%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET628+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 : n018.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 08:57:10 AM UTC 2026
% Result : Theorem 2.55s 7.87s
% Output : Proof 2.55s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('theBenchmark.p',not_equal_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(prove_th110,conjecture,
! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
file('theBenchmark.p',prove_th110) ).
fof(f_1_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_1_2,plain,
! [U_3,U_2] :
( ( intersect(U_3,U_2)
| ! [U_1] :
( ~ member(U_1,U_2)
| ~ member(U_1,U_3) ) )
& ( ? [U_0] :
( member(U_0,U_2)
& member(U_0,U_3) )
| ~ intersect(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( intersect(U_7,U_5)
| ! [U_1] :
( ~ member(U_1,U_5)
| ~ member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ? [U_0] :
( member(U_0,U_4)
& member(U_0,U_6) )
| ~ intersect(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( intersect(U_7,U_5)
| ! [U_1] :
( ~ member(U_1,U_5)
| ~ member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ( member(sK1(U_6,U_4),U_4)
& member(sK1(U_6,U_4),U_6) )
| ~ intersect(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_6,U_4))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(sK1(U_6,U_4),U_6)
| ~ intersect(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK1(U_6,U_4),U_4)
| ~ intersect(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( intersect(U_7,U_5)
| ~ member(U_1,U_5)
| ~ member(U_1,U_7) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_2_2,plain,
! [U_8] : ~ member(U_8,empty_set),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ member(U_8,empty_set),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_12,U_11] :
( ( U_12 = U_11
| ? [U_10] :
( ( ~ member(U_10,U_12)
& member(U_10,U_11) )
| ( ~ member(U_10,U_11)
& member(U_10,U_12) ) ) )
& ( ! [U_9] :
( ( member(U_9,U_12)
| ~ member(U_9,U_11) )
& ( member(U_9,U_11)
| ~ member(U_9,U_12) ) )
| U_12 != U_11 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_20,U_18] :
( U_20 = U_18
| ? [U_16] :
( ~ member(U_16,U_20)
& member(U_16,U_18) )
| ? [U_15] :
( ~ member(U_15,U_18)
& member(U_15,U_20) ) )
& ! [U_19,U_17] :
( ( ! [U_14] :
( member(U_14,U_19)
| ~ member(U_14,U_17) )
& ! [U_13] :
( member(U_13,U_17)
| ~ member(U_13,U_19) ) )
| U_19 != U_17 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_20,U_18] :
( U_20 = U_18
| ? [U_16] :
( ~ member(U_16,U_20)
& member(U_16,U_18) )
| ( ~ member(sK2(U_20,U_18),U_18)
& member(sK2(U_20,U_18),U_20) ) )
& ! [U_19,U_17] :
( ( ! [U_14] :
( member(U_14,U_19)
| ~ member(U_14,U_17) )
& ! [U_13] :
( member(U_13,U_17)
| ~ member(U_13,U_19) ) )
| U_19 != U_17 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_20,U_18))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_20,U_18] :
( U_20 = U_18
| ( ~ member(sK3(U_20,U_18),U_20)
& member(sK3(U_20,U_18),U_18) )
| ( ~ member(sK2(U_20,U_18),U_18)
& member(sK2(U_20,U_18),U_20) ) )
& ! [U_19,U_17] :
( ( ! [U_14] :
( member(U_14,U_19)
| ~ member(U_14,U_17) )
& ! [U_13] :
( member(U_13,U_17)
| ~ member(U_13,U_19) ) )
| U_19 != U_17 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_20,U_18))],[f_3_4]) ).
cnf(f_3_6,plain,
( member(U_13,U_17)
| ~ member(U_13,U_19)
| U_19 != U_17 ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( member(U_14,U_19)
| ~ member(U_14,U_17)
| U_19 != U_17 ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( member(sK3(U_20,U_18),U_18)
| member(sK2(U_20,U_18),U_20)
| U_20 = U_18 ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ member(sK3(U_20,U_18),U_20)
| member(sK2(U_20,U_18),U_20)
| U_20 = U_18 ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( member(sK3(U_20,U_18),U_18)
| ~ member(sK2(U_20,U_18),U_18)
| U_20 = U_18 ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ member(sK3(U_20,U_18),U_20)
| ~ member(sK2(U_20,U_18),U_18)
| U_20 = U_18 ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [B,C] :
( ( not_equal(B,C)
| B = C )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(fof_nnf,[status(thm)],[not_equal_defn]) ).
fof(f_4_2,plain,
! [U_22,U_21] :
( ( not_equal(U_22,U_21)
| U_22 = U_21 )
& ( U_22 != U_21
| ~ not_equal(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_26,U_24] :
( not_equal(U_26,U_24)
| U_26 = U_24 )
& ! [U_25,U_23] :
( U_25 != U_23
| ~ not_equal(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( U_25 != U_23
| ~ not_equal(U_25,U_23) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( not_equal(U_26,U_24)
| U_26 = U_24 ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_5_2,plain,
! [U_28,U_27] :
( intersect(U_27,U_28)
| ~ intersect(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( intersect(U_27,U_28)
| ~ intersect(U_28,U_27) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_6_2,plain,
! [U_31] :
( ( empty(U_31)
| ? [U_30] : member(U_30,U_31) )
& ( ! [U_29] : ~ member(U_29,U_31)
| ~ empty(U_31) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_33] :
( empty(U_33)
| ? [U_30] : member(U_30,U_33) )
& ! [U_32] :
( ! [U_29] : ~ member(U_29,U_32)
| ~ empty(U_32) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_33] :
( empty(U_33)
| member(sK4(U_33),U_33) )
& ! [U_32] :
( ! [U_29] : ~ member(U_29,U_32)
| ~ empty(U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_30,sK4(U_33))],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ member(U_29,U_32)
| ~ empty(U_32) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( empty(U_33)
| member(sK4(U_33),U_33) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,negated_conjecture,
~ ! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
inference(negate,[status(cth)],[prove_th110]) ).
fof(f_7_2,negated_conjecture,
? [B] :
( ( ~ intersect(B,B)
& not_equal(B,empty_set) )
| ( ~ not_equal(B,empty_set)
& intersect(B,B) ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_34] :
( ( ~ intersect(U_34,U_34)
& not_equal(U_34,empty_set) )
| ( ~ not_equal(U_34,empty_set)
& intersect(U_34,U_34) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ? [U_36] :
( ~ intersect(U_36,U_36)
& not_equal(U_36,empty_set) )
| ? [U_35] :
( ~ not_equal(U_35,empty_set)
& intersect(U_35,U_35) ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_36] :
( ~ intersect(U_36,U_36)
& not_equal(U_36,empty_set) )
| ( ~ not_equal(sK5,empty_set)
& intersect(sK5,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_35,sK5)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ( ~ intersect(sK6,sK6)
& not_equal(sK6,empty_set) )
| ( ~ not_equal(sK5,empty_set)
& intersect(sK5,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ( ~ intersect(sK6,sK6)
| ~ sP1 )
& ( not_equal(sK6,empty_set)
| ~ sP1 )
& ( ~ not_equal(sK5,empty_set)
| ~ sP0 )
& ( intersect(sK5,sK5)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
( intersect(sK5,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,negated_conjecture,
( ~ not_equal(sK5,empty_set)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,negated_conjecture,
( not_equal(sK6,empty_set)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,negated_conjecture,
( ~ intersect(sK6,sK6)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_7]) ).
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,
( 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_5,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_6,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_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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(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,
( not_equal(Eq_y_0,Eq_y_1)
| ~ not_equal(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| 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 : SET628+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
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 22:46:01 UTC 2026
% 0.09/5.37 % CPUTime :
% 2.55/7.87 % SZS status Theorem for theBenchmark
% 2.55/7.87 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------