%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET027+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 : n005.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 08:55:59 AM UTC 2026
% Result : Theorem 0.14s 10.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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_transitivity_of_subset,conjecture,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('theBenchmark.p',prove_transitivity_of_subset) ).
fof(f_1_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_1_2,plain,
! [U_3,U_2] :
( ( subset(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) )
| ~ subset(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subset(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) )
| ~ subset(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK1(U_7,U_5),U_7)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(sK1(U_7,U_5),U_5)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_2_2,plain,
! [U_8] : subset(U_8,U_8),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
subset(U_8,U_8),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(negate,[status(cth)],[prove_transitivity_of_subset]) ).
fof(f_3_2,negated_conjecture,
? [B,C,D] :
( ~ subset(B,D)
& subset(C,D)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_11,U_10,U_9] :
( ~ subset(U_11,U_9)
& subset(U_10,U_9)
& subset(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
? [U_10,U_9] :
( ~ subset(sK2,U_9)
& subset(U_10,U_9)
& subset(sK2,U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
? [U_9] :
( ~ subset(sK2,U_9)
& subset(sK3,U_9)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_10,sK3)],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ~ subset(sK2,sK4)
& subset(sK3,sK4)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4)],[f_3_5]) ).
fof(f_3_7,negated_conjecture,
( ~ subset(sK2,sK4)
& subset(sK3,sK4)
& subset(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_3_6]) ).
cnf(f_3_8,negated_conjecture,
subset(sK2,sK3),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_9,negated_conjecture,
subset(sK3,sK4),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_10,negated_conjecture,
~ subset(sK2,sK4),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027+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
% 0.10/10.39 % Computer : n005.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 19 21:29:44 UTC 2026
% 0.14/10.40 % CPUTime :
% 0.14/10.42 % SZS status Theorem for theBenchmark
% 0.14/10.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------