%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET626+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 : n002.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 08:57:09 AM UTC 2026
% Result : Theorem 0.12s 0.65s
% Output : Proof 0.12s
% 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(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th102,conjecture,
! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
file('theBenchmark.p',prove_th102) ).
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] :
( ( intersect(B,C)
| ! [D] :
( ~ member(D,C)
| ~ member(D,B) ) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11] :
( ( intersect(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) )
| ~ intersect(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( intersect(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) )
| ~ intersect(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ( member(sK1(U_15,U_13),U_13)
& member(sK1(U_15,U_13),U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_15,U_13))],[f_2_3]) ).
cnf(f_2_5,plain,
( member(sK1(U_15,U_13),U_15)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(sK1(U_15,U_13),U_13)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( intersect(U_16,U_14)
| ~ member(U_10,U_14)
| ~ member(U_10,U_16) ),
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,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_4_2,plain,
! [U_20,U_19] :
( intersect(U_19,U_20)
| ~ intersect(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( intersect(U_19,U_20)
| ~ intersect(U_20,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_24,U_23] :
( ( U_24 = U_23
| ? [U_22] :
( ( ~ member(U_22,U_24)
& member(U_22,U_23) )
| ( ~ member(U_22,U_23)
& member(U_22,U_24) ) ) )
& ( ! [U_21] :
( ( member(U_21,U_24)
| ~ member(U_21,U_23) )
& ( member(U_21,U_23)
| ~ member(U_21,U_24) ) )
| U_24 != U_23 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_32,U_30] :
( U_32 = U_30
| ? [U_28] :
( ~ member(U_28,U_32)
& member(U_28,U_30) )
| ? [U_27] :
( ~ member(U_27,U_30)
& member(U_27,U_32) ) )
& ! [U_31,U_29] :
( ( ! [U_26] :
( member(U_26,U_31)
| ~ member(U_26,U_29) )
& ! [U_25] :
( member(U_25,U_29)
| ~ member(U_25,U_31) ) )
| U_31 != U_29 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_32,U_30] :
( U_32 = U_30
| ? [U_28] :
( ~ member(U_28,U_32)
& member(U_28,U_30) )
| ( ~ member(sK2(U_32,U_30),U_30)
& member(sK2(U_32,U_30),U_32) ) )
& ! [U_31,U_29] :
( ( ! [U_26] :
( member(U_26,U_31)
| ~ member(U_26,U_29) )
& ! [U_25] :
( member(U_25,U_29)
| ~ member(U_25,U_31) ) )
| U_31 != U_29 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2(U_32,U_30))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_32,U_30] :
( U_32 = U_30
| ( ~ member(sK3(U_32,U_30),U_32)
& member(sK3(U_32,U_30),U_30) )
| ( ~ member(sK2(U_32,U_30),U_30)
& member(sK2(U_32,U_30),U_32) ) )
& ! [U_31,U_29] :
( ( ! [U_26] :
( member(U_26,U_31)
| ~ member(U_26,U_29) )
& ! [U_25] :
( member(U_25,U_29)
| ~ member(U_25,U_31) ) )
| U_31 != U_29 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3(U_32,U_30))],[f_5_4]) ).
cnf(f_5_6,plain,
( member(U_25,U_29)
| ~ member(U_25,U_31)
| U_31 != U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( member(U_26,U_31)
| ~ member(U_26,U_29)
| U_31 != U_29 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( member(sK3(U_32,U_30),U_30)
| member(sK2(U_32,U_30),U_32)
| U_32 = U_30 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ member(sK3(U_32,U_30),U_32)
| member(sK2(U_32,U_30),U_32)
| U_32 = U_30 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( member(sK3(U_32,U_30),U_30)
| ~ member(sK2(U_32,U_30),U_30)
| U_32 = U_30 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ member(sK3(U_32,U_30),U_32)
| ~ member(sK2(U_32,U_30),U_30)
| U_32 = U_30 ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
inference(negate,[status(cth)],[prove_th102]) ).
fof(f_6_2,negated_conjecture,
? [B,C,D] :
( ~ intersect(B,C)
& intersect(B,intersection(C,D)) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_35,U_34,U_33] :
( ~ intersect(U_35,U_34)
& intersect(U_35,intersection(U_34,U_33)) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_35,U_34] :
( ? [U_33] : intersect(U_35,intersection(U_34,U_33))
& ~ intersect(U_35,U_34) ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_34] :
( ? [U_33] : intersect(sK4,intersection(U_34,U_33))
& ~ intersect(sK4,U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ? [U_33] : intersect(sK4,intersection(sK5,U_33))
& ~ intersect(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_34,sK5)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( intersect(sK4,intersection(sK5,sK6))
& ~ intersect(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_33,sK6)],[f_6_6]) ).
fof(f_6_8,negated_conjecture,
( intersect(sK4,intersection(sK5,sK6))
& ~ intersect(sK4,sK5) ),
inference(definitional_conversion,[status(esa)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
~ intersect(sK4,sK5),
inference(clausify,[status(thm)],[f_6_8]) ).
cnf(f_6_10,negated_conjecture,
intersect(sK4,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,
( intersect(Eq_y_0,Eq_y_1)
| ~ intersect(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
% 0.00/0.02 % Problem : SET626+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.59 % Computer : n002.cluster.edu
% 0.09/0.59 % Model : x86_64 x86_64
% 0.09/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.59 % Memory : 8046.5625MB
% 0.09/0.59 % OS : Linux 6.8.0-71-generic
% 0.09/0.59 % CPULimit : 300
% 0.09/0.60 % WCLimit : 300
% 0.09/0.60 % DateTime : Sat Sep 19 22:46:33 UTC 2026
% 0.09/0.60 % CPUTime :
% 0.12/0.65 % SZS status Theorem for theBenchmark
% 0.12/0.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------