%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET144+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 : n019.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 08:56:26 AM UTC 2026
% Result : Theorem 179.95s 180.41s
% Output : Proof 182.02s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_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(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_th44,conjecture,
! [B,C,D] :
( subset(B,C)
=> union(B,intersection(D,C)) = intersection(union(B,D),C) ),
file('theBenchmark.p',prove_th44) ).
fof(f_1_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_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,union(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,union(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,union(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,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_8,U_4,U_6] :
( ~ member(U_4,U_6)
| ~ sP0(U_8,U_4,U_6) )
& ! [U_8,U_4,U_6] :
( ~ member(U_4,U_8)
| ~ sP0(U_8,U_4,U_6) )
& ! [U_8,U_4,U_6] :
( member(U_4,union(U_8,U_6))
| sP0(U_8,U_4,U_6) )
& ! [U_5,U_3,U_7] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(U_4,union(U_8,U_6))
| sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(U_4,U_8)
| ~ sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( ~ member(U_4,U_6)
| ~ sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_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_2_2,plain,
! [U_11,U_10,U_9] :
( ( member(U_9,intersection(U_11,U_10))
| ~ member(U_9,U_10)
| ~ member(U_9,U_11) )
& ( ( member(U_9,U_10)
& member(U_9,U_11) )
| ~ member(U_9,intersection(U_11,U_10)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_17,U_15,U_13] :
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_16,U_14,U_12] :
( ( member(U_12,U_14)
& member(U_12,U_16) )
| ~ member(U_12,intersection(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_12,U_14,U_16] :
( member(U_12,U_14)
| ~ sP1(U_12,U_14,U_16) )
& ! [U_12,U_14,U_16] :
( member(U_12,U_16)
| ~ sP1(U_12,U_14,U_16) )
& ! [U_13,U_17,U_15] :
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_12,U_14,U_16] :
( sP1(U_12,U_14,U_16)
| ~ member(U_12,intersection(U_16,U_14)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_2_3]) ).
cnf(f_2_5,plain,
( sP1(U_12,U_14,U_16)
| ~ member(U_12,intersection(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( member(U_12,U_16)
| ~ sP1(U_12,U_14,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_8,plain,
( member(U_12,U_14)
| ~ sP1(U_12,U_14,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_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_3_2,plain,
! [U_21,U_20] :
( ( subset(U_21,U_20)
| ? [U_19] :
( ~ member(U_19,U_20)
& member(U_19,U_21) ) )
& ( ! [U_18] :
( member(U_18,U_20)
| ~ member(U_18,U_21) )
| ~ subset(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ? [U_19] :
( ~ member(U_19,U_23)
& member(U_19,U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ( ~ member(sK1(U_25,U_23),U_23)
& member(sK1(U_25,U_23),U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_25,U_23))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_23,U_25] :
( ~ member(sK1(U_25,U_23),U_23)
| ~ sP2(U_23,U_25) )
& ! [U_23,U_25] :
( member(sK1(U_25,U_23),U_25)
| ~ sP2(U_23,U_25) )
& ! [U_23,U_25] :
( subset(U_25,U_23)
| sP2(U_23,U_25) )
& ! [U_18,U_22,U_24] :
( member(U_18,U_22)
| ~ member(U_18,U_24)
| ~ subset(U_24,U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_3_4]) ).
cnf(f_3_6,plain,
( member(U_18,U_22)
| ~ member(U_18,U_24)
| ~ subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( subset(U_25,U_23)
| sP2(U_23,U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( member(sK1(U_25,U_23),U_25)
| ~ sP2(U_23,U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ member(sK1(U_25,U_23),U_23)
| ~ sP2(U_23,U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_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_4_2,plain,
! [U_27,U_26] :
( ( U_27 = U_26
| ~ subset(U_26,U_27)
| ~ subset(U_27,U_26) )
& ( ( subset(U_26,U_27)
& subset(U_27,U_26) )
| U_27 != U_26 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) )
& ! [U_30,U_28] :
( ( subset(U_28,U_30)
& subset(U_30,U_28) )
| U_30 != U_28 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_30,U_28] :
( subset(U_28,U_30)
| ~ sP3(U_30,U_28) )
& ! [U_30,U_28] :
( subset(U_30,U_28)
| ~ sP3(U_30,U_28) )
& ! [U_29,U_31] :
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) )
& ! [U_30,U_28] :
( sP3(U_30,U_28)
| U_30 != U_28 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP3(U_30,U_28)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( subset(U_30,U_28)
| ~ sP3(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( subset(U_28,U_30)
| ~ sP3(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_5_2,plain,
! [U_33,U_32] : union(U_33,U_32) = union(U_32,U_33),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_32,U_33] : union(U_33,U_32) = union(U_32,U_33),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
union(U_33,U_32) = union(U_32,U_33),
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_35,U_34] : intersection(U_35,U_34) = intersection(U_34,U_35),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_34,U_35] : intersection(U_35,U_34) = intersection(U_34,U_35),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
intersection(U_35,U_34) = intersection(U_34,U_35),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_7_2,plain,
! [U_36] : subset(U_36,U_36),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_36] : subset(U_36,U_36),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
subset(U_36,U_36),
inference(clausify,[status(thm)],[f_7_3]) ).
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_40,U_39] :
( ( U_40 = U_39
| ? [U_38] :
( ( ~ member(U_38,U_40)
& member(U_38,U_39) )
| ( ~ member(U_38,U_39)
& member(U_38,U_40) ) ) )
& ( ! [U_37] :
( ( member(U_37,U_40)
| ~ member(U_37,U_39) )
& ( member(U_37,U_39)
| ~ member(U_37,U_40) ) )
| U_40 != U_39 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ? [U_44] :
( ~ member(U_44,U_48)
& member(U_44,U_46) )
| ? [U_43] :
( ~ member(U_43,U_46)
& member(U_43,U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ? [U_44] :
( ~ member(U_44,U_48)
& member(U_44,U_46) )
| ( ~ member(sK2(U_48,U_46),U_46)
& member(sK2(U_48,U_46),U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_43,sK2(U_48,U_46))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ( ~ member(sK3(U_48,U_46),U_48)
& member(sK3(U_48,U_46),U_46) )
| ( ~ member(sK2(U_48,U_46),U_46)
& member(sK2(U_48,U_46),U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_44,sK3(U_48,U_46))],[f_8_4]) ).
fof(f_8_6,plain,
( ! [U_46,U_48] :
( ~ member(sK3(U_48,U_46),U_48)
| ~ sP6(U_46,U_48) )
& ! [U_46,U_48] :
( member(sK3(U_48,U_46),U_46)
| ~ sP6(U_46,U_48) )
& ! [U_46,U_48] :
( ~ member(sK2(U_48,U_46),U_46)
| ~ sP5(U_46,U_48) )
& ! [U_46,U_48] :
( member(sK2(U_48,U_46),U_48)
| ~ sP5(U_46,U_48) )
& ! [U_47,U_41,U_42,U_45] :
( member(U_42,U_47)
| ~ member(U_42,U_45)
| ~ sP4(U_47,U_41,U_42,U_45) )
& ! [U_47,U_41,U_42,U_45] :
( member(U_41,U_45)
| ~ member(U_41,U_47)
| ~ sP4(U_47,U_41,U_42,U_45) )
& ! [U_46,U_48] :
( U_48 = U_46
| sP6(U_46,U_48)
| sP5(U_46,U_48) )
& ! [U_47,U_41,U_42,U_45] :
( sP4(U_47,U_41,U_42,U_45)
| U_47 != U_45 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6])],[f_8_5]) ).
cnf(f_8_7,plain,
( sP4(U_47,U_41,U_42,U_45)
| U_47 != U_45 ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_8,plain,
( U_48 = U_46
| sP6(U_46,U_48)
| sP5(U_46,U_48) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_9,plain,
( member(U_41,U_45)
| ~ member(U_41,U_47)
| ~ sP4(U_47,U_41,U_42,U_45) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_10,plain,
( member(U_42,U_47)
| ~ member(U_42,U_45)
| ~ sP4(U_47,U_41,U_42,U_45) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_11,plain,
( member(sK2(U_48,U_46),U_48)
| ~ sP5(U_46,U_48) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_12,plain,
( ~ member(sK2(U_48,U_46),U_46)
| ~ sP5(U_46,U_48) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_13,plain,
( member(sK3(U_48,U_46),U_46)
| ~ sP6(U_46,U_48) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_14,plain,
( ~ member(sK3(U_48,U_46),U_48)
| ~ sP6(U_46,U_48) ),
inference(clausify,[status(thm)],[f_8_6]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> union(B,intersection(D,C)) = intersection(union(B,D),C) ),
inference(negate,[status(cth)],[prove_th44]) ).
fof(f_9_2,negated_conjecture,
? [B,C,D] :
( union(B,intersection(D,C)) != intersection(union(B,D),C)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_51,U_50,U_49] :
( union(U_51,intersection(U_49,U_50)) != intersection(union(U_51,U_49),U_50)
& subset(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_51,U_50] :
( ? [U_49] : union(U_51,intersection(U_49,U_50)) != intersection(union(U_51,U_49),U_50)
& subset(U_51,U_50) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_50] :
( ? [U_49] : union(sK4,intersection(U_49,U_50)) != intersection(union(sK4,U_49),U_50)
& subset(sK4,U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_51,sK4)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_49] : union(sK4,intersection(U_49,sK5)) != intersection(union(sK4,U_49),sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_50,sK5)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( union(sK4,intersection(sK6,sK5)) != intersection(union(sK4,sK6),sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( union(sK4,intersection(sK6,sK5)) != intersection(union(sK4,sK6),sK5)
& subset(sK4,sK5) ),
inference(definitional_conversion,[status(esa)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
union(sK4,intersection(sK6,sK5)) != intersection(union(sK4,sK6),sK5),
inference(clausify,[status(thm)],[f_9_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,
( 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 : SET144+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
% 0.10/0.57 % Computer : n019.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 19 21:50:51 UTC 2026
% 0.10/0.58 % CPUTime :
% 179.95/180.41 % SZS status Theorem for theBenchmark
% 179.95/180.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------