
( ( ~ disjoint(B,C)
& intersection(B,C) = empty_set )
| ( intersection(B,C) != empty_set
& disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_61,U_60] :
( ( ~ disjoint(U_61,U_60)
& intersection(U_61,U_60) = empty_set )
| ( intersection(U_61,U_60) != empty_set
& disjoint(U_61,U_60) ) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
( ? [U_65,U_63] :
( ~ disjoint(U_65,U_63)
& intersection(U_65,U_63) = empty_set )
| ? [U_64,U_62] :
( intersection(U_64,U_62) != empty_set
& disjoint(U_64,U_62) ) ),
inference(miniscope,[status(thm)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ? [U_65,U_63] :
( ~ disjoint(U_65,U_63)
& intersection(U_65,U_63) = empty_set )
| ? [U_62] :
( intersection(sK6,U_62) != empty_set
& disjoint(sK6,U_62) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_64,sK6)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
( ? [U_65,U_63] :
( ~ disjoint(U_65,U_63)
& intersection(U_65,U_63) = empty_set )
| ( intersection(sK6,sK7) != empty_set
& disjoint(sK6,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_62,sK7)],[f_12_5]) ).
fof(f_12_7,negated_conjecture,
( ? [U_63] :
( ~ disjoint(sK8,U_63)
& intersection(sK8,U_63) = empty_set )
| ( intersection(sK6,sK7) != empty_set
& disjoint(sK6,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_65,sK8)],[f_12_6]) ).
fof(f_12_8,negated_conjecture,
( ( ~ disjoint(sK8,sK9)
& intersection(sK8,sK9) = empty_set )
| ( intersection(sK6,sK7) != empty_set
& disjoint(sK6,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_63,sK9)],[f_12_7]) ).
cnf(f_12_9,negated_conjecture,
( intersection(sK8,sK9) = empty_set
| disjoint(sK6,sK7) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_10,negated_conjecture,
( ~ disjoint(sK8,sK9)
| disjoint(sK6,sK7) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_11,negated_conjecture,
( intersection(sK8,sK9) = empty_set
| intersection(sK6,sK7) != empty_set ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_12,negated_conjecture,
( ~ disjoint(sK8,sK9)
| intersection(sK6,sK7) != empty_set ),
inference(clausify,[status(thm)],[f_12_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,
( intersection(Eq_x_0,Eq_x_1) = intersection(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,
( 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_6,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_7,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( intersect(Eq_y_0,Eq_y_1)
| ~ intersect(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET636+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
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/20.43 % CPULimit : 300
% 0.08/20.43 % WCLimit : 300
% 0.08/20.43 % DateTime : Sat Sep 19 22:47:21 UTC 2026
% 0.08/20.43 % CPUTime :
% 263.01/283.18 % SZS status Theorem for theBenchmark
% 263.01/283.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------