%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET604+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 : n001.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 08:57:05 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [B] : subset(empty_set,B),
file('theBenchmark.p',empty_set_subset) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('theBenchmark.p',difference_empty_set) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
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(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(prove_no_difference_with_empty_set,conjecture,
! [B] : difference(empty_set,B) = empty_set,
file('theBenchmark.p',prove_no_difference_with_empty_set) ).
fof(f_1_1,plain,
! [B] : subset(empty_set,B),
inference(fof_nnf,[status(thm)],[empty_set_subset]) ).
fof(f_1_2,plain,
! [U_0] : subset(empty_set,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
subset(empty_set,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C] :
( ( difference(B,C) = empty_set
| ~ subset(B,C) )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(fof_nnf,[status(thm)],[difference_empty_set]) ).
fof(f_2_2,plain,
! [U_2,U_1] :
( ( difference(U_2,U_1) = empty_set
| ~ subset(U_2,U_1) )
& ( subset(U_2,U_1)
| difference(U_2,U_1) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_6,U_4] :
( difference(U_6,U_4) = empty_set
| ~ subset(U_6,U_4) )
& ! [U_5,U_3] :
( subset(U_5,U_3)
| difference(U_5,U_3) != empty_set ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_5,U_3)
| difference(U_5,U_3) != empty_set ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( difference(U_6,U_4) = empty_set
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_3_2,plain,
! [U_7] : ~ member(U_7,empty_set),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ member(U_7,empty_set),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [B,C,D] :
( ( member(D,difference(B,C))
| member(D,C)
| ~ member(D,B) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(fof_nnf,[status(thm)],[difference_defn]) ).
fof(f_4_2,plain,
! [U_10,U_9,U_8] :
( ( member(U_8,difference(U_10,U_9))
| member(U_8,U_9)
| ~ member(U_8,U_10) )
& ( ( ~ member(U_8,U_9)
& member(U_8,U_10) )
| ~ member(U_8,difference(U_10,U_9)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_16,U_14,U_12] :
( member(U_12,difference(U_16,U_14))
| member(U_12,U_14)
| ~ member(U_12,U_16) )
& ! [U_15,U_13,U_11] :
( ( ~ member(U_11,U_13)
& member(U_11,U_15) )
| ~ member(U_11,difference(U_15,U_13)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_11,U_15)
| ~ member(U_11,difference(U_15,U_13)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ member(U_11,U_13)
| ~ member(U_11,difference(U_15,U_13)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( member(U_12,difference(U_16,U_14))
| member(U_12,U_14)
| ~ member(U_12,U_16) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_18,U_17] :
( ( U_18 = U_17
| ~ subset(U_17,U_18)
| ~ subset(U_18,U_17) )
& ( ( subset(U_17,U_18)
& subset(U_18,U_17) )
| U_18 != U_17 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_22,U_20] :
( U_22 = U_20
| ~ subset(U_20,U_22)
| ~ subset(U_22,U_20) )
& ! [U_21,U_19] :
( ( subset(U_19,U_21)
& subset(U_21,U_19) )
| U_21 != U_19 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_21,U_19)
| U_21 != U_19 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_19,U_21)
| U_21 != U_19 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_22 = U_20
| ~ subset(U_20,U_22)
| ~ subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_26,U_25] :
( ( subset(U_26,U_25)
| ? [U_24] :
( ~ member(U_24,U_25)
& member(U_24,U_26) ) )
& ( ! [U_23] :
( member(U_23,U_25)
| ~ member(U_23,U_26) )
| ~ subset(U_26,U_25) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_30,U_28] :
( subset(U_30,U_28)
| ? [U_24] :
( ~ member(U_24,U_28)
& member(U_24,U_30) ) )
& ! [U_29,U_27] :
( ! [U_23] :
( member(U_23,U_27)
| ~ member(U_23,U_29) )
| ~ subset(U_29,U_27) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_30,U_28] :
( subset(U_30,U_28)
| ( ~ member(sK1(U_30,U_28),U_28)
& member(sK1(U_30,U_28),U_30) ) )
& ! [U_29,U_27] :
( ! [U_23] :
( member(U_23,U_27)
| ~ member(U_23,U_29) )
| ~ subset(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_24,sK1(U_30,U_28))],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_23,U_27)
| ~ member(U_23,U_29)
| ~ subset(U_29,U_27) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( member(sK1(U_30,U_28),U_30)
| subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ member(sK1(U_30,U_28),U_28)
| subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_7_2,plain,
! [U_31] : subset(U_31,U_31),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
subset(U_31,U_31),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_8_2,plain,
! [U_34] :
( ( empty(U_34)
| ? [U_33] : member(U_33,U_34) )
& ( ! [U_32] : ~ member(U_32,U_34)
| ~ empty(U_34) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_36] :
( empty(U_36)
| ? [U_33] : member(U_33,U_36) )
& ! [U_35] :
( ! [U_32] : ~ member(U_32,U_35)
| ~ empty(U_35) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_36] :
( empty(U_36)
| member(sK2(U_36),U_36) )
& ! [U_35] :
( ! [U_32] : ~ member(U_32,U_35)
| ~ empty(U_35) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_33,sK2(U_36))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ member(U_32,U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( empty(U_36)
| member(sK2(U_36),U_36) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,negated_conjecture,
~ ! [B] : difference(empty_set,B) = empty_set,
inference(negate,[status(cth)],[prove_no_difference_with_empty_set]) ).
fof(f_9_2,negated_conjecture,
? [B] : difference(empty_set,B) != empty_set,
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_37] : difference(empty_set,U_37) != empty_set,
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
difference(empty_set,sK3) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_37,sK3)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
difference(empty_set,sK3) != empty_set,
inference(definitional_conversion,[status(esa)],[f_9_4]) ).
cnf(f_9_6,negated_conjecture,
difference(empty_set,sK3) != empty_set,
inference(clausify,[status(thm)],[f_9_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,
( difference(Eq_x_0,Eq_x_1) = difference(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) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_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,
( 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
% 0.00/0.03 % Problem : SET604+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
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 22:47:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------