%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET579+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 : n006.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 08:57:00 AM UTC 2026
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(prove_th20,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
file('theBenchmark.p',prove_th20) ).
fof(f_1_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_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,difference(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,difference(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,difference(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,difference(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_3,U_7)
| ~ member(U_3,difference(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ member(U_3,U_5)
| ~ member(U_3,difference(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( member(U_4,difference(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] :
( ( 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_2_2,plain,
! [U_10,U_9] :
( ( U_10 = U_9
| ~ subset(U_9,U_10)
| ~ subset(U_10,U_9) )
& ( ( subset(U_9,U_10)
& subset(U_10,U_9) )
| U_10 != U_9 ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_14,U_12] :
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) )
& ! [U_13,U_11] :
( ( subset(U_11,U_13)
& subset(U_13,U_11) )
| U_13 != U_11 ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_13,U_11)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( subset(U_11,U_13)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_18,U_17] :
( ( subset(U_18,U_17)
| ? [U_16] :
( ~ member(U_16,U_17)
& member(U_16,U_18) ) )
& ( ! [U_15] :
( member(U_15,U_17)
| ~ member(U_15,U_18) )
| ~ subset(U_18,U_17) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ? [U_16] :
( ~ member(U_16,U_20)
& member(U_16,U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( member(U_15,U_19)
| ~ member(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ( ~ member(sK1(U_22,U_20),U_20)
& member(sK1(U_22,U_20),U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( member(U_15,U_19)
| ~ member(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_16,sK1(U_22,U_20))],[f_3_3]) ).
cnf(f_3_5,plain,
( member(U_15,U_19)
| ~ member(U_15,U_21)
| ~ subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( member(sK1(U_22,U_20),U_22)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( ~ member(sK1(U_22,U_20),U_20)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_4_2,plain,
! [U_23] : subset(U_23,U_23),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
subset(U_23,U_23),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
inference(negate,[status(cth)],[prove_th20]) ).
fof(f_5_2,negated_conjecture,
? [B,C,D] :
( B != difference(C,D)
& ! [E] :
( ( member(E,B)
| member(E,D)
| ~ member(E,C) )
& ( ( ~ member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_27,U_26,U_25] :
( U_27 != difference(U_26,U_25)
& ! [U_24] :
( ( member(U_24,U_27)
| member(U_24,U_25)
| ~ member(U_24,U_26) )
& ( ( ~ member(U_24,U_25)
& member(U_24,U_26) )
| ~ member(U_24,U_27) ) ) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
? [U_27,U_26,U_25] :
( U_27 != difference(U_26,U_25)
& ! [U_29] :
( member(U_29,U_27)
| member(U_29,U_25)
| ~ member(U_29,U_26) )
& ! [U_28] :
( ( ~ member(U_28,U_25)
& member(U_28,U_26) )
| ~ member(U_28,U_27) ) ),
inference(miniscope,[status(thm)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
? [U_26,U_25] :
( sK2 != difference(U_26,U_25)
& ! [U_29] :
( member(U_29,sK2)
| member(U_29,U_25)
| ~ member(U_29,U_26) )
& ! [U_28] :
( ( ~ member(U_28,U_25)
& member(U_28,U_26) )
| ~ member(U_28,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
? [U_25] :
( sK2 != difference(sK3,U_25)
& ! [U_29] :
( member(U_29,sK2)
| member(U_29,U_25)
| ~ member(U_29,sK3) )
& ! [U_28] :
( ( ~ member(U_28,U_25)
& member(U_28,sK3) )
| ~ member(U_28,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( sK2 != difference(sK3,sK4)
& ! [U_29] :
( member(U_29,sK2)
| member(U_29,sK4)
| ~ member(U_29,sK3) )
& ! [U_28] :
( ( ~ member(U_28,sK4)
& member(U_28,sK3) )
| ~ member(U_28,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4)],[f_5_6]) ).
fof(f_5_8,negated_conjecture,
( ! [U_28] :
( ~ member(U_28,sK4)
| ~ sP0(U_28) )
& ! [U_28] :
( member(U_28,sK3)
| ~ sP0(U_28) )
& sK2 != difference(sK3,sK4)
& ! [U_29] :
( member(U_29,sK2)
| member(U_29,sK4)
| ~ member(U_29,sK3) )
& ! [U_28] :
( sP0(U_28)
| ~ member(U_28,sK2) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_7]) ).
cnf(f_5_9,negated_conjecture,
( sP0(U_28)
| ~ member(U_28,sK2) ),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_10,negated_conjecture,
( member(U_29,sK2)
| member(U_29,sK4)
| ~ member(U_29,sK3) ),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_11,negated_conjecture,
sK2 != difference(sK3,sK4),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_12,negated_conjecture,
( member(U_28,sK3)
| ~ sP0(U_28) ),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_13,negated_conjecture,
( ~ member(U_28,sK4)
| ~ sP0(U_28) ),
inference(clausify,[status(thm)],[f_5_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,
( 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,
( 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_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,
( sP0(Eq_y_0)
| ~ sP0(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 : SET579+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
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 22:40:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------