%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:55:50 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(subset_union,axiom,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('theBenchmark.p',subset_union) ).
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_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(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_idempotency_of_union,conjecture,
! [B] : union(B,B) = B,
file('theBenchmark.p',prove_idempotency_of_union) ).
fof(f_1_1,plain,
! [B,C] :
( union(B,C) = C
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[subset_union]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( union(U_1,U_0) = U_0
| ~ subset(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( union(U_1,U_0) = U_0
| ~ subset(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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_4,U_3,U_2] :
( ( member(U_2,union(U_4,U_3))
| ( ~ member(U_2,U_3)
& ~ member(U_2,U_4) ) )
& ( member(U_2,U_3)
| member(U_2,U_4)
| ~ member(U_2,union(U_4,U_3)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_10,U_8,U_6] :
( member(U_6,union(U_10,U_8))
| ( ~ member(U_6,U_8)
& ~ member(U_6,U_10) ) )
& ! [U_9,U_7,U_5] :
( member(U_5,U_7)
| member(U_5,U_9)
| ~ member(U_5,union(U_9,U_7)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( member(U_5,U_7)
| member(U_5,U_9)
| ~ member(U_5,union(U_9,U_7)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ member(U_6,U_10)
| member(U_6,union(U_10,U_8)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( ~ member(U_6,U_8)
| member(U_6,union(U_10,U_8)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_12,U_11] :
( ( U_12 = U_11
| ~ subset(U_11,U_12)
| ~ subset(U_12,U_11) )
& ( ( subset(U_11,U_12)
& subset(U_12,U_11) )
| U_12 != U_11 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_16,U_14] :
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) )
& ! [U_15,U_13] :
( ( subset(U_13,U_15)
& subset(U_15,U_13) )
| U_15 != U_13 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(U_15,U_13)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(U_13,U_15)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_4_2,plain,
! [U_18,U_17] : union(U_18,U_17) = union(U_17,U_18),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
union(U_18,U_17) = union(U_17,U_18),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_22,U_21] :
( ( subset(U_22,U_21)
| ? [U_20] :
( ~ member(U_20,U_21)
& member(U_20,U_22) ) )
& ( ! [U_19] :
( member(U_19,U_21)
| ~ member(U_19,U_22) )
| ~ subset(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ? [U_20] :
( ~ member(U_20,U_24)
& member(U_20,U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( member(U_19,U_23)
| ~ member(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ( ~ member(sK1(U_26,U_24),U_24)
& member(sK1(U_26,U_24),U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( member(U_19,U_23)
| ~ member(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_20,sK1(U_26,U_24))],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_19,U_23)
| ~ member(U_19,U_25)
| ~ subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( member(sK1(U_26,U_24),U_26)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(sK1(U_26,U_24),U_24)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_6_2,plain,
! [U_27] : subset(U_27,U_27),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
subset(U_27,U_27),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_31,U_30] :
( ( U_31 = U_30
| ? [U_29] :
( ( ~ member(U_29,U_31)
& member(U_29,U_30) )
| ( ~ member(U_29,U_30)
& member(U_29,U_31) ) ) )
& ( ! [U_28] :
( ( member(U_28,U_31)
| ~ member(U_28,U_30) )
& ( member(U_28,U_30)
| ~ member(U_28,U_31) ) )
| U_31 != U_30 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_39,U_37] :
( U_39 = U_37
| ? [U_35] :
( ~ member(U_35,U_39)
& member(U_35,U_37) )
| ? [U_34] :
( ~ member(U_34,U_37)
& member(U_34,U_39) ) )
& ! [U_38,U_36] :
( ( ! [U_33] :
( member(U_33,U_38)
| ~ member(U_33,U_36) )
& ! [U_32] :
( member(U_32,U_36)
| ~ member(U_32,U_38) ) )
| U_38 != U_36 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_39,U_37] :
( U_39 = U_37
| ? [U_35] :
( ~ member(U_35,U_39)
& member(U_35,U_37) )
| ( ~ member(sK2(U_39,U_37),U_37)
& member(sK2(U_39,U_37),U_39) ) )
& ! [U_38,U_36] :
( ( ! [U_33] :
( member(U_33,U_38)
| ~ member(U_33,U_36) )
& ! [U_32] :
( member(U_32,U_36)
| ~ member(U_32,U_38) ) )
| U_38 != U_36 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_34,sK2(U_39,U_37))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_39,U_37] :
( U_39 = U_37
| ( ~ member(sK3(U_39,U_37),U_39)
& member(sK3(U_39,U_37),U_37) )
| ( ~ member(sK2(U_39,U_37),U_37)
& member(sK2(U_39,U_37),U_39) ) )
& ! [U_38,U_36] :
( ( ! [U_33] :
( member(U_33,U_38)
| ~ member(U_33,U_36) )
& ! [U_32] :
( member(U_32,U_36)
| ~ member(U_32,U_38) ) )
| U_38 != U_36 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_35,sK3(U_39,U_37))],[f_7_4]) ).
cnf(f_7_6,plain,
( member(U_32,U_36)
| ~ member(U_32,U_38)
| U_38 != U_36 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( member(U_33,U_38)
| ~ member(U_33,U_36)
| U_38 != U_36 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( member(sK3(U_39,U_37),U_37)
| member(sK2(U_39,U_37),U_39)
| U_39 = U_37 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ member(sK3(U_39,U_37),U_39)
| member(sK2(U_39,U_37),U_39)
| U_39 = U_37 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( member(sK3(U_39,U_37),U_37)
| ~ member(sK2(U_39,U_37),U_37)
| U_39 = U_37 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ member(sK3(U_39,U_37),U_39)
| ~ member(sK2(U_39,U_37),U_37)
| U_39 = U_37 ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,negated_conjecture,
~ ! [B] : union(B,B) = B,
inference(negate,[status(cth)],[prove_idempotency_of_union]) ).
fof(f_8_2,negated_conjecture,
? [B] : union(B,B) != B,
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_40] : union(U_40,U_40) != U_40,
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
union(sK4,sK4) != sK4,
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
union(sK4,sK4) != sK4,
inference(definitional_conversion,[status(esa)],[f_8_4]) ).
cnf(f_8_6,negated_conjecture,
union(sK4,sK4) != sK4,
inference(clausify,[status(thm)],[f_8_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,
( 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,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_8,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_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 21:26:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------