%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET009+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 : n007.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 08:55:51 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : Proof 0.10s
% 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(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_subset_difference,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('theBenchmark.p',prove_subset_difference) ).
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] :
( ( 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] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_3_2,plain,
! [U_17] : subset(U_17,U_17),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
subset(U_17,U_17),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negate,[status(cth)],[prove_subset_difference]) ).
fof(f_4_2,negated_conjecture,
? [B,C,D] :
( ~ subset(difference(D,C),difference(D,B))
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_20,U_19,U_18] :
( ~ subset(difference(U_18,U_19),difference(U_18,U_20))
& subset(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_20,U_19] :
( ? [U_18] : ~ subset(difference(U_18,U_19),difference(U_18,U_20))
& subset(U_20,U_19) ),
inference(miniscope,[status(thm)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
? [U_19] :
( ? [U_18] : ~ subset(difference(U_18,U_19),difference(U_18,sK2))
& subset(sK2,U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_20,sK2)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ? [U_18] : ~ subset(difference(U_18,sK3),difference(U_18,sK2))
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( ~ subset(difference(sK4,sK3),difference(sK4,sK2))
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_18,sK4)],[f_4_6]) ).
fof(f_4_8,negated_conjecture,
( ~ subset(difference(sK4,sK3),difference(sK4,sK2))
& subset(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_4_7]) ).
cnf(f_4_9,negated_conjecture,
subset(sK2,sK3),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(f_4_10,negated_conjecture,
~ subset(difference(sK4,sK3),difference(sK4,sK2)),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ 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
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 21:24:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------