%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET631+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 08:57:10 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% 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(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_th113,conjecture,
! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
file('theBenchmark.p',prove_th113) ).
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] :
( ( 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] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_3_2,plain,
! [U_18,U_17] :
( intersect(U_17,U_18)
| ~ intersect(U_18,U_17) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( intersect(U_17,U_18)
| ~ intersect(U_18,U_17) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
inference(negate,[status(cth)],[prove_th113]) ).
fof(f_4_2,negated_conjecture,
? [B,C,D] :
( ~ intersect(B,C)
& intersect(B,difference(C,D)) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_21,U_20,U_19] :
( ~ intersect(U_21,U_20)
& intersect(U_21,difference(U_20,U_19)) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_21,U_20] :
( ? [U_19] : intersect(U_21,difference(U_20,U_19))
& ~ intersect(U_21,U_20) ),
inference(miniscope,[status(thm)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
? [U_20] :
( ? [U_19] : intersect(sK2,difference(U_20,U_19))
& ~ intersect(sK2,U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ? [U_19] : intersect(sK2,difference(sK3,U_19))
& ~ intersect(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( intersect(sK2,difference(sK3,sK4))
& ~ intersect(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_19,sK4)],[f_4_6]) ).
fof(f_4_8,negated_conjecture,
( intersect(sK2,difference(sK3,sK4))
& ~ intersect(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_4_7]) ).
cnf(f_4_9,negated_conjecture,
~ intersect(sK2,sK3),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(f_4_10,negated_conjecture,
intersect(sK2,difference(sK3,sK4)),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET631+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.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 22:43:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------