%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET613+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 : n003.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 08:57:07 AM UTC 2026
% Result : Theorem 192.35s 192.67s
% Output : Proof 192.91s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('theBenchmark.p',member_equal) ).
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(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
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(prove_difference_union_intersection,conjecture,
! [B,C] : difference(union(B,C),intersection(B,C)) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',prove_difference_union_intersection) ).
fof(f_1_1,plain,
! [B,C] :
( B = C
| ? [D] :
( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) ) ),
inference(fof_nnf,[status(thm)],[member_equal]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_0] :
( ( ~ member(U_0,U_2)
& member(U_0,U_1) )
| ( ~ member(U_0,U_1)
& member(U_0,U_2) ) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_4] :
( ~ member(U_4,U_2)
& member(U_4,U_1) )
| ? [U_3] :
( ~ member(U_3,U_1)
& member(U_3,U_2) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_4] :
( ~ member(U_4,U_2)
& member(U_4,U_1) )
| ( ~ member(sK1(U_2,U_1),U_1)
& member(sK1(U_2,U_1),U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_2,U_1))],[f_1_3]) ).
fof(f_1_5,plain,
! [U_2,U_1] :
( U_2 = U_1
| ( ~ member(sK2(U_2,U_1),U_2)
& member(sK2(U_2,U_1),U_1) )
| ( ~ member(sK1(U_2,U_1),U_1)
& member(sK1(U_2,U_1),U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_2,U_1))],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK2(U_2,U_1),U_1)
| member(sK1(U_2,U_1),U_2)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( ~ member(sK2(U_2,U_1),U_2)
| member(sK1(U_2,U_1),U_2)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( member(sK2(U_2,U_1),U_1)
| ~ member(sK1(U_2,U_1),U_1)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,plain,
( ~ member(sK2(U_2,U_1),U_2)
| ~ member(sK1(U_2,U_1),U_1)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_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_2_2,plain,
! [U_7,U_6,U_5] :
( ( member(U_5,union(U_7,U_6))
| ( ~ member(U_5,U_6)
& ~ member(U_5,U_7) ) )
& ( member(U_5,U_6)
| member(U_5,U_7)
| ~ member(U_5,union(U_7,U_6)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11,U_9] :
( member(U_9,union(U_13,U_11))
| ( ~ member(U_9,U_11)
& ~ member(U_9,U_13) ) )
& ! [U_12,U_10,U_8] :
( member(U_8,U_10)
| member(U_8,U_12)
| ~ member(U_8,union(U_12,U_10)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( member(U_8,U_10)
| member(U_8,U_12)
| ~ member(U_8,union(U_12,U_10)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ member(U_9,U_13)
| member(U_9,union(U_13,U_11)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( ~ member(U_9,U_11)
| member(U_9,union(U_13,U_11)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_16,U_15,U_14] :
( ( member(U_14,intersection(U_16,U_15))
| ~ member(U_14,U_15)
| ~ member(U_14,U_16) )
& ( ( member(U_14,U_15)
& member(U_14,U_16) )
| ~ member(U_14,intersection(U_16,U_15)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_22,U_20,U_18] :
( member(U_18,intersection(U_22,U_20))
| ~ member(U_18,U_20)
| ~ member(U_18,U_22) )
& ! [U_21,U_19,U_17] :
( ( member(U_17,U_19)
& member(U_17,U_21) )
| ~ member(U_17,intersection(U_21,U_19)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( member(U_17,U_21)
| ~ member(U_17,intersection(U_21,U_19)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( member(U_17,U_19)
| ~ member(U_17,intersection(U_21,U_19)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( member(U_18,intersection(U_22,U_20))
| ~ member(U_18,U_20)
| ~ member(U_18,U_22) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B,C,D] :
( ( member(D,difference(B,C))
| member(D,C)
| ~ member(D,B) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(fof_nnf,[status(thm)],[difference_defn]) ).
fof(f_4_2,plain,
! [U_25,U_24,U_23] :
( ( member(U_23,difference(U_25,U_24))
| member(U_23,U_24)
| ~ member(U_23,U_25) )
& ( ( ~ member(U_23,U_24)
& member(U_23,U_25) )
| ~ member(U_23,difference(U_25,U_24)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_31,U_29,U_27] :
( member(U_27,difference(U_31,U_29))
| member(U_27,U_29)
| ~ member(U_27,U_31) )
& ! [U_30,U_28,U_26] :
( ( ~ member(U_26,U_28)
& member(U_26,U_30) )
| ~ member(U_26,difference(U_30,U_28)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_26,U_30)
| ~ member(U_26,difference(U_30,U_28)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ member(U_26,U_28)
| ~ member(U_26,difference(U_30,U_28)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( member(U_27,difference(U_31,U_29))
| member(U_27,U_29)
| ~ member(U_27,U_31) ),
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_33,U_32] :
( ( U_33 = U_32
| ~ subset(U_32,U_33)
| ~ subset(U_33,U_32) )
& ( ( subset(U_32,U_33)
& subset(U_33,U_32) )
| U_33 != U_32 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) )
& ! [U_36,U_34] :
( ( subset(U_34,U_36)
& subset(U_36,U_34) )
| U_36 != U_34 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_36,U_34)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_34,U_36)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_6_2,plain,
! [U_39,U_38] : union(U_39,U_38) = union(U_38,U_39),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
union(U_39,U_38) = union(U_38,U_39),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_7_2,plain,
! [U_41,U_40] : intersection(U_41,U_40) = intersection(U_40,U_41),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
intersection(U_41,U_40) = intersection(U_40,U_41),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_45,U_44] :
( ( U_45 = U_44
| ? [U_43] :
( ( ~ member(U_43,U_45)
& member(U_43,U_44) )
| ( ~ member(U_43,U_44)
& member(U_43,U_45) ) ) )
& ( ! [U_42] :
( ( member(U_42,U_45)
| ~ member(U_42,U_44) )
& ( member(U_42,U_44)
| ~ member(U_42,U_45) ) )
| U_45 != U_44 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_53,U_51] :
( U_53 = U_51
| ? [U_49] :
( ~ member(U_49,U_53)
& member(U_49,U_51) )
| ? [U_48] :
( ~ member(U_48,U_51)
& member(U_48,U_53) ) )
& ! [U_52,U_50] :
( ( ! [U_47] :
( member(U_47,U_52)
| ~ member(U_47,U_50) )
& ! [U_46] :
( member(U_46,U_50)
| ~ member(U_46,U_52) ) )
| U_52 != U_50 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_53,U_51] :
( U_53 = U_51
| ? [U_49] :
( ~ member(U_49,U_53)
& member(U_49,U_51) )
| ( ~ member(sK3(U_53,U_51),U_51)
& member(sK3(U_53,U_51),U_53) ) )
& ! [U_52,U_50] :
( ( ! [U_47] :
( member(U_47,U_52)
| ~ member(U_47,U_50) )
& ! [U_46] :
( member(U_46,U_50)
| ~ member(U_46,U_52) ) )
| U_52 != U_50 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_48,sK3(U_53,U_51))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_53,U_51] :
( U_53 = U_51
| ( ~ member(sK4(U_53,U_51),U_53)
& member(sK4(U_53,U_51),U_51) )
| ( ~ member(sK3(U_53,U_51),U_51)
& member(sK3(U_53,U_51),U_53) ) )
& ! [U_52,U_50] :
( ( ! [U_47] :
( member(U_47,U_52)
| ~ member(U_47,U_50) )
& ! [U_46] :
( member(U_46,U_50)
| ~ member(U_46,U_52) ) )
| U_52 != U_50 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_49,sK4(U_53,U_51))],[f_8_4]) ).
cnf(f_8_6,plain,
( member(U_46,U_50)
| ~ member(U_46,U_52)
| U_52 != U_50 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( member(U_47,U_52)
| ~ member(U_47,U_50)
| U_52 != U_50 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( member(sK4(U_53,U_51),U_51)
| member(sK3(U_53,U_51),U_53)
| U_53 = U_51 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ member(sK4(U_53,U_51),U_53)
| member(sK3(U_53,U_51),U_53)
| U_53 = U_51 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( member(sK4(U_53,U_51),U_51)
| ~ member(sK3(U_53,U_51),U_51)
| U_53 = U_51 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ member(sK4(U_53,U_51),U_53)
| ~ member(sK3(U_53,U_51),U_51)
| U_53 = U_51 ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_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_9_2,plain,
! [U_57,U_56] :
( ( subset(U_57,U_56)
| ? [U_55] :
( ~ member(U_55,U_56)
& member(U_55,U_57) ) )
& ( ! [U_54] :
( member(U_54,U_56)
| ~ member(U_54,U_57) )
| ~ subset(U_57,U_56) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_61,U_59] :
( subset(U_61,U_59)
| ? [U_55] :
( ~ member(U_55,U_59)
& member(U_55,U_61) ) )
& ! [U_60,U_58] :
( ! [U_54] :
( member(U_54,U_58)
| ~ member(U_54,U_60) )
| ~ subset(U_60,U_58) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_61,U_59] :
( subset(U_61,U_59)
| ( ~ member(sK5(U_61,U_59),U_59)
& member(sK5(U_61,U_59),U_61) ) )
& ! [U_60,U_58] :
( ! [U_54] :
( member(U_54,U_58)
| ~ member(U_54,U_60) )
| ~ subset(U_60,U_58) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_55,sK5(U_61,U_59))],[f_9_3]) ).
cnf(f_9_5,plain,
( member(U_54,U_58)
| ~ member(U_54,U_60)
| ~ subset(U_60,U_58) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( member(sK5(U_61,U_59),U_61)
| subset(U_61,U_59) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,plain,
( ~ member(sK5(U_61,U_59),U_59)
| subset(U_61,U_59) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_10_2,plain,
! [U_62] : subset(U_62,U_62),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
subset(U_62,U_62),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,negated_conjecture,
~ ! [B,C] : difference(union(B,C),intersection(B,C)) = union(difference(B,C),difference(C,B)),
inference(negate,[status(cth)],[prove_difference_union_intersection]) ).
fof(f_11_2,negated_conjecture,
? [B,C] : difference(union(B,C),intersection(B,C)) != union(difference(B,C),difference(C,B)),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_64,U_63] : difference(union(U_64,U_63),intersection(U_64,U_63)) != union(difference(U_64,U_63),difference(U_63,U_64)),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_63] : difference(union(sK6,U_63),intersection(sK6,U_63)) != union(difference(sK6,U_63),difference(U_63,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_64,sK6)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
difference(union(sK6,sK7),intersection(sK6,sK7)) != union(difference(sK6,sK7),difference(sK7,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_63,sK7)],[f_11_4]) ).
cnf(f_11_6,negated_conjecture,
difference(union(sK6,sK7),intersection(sK6,sK7)) != union(difference(sK6,sK7),difference(sK7,sK6)),
inference(clausify,[status(thm)],[f_11_5]) ).
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,
( difference(Eq_x_0,Eq_x_1) = difference(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,
( 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_8,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_9,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_10,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_11,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_12,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_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET613+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 : n003.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 22:44:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 192.35/192.67 % SZS status Theorem for theBenchmark
% 192.35/192.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------