%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET586+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 : 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 08:57:01 AM UTC 2026
% Result : Theorem 0.14s 5.46s
% Output : Proof 0.14s
% 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(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
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_intersection_of_subset,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('theBenchmark.p',prove_intersection_of_subset) ).
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] :
( ( 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_2_2,plain,
! [U_12,U_11] :
( ( subset(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) )
| ~ subset(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( subset(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) )
| ~ subset(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( subset(U_16,U_14)
| ( ~ member(sK1(U_16,U_14),U_14)
& member(sK1(U_16,U_14),U_16) ) )
& ! [U_15,U_13] :
( ! [U_9] :
( member(U_9,U_13)
| ~ member(U_9,U_15) )
| ~ subset(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_16,U_14))],[f_2_3]) ).
cnf(f_2_5,plain,
( member(U_9,U_13)
| ~ member(U_9,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(sK1(U_16,U_14),U_16)
| subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( ~ member(sK1(U_16,U_14),U_14)
| subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_3_2,plain,
! [U_18,U_17] : intersection(U_18,U_17) = intersection(U_17,U_18),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
intersection(U_18,U_17) = intersection(U_17,U_18),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_4_2,plain,
! [U_19] : subset(U_19,U_19),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
subset(U_19,U_19),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_23,U_22] :
( ( U_23 = U_22
| ? [U_21] :
( ( ~ member(U_21,U_23)
& member(U_21,U_22) )
| ( ~ member(U_21,U_22)
& member(U_21,U_23) ) ) )
& ( ! [U_20] :
( ( member(U_20,U_23)
| ~ member(U_20,U_22) )
& ( member(U_20,U_22)
| ~ member(U_20,U_23) ) )
| U_23 != U_22 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ? [U_27] :
( ~ member(U_27,U_31)
& member(U_27,U_29) )
| ? [U_26] :
( ~ member(U_26,U_29)
& member(U_26,U_31) ) )
& ! [U_30,U_28] :
( ( ! [U_25] :
( member(U_25,U_30)
| ~ member(U_25,U_28) )
& ! [U_24] :
( member(U_24,U_28)
| ~ member(U_24,U_30) ) )
| U_30 != U_28 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ? [U_27] :
( ~ member(U_27,U_31)
& member(U_27,U_29) )
| ( ~ member(sK2(U_31,U_29),U_29)
& member(sK2(U_31,U_29),U_31) ) )
& ! [U_30,U_28] :
( ( ! [U_25] :
( member(U_25,U_30)
| ~ member(U_25,U_28) )
& ! [U_24] :
( member(U_24,U_28)
| ~ member(U_24,U_30) ) )
| U_30 != U_28 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2(U_31,U_29))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ( ~ member(sK3(U_31,U_29),U_31)
& member(sK3(U_31,U_29),U_29) )
| ( ~ member(sK2(U_31,U_29),U_29)
& member(sK2(U_31,U_29),U_31) ) )
& ! [U_30,U_28] :
( ( ! [U_25] :
( member(U_25,U_30)
| ~ member(U_25,U_28) )
& ! [U_24] :
( member(U_24,U_28)
| ~ member(U_24,U_30) ) )
| U_30 != U_28 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_27,sK3(U_31,U_29))],[f_5_4]) ).
cnf(f_5_6,plain,
( member(U_24,U_28)
| ~ member(U_24,U_30)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( member(U_25,U_30)
| ~ member(U_25,U_28)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( member(sK3(U_31,U_29),U_29)
| member(sK2(U_31,U_29),U_31)
| U_31 = U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ member(sK3(U_31,U_29),U_31)
| member(sK2(U_31,U_29),U_31)
| U_31 = U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( member(sK3(U_31,U_29),U_29)
| ~ member(sK2(U_31,U_29),U_29)
| U_31 = U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ member(sK3(U_31,U_29),U_31)
| ~ member(sK2(U_31,U_29),U_29)
| U_31 = U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(negate,[status(cth)],[prove_intersection_of_subset]) ).
fof(f_6_2,negated_conjecture,
? [B,C,D] :
( ~ subset(intersection(B,D),intersection(C,D))
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_34,U_33,U_32] :
( ~ subset(intersection(U_34,U_32),intersection(U_33,U_32))
& subset(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_34,U_33] :
( ? [U_32] : ~ subset(intersection(U_34,U_32),intersection(U_33,U_32))
& subset(U_34,U_33) ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_33] :
( ? [U_32] : ~ subset(intersection(sK4,U_32),intersection(U_33,U_32))
& subset(sK4,U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ? [U_32] : ~ subset(intersection(sK4,U_32),intersection(sK5,U_32))
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_33,sK5)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ~ subset(intersection(sK4,sK6),intersection(sK5,sK6))
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6)],[f_6_6]) ).
fof(f_6_8,negated_conjecture,
( ~ subset(intersection(sK4,sK6),intersection(sK5,sK6))
& subset(sK4,sK5) ),
inference(definitional_conversion,[status(esa)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_6_8]) ).
cnf(f_6_10,negated_conjecture,
~ subset(intersection(sK4,sK6),intersection(sK5,sK6)),
inference(clausify,[status(thm)],[f_6_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,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,
( 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_9,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 : SET586+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
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 19 22:42:22 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.14/5.46 % SZS status Theorem for theBenchmark
% 0.14/5.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------