%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET601+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 : n008.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 08:57:04 AM UTC 2026
% Result : Theorem 234.25s 234.57s
% Output : Proof 235.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_union,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('theBenchmark.p',associativity_of_union) ).
fof(idempotency_of_intersection,axiom,
! [B] : intersection(B,B) = B,
file('theBenchmark.p',idempotency_of_intersection) ).
fof(associativity_of_intersection,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('theBenchmark.p',associativity_of_intersection) ).
fof(union_intersection,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('theBenchmark.p',union_intersection) ).
fof(union_distributes_over_intersection,axiom,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
file('theBenchmark.p',union_distributes_over_intersection) ).
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th72,conjecture,
! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
file('theBenchmark.p',prove_th72) ).
fof(f_1_1,plain,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(fof_nnf,[status(thm)],[associativity_of_union]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] : union(union(U_2,U_1),U_0) = union(U_2,union(U_1,U_0)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_2,U_0] : union(union(U_2,U_1),U_0) = union(U_2,union(U_1,U_0)),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
union(union(U_2,U_1),U_0) = union(U_2,union(U_1,U_0)),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B] : intersection(B,B) = B,
inference(fof_nnf,[status(thm)],[idempotency_of_intersection]) ).
fof(f_2_2,plain,
! [U_3] : intersection(U_3,U_3) = U_3,
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3] : intersection(U_3,U_3) = U_3,
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
intersection(U_3,U_3) = U_3,
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(fof_nnf,[status(thm)],[associativity_of_intersection]) ).
fof(f_3_2,plain,
! [U_6,U_5,U_4] : intersection(intersection(U_6,U_5),U_4) = intersection(U_6,intersection(U_5,U_4)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4,U_5,U_6] : intersection(intersection(U_6,U_5),U_4) = intersection(U_6,intersection(U_5,U_4)),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
intersection(intersection(U_6,U_5),U_4) = intersection(U_6,intersection(U_5,U_4)),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(fof_nnf,[status(thm)],[union_intersection]) ).
fof(f_4_2,plain,
! [U_8,U_7] : union(U_8,intersection(U_8,U_7)) = U_8,
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_7,U_8] : union(U_8,intersection(U_8,U_7)) = U_8,
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
union(U_8,intersection(U_8,U_7)) = U_8,
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
inference(fof_nnf,[status(thm)],[union_distributes_over_intersection]) ).
fof(f_5_2,plain,
! [U_11,U_10,U_9] : union(U_11,intersection(U_10,U_9)) = intersection(union(U_11,U_10),union(U_11,U_9)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9,U_10,U_11] : union(U_11,intersection(U_10,U_9)) = intersection(union(U_11,U_10),union(U_11,U_9)),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
union(U_11,intersection(U_10,U_9)) = intersection(union(U_11,U_10),union(U_11,U_9)),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B,C,D] :
( ( member(D,union(B,C))
| ( ~ member(D,C)
& ~ member(D,B) ) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(fof_nnf,[status(thm)],[union_defn]) ).
fof(f_6_2,plain,
! [U_14,U_13,U_12] :
( ( member(U_12,union(U_14,U_13))
| ( ~ member(U_12,U_13)
& ~ member(U_12,U_14) ) )
& ( member(U_12,U_13)
| member(U_12,U_14)
| ~ member(U_12,union(U_14,U_13)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_20,U_18,U_16] :
( member(U_16,union(U_20,U_18))
| ( ~ member(U_16,U_18)
& ~ member(U_16,U_20) ) )
& ! [U_19,U_17,U_15] :
( member(U_15,U_17)
| member(U_15,U_19)
| ~ member(U_15,union(U_19,U_17)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_20,U_16,U_18] :
( ~ member(U_16,U_18)
| ~ sP0(U_20,U_16,U_18) )
& ! [U_20,U_16,U_18] :
( ~ member(U_16,U_20)
| ~ sP0(U_20,U_16,U_18) )
& ! [U_20,U_16,U_18] :
( member(U_16,union(U_20,U_18))
| sP0(U_20,U_16,U_18) )
& ! [U_15,U_17,U_19] :
( member(U_15,U_17)
| member(U_15,U_19)
| ~ member(U_15,union(U_19,U_17)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_15,U_17)
| member(U_15,U_19)
| ~ member(U_15,union(U_19,U_17)) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( member(U_16,union(U_20,U_18))
| sP0(U_20,U_16,U_18) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ member(U_16,U_20)
| ~ sP0(U_20,U_16,U_18) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_8,plain,
( ~ member(U_16,U_18)
| ~ sP0(U_20,U_16,U_18) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_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_7_2,plain,
! [U_23,U_22,U_21] :
( ( member(U_21,intersection(U_23,U_22))
| ~ member(U_21,U_22)
| ~ member(U_21,U_23) )
& ( ( member(U_21,U_22)
& member(U_21,U_23) )
| ~ member(U_21,intersection(U_23,U_22)) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_29,U_27,U_25] :
( member(U_25,intersection(U_29,U_27))
| ~ member(U_25,U_27)
| ~ member(U_25,U_29) )
& ! [U_28,U_26,U_24] :
( ( member(U_24,U_26)
& member(U_24,U_28) )
| ~ member(U_24,intersection(U_28,U_26)) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_24,U_26,U_28] :
( member(U_24,U_26)
| ~ sP1(U_24,U_26,U_28) )
& ! [U_24,U_26,U_28] :
( member(U_24,U_28)
| ~ sP1(U_24,U_26,U_28) )
& ! [U_25,U_27,U_29] :
( member(U_25,intersection(U_29,U_27))
| ~ member(U_25,U_27)
| ~ member(U_25,U_29) )
& ! [U_24,U_26,U_28] :
( sP1(U_24,U_26,U_28)
| ~ member(U_24,intersection(U_28,U_26)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_3]) ).
cnf(f_7_5,plain,
( sP1(U_24,U_26,U_28)
| ~ member(U_24,intersection(U_28,U_26)) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( member(U_25,intersection(U_29,U_27))
| ~ member(U_25,U_27)
| ~ member(U_25,U_29) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( member(U_24,U_28)
| ~ sP1(U_24,U_26,U_28) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_8,plain,
( member(U_24,U_26)
| ~ sP1(U_24,U_26,U_28) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_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_8_2,plain,
! [U_31,U_30] :
( ( U_31 = U_30
| ~ subset(U_30,U_31)
| ~ subset(U_31,U_30) )
& ( ( subset(U_30,U_31)
& subset(U_31,U_30) )
| U_31 != U_30 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_35,U_33] :
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) )
& ! [U_34,U_32] :
( ( subset(U_32,U_34)
& subset(U_34,U_32) )
| U_34 != U_32 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_34,U_32] :
( subset(U_32,U_34)
| ~ sP2(U_34,U_32) )
& ! [U_34,U_32] :
( subset(U_34,U_32)
| ~ sP2(U_34,U_32) )
& ! [U_33,U_35] :
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) )
& ! [U_34,U_32] :
( sP2(U_34,U_32)
| U_34 != U_32 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_3]) ).
cnf(f_8_5,plain,
( sP2(U_34,U_32)
| U_34 != U_32 ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( subset(U_34,U_32)
| ~ sP2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( subset(U_32,U_34)
| ~ sP2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_9_2,plain,
! [U_37,U_36] : union(U_37,U_36) = union(U_36,U_37),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_36,U_37] : union(U_37,U_36) = union(U_36,U_37),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
union(U_37,U_36) = union(U_36,U_37),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_10_2,plain,
! [U_39,U_38] : intersection(U_39,U_38) = intersection(U_38,U_39),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_39,U_38] : intersection(U_39,U_38) = intersection(U_38,U_39),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
intersection(U_39,U_38) = intersection(U_38,U_39),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_43,U_42] :
( ( subset(U_43,U_42)
| ? [U_41] :
( ~ member(U_41,U_42)
& member(U_41,U_43) ) )
& ( ! [U_40] :
( member(U_40,U_42)
| ~ member(U_40,U_43) )
| ~ subset(U_43,U_42) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_47,U_45] :
( subset(U_47,U_45)
| ? [U_41] :
( ~ member(U_41,U_45)
& member(U_41,U_47) ) )
& ! [U_46,U_44] :
( ! [U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46) )
| ~ subset(U_46,U_44) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_47,U_45] :
( subset(U_47,U_45)
| ( ~ member(sK1(U_47,U_45),U_45)
& member(sK1(U_47,U_45),U_47) ) )
& ! [U_46,U_44] :
( ! [U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46) )
| ~ subset(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_41,sK1(U_47,U_45))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_45,U_47] :
( ~ member(sK1(U_47,U_45),U_45)
| ~ sP3(U_45,U_47) )
& ! [U_45,U_47] :
( member(sK1(U_47,U_45),U_47)
| ~ sP3(U_45,U_47) )
& ! [U_45,U_47] :
( subset(U_47,U_45)
| sP3(U_45,U_47) )
& ! [U_44,U_46,U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46)
| ~ subset(U_46,U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_11_4]) ).
cnf(f_11_6,plain,
( member(U_40,U_44)
| ~ member(U_40,U_46)
| ~ subset(U_46,U_44) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( subset(U_47,U_45)
| sP3(U_45,U_47) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( member(sK1(U_47,U_45),U_47)
| ~ sP3(U_45,U_47) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( ~ member(sK1(U_47,U_45),U_45)
| ~ sP3(U_45,U_47) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_12_2,plain,
! [U_48] : subset(U_48,U_48),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_48] : subset(U_48,U_48),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
subset(U_48,U_48),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_52,U_51] :
( ( U_52 = U_51
| ? [U_50] :
( ( ~ member(U_50,U_52)
& member(U_50,U_51) )
| ( ~ member(U_50,U_51)
& member(U_50,U_52) ) ) )
& ( ! [U_49] :
( ( member(U_49,U_52)
| ~ member(U_49,U_51) )
& ( member(U_49,U_51)
| ~ member(U_49,U_52) ) )
| U_52 != U_51 ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_60,U_58] :
( U_60 = U_58
| ? [U_56] :
( ~ member(U_56,U_60)
& member(U_56,U_58) )
| ? [U_55] :
( ~ member(U_55,U_58)
& member(U_55,U_60) ) )
& ! [U_59,U_57] :
( ( ! [U_54] :
( member(U_54,U_59)
| ~ member(U_54,U_57) )
& ! [U_53] :
( member(U_53,U_57)
| ~ member(U_53,U_59) ) )
| U_59 != U_57 ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_60,U_58] :
( U_60 = U_58
| ? [U_56] :
( ~ member(U_56,U_60)
& member(U_56,U_58) )
| ( ~ member(sK2(U_60,U_58),U_58)
& member(sK2(U_60,U_58),U_60) ) )
& ! [U_59,U_57] :
( ( ! [U_54] :
( member(U_54,U_59)
| ~ member(U_54,U_57) )
& ! [U_53] :
( member(U_53,U_57)
| ~ member(U_53,U_59) ) )
| U_59 != U_57 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_55,sK2(U_60,U_58))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_60,U_58] :
( U_60 = U_58
| ( ~ member(sK3(U_60,U_58),U_60)
& member(sK3(U_60,U_58),U_58) )
| ( ~ member(sK2(U_60,U_58),U_58)
& member(sK2(U_60,U_58),U_60) ) )
& ! [U_59,U_57] :
( ( ! [U_54] :
( member(U_54,U_59)
| ~ member(U_54,U_57) )
& ! [U_53] :
( member(U_53,U_57)
| ~ member(U_53,U_59) ) )
| U_59 != U_57 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_56,sK3(U_60,U_58))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_58,U_60] :
( ~ member(sK3(U_60,U_58),U_60)
| ~ sP6(U_58,U_60) )
& ! [U_58,U_60] :
( member(sK3(U_60,U_58),U_58)
| ~ sP6(U_58,U_60) )
& ! [U_58,U_60] :
( ~ member(sK2(U_60,U_58),U_58)
| ~ sP5(U_58,U_60) )
& ! [U_58,U_60] :
( member(sK2(U_60,U_58),U_60)
| ~ sP5(U_58,U_60) )
& ! [U_53,U_54,U_57,U_59] :
( member(U_54,U_59)
| ~ member(U_54,U_57)
| ~ sP4(U_53,U_54,U_57,U_59) )
& ! [U_53,U_54,U_57,U_59] :
( member(U_53,U_57)
| ~ member(U_53,U_59)
| ~ sP4(U_53,U_54,U_57,U_59) )
& ! [U_58,U_60] :
( U_60 = U_58
| sP6(U_58,U_60)
| sP5(U_58,U_60) )
& ! [U_53,U_54,U_57,U_59] :
( sP4(U_53,U_54,U_57,U_59)
| U_59 != U_57 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6])],[f_13_5]) ).
cnf(f_13_7,plain,
( sP4(U_53,U_54,U_57,U_59)
| U_59 != U_57 ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
( U_60 = U_58
| sP6(U_58,U_60)
| sP5(U_58,U_60) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
( member(U_53,U_57)
| ~ member(U_53,U_59)
| ~ sP4(U_53,U_54,U_57,U_59) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,plain,
( member(U_54,U_59)
| ~ member(U_54,U_57)
| ~ sP4(U_53,U_54,U_57,U_59) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,plain,
( member(sK2(U_60,U_58),U_60)
| ~ sP5(U_58,U_60) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_12,plain,
( ~ member(sK2(U_60,U_58),U_58)
| ~ sP5(U_58,U_60) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_13,plain,
( member(sK3(U_60,U_58),U_58)
| ~ sP6(U_58,U_60) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_14,plain,
( ~ member(sK3(U_60,U_58),U_60)
| ~ sP6(U_58,U_60) ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,negated_conjecture,
~ ! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(negate,[status(cth)],[prove_th72]) ).
fof(f_14_2,negated_conjecture,
? [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) != intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(fof_nnf,[status(thm)],[f_14_1]) ).
fof(f_14_3,negated_conjecture,
? [U_63,U_62,U_61] : union(union(intersection(U_63,U_62),intersection(U_62,U_61)),intersection(U_61,U_63)) != intersection(intersection(union(U_63,U_62),union(U_62,U_61)),union(U_61,U_63)),
inference(variable_rename,[status(thm)],[f_14_2]) ).
fof(f_14_4,negated_conjecture,
? [U_62,U_61] : union(union(intersection(sK4,U_62),intersection(U_62,U_61)),intersection(U_61,sK4)) != intersection(intersection(union(sK4,U_62),union(U_62,U_61)),union(U_61,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_63,sK4)],[f_14_3]) ).
fof(f_14_5,negated_conjecture,
? [U_61] : union(union(intersection(sK4,sK5),intersection(sK5,U_61)),intersection(U_61,sK4)) != intersection(intersection(union(sK4,sK5),union(sK5,U_61)),union(U_61,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_62,sK5)],[f_14_4]) ).
fof(f_14_6,negated_conjecture,
union(union(intersection(sK4,sK5),intersection(sK5,sK6)),intersection(sK6,sK4)) != intersection(intersection(union(sK4,sK5),union(sK5,sK6)),union(sK6,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_61,sK6)],[f_14_5]) ).
fof(f_14_7,negated_conjecture,
union(union(intersection(sK4,sK5),intersection(sK5,sK6)),intersection(sK6,sK4)) != intersection(intersection(union(sK4,sK5),union(sK5,sK6)),union(sK6,sK4)),
inference(definitional_conversion,[status(esa)],[f_14_6]) ).
cnf(f_14_8,negated_conjecture,
union(union(intersection(sK4,sK5),intersection(sK5,sK6)),intersection(sK6,sK4)) != intersection(intersection(union(sK4,sK5),union(sK5,sK6)),union(sK6,sK4)),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( union(Eq_x_0,Eq_x_1) = union(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,
( 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_6,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_7,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_8,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_9,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_10,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_11,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_12,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(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,
( 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_15,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP4(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_16,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_17,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 22:42:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 234.25/234.57 % SZS status Theorem for theBenchmark
% 234.25/234.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------