%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET062+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 : n011.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 08:56:08 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 15 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 24 ~; 14 |; 8 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_empty_set_subset,conjecture,
! [B] : subset(empty_set,B),
file('theBenchmark.p',prove_empty_set_subset) ).
fof(f_1_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_1_2,plain,
! [U_0] : ~ member(U_0,empty_set),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
~ member(U_0,empty_set),
inference(clausify,[status(thm)],[f_1_2]) ).
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_4,U_3] :
( ( subset(U_4,U_3)
| ? [U_2] :
( ~ member(U_2,U_3)
& member(U_2,U_4) ) )
& ( ! [U_1] :
( member(U_1,U_3)
| ~ member(U_1,U_4) )
| ~ subset(U_4,U_3) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_8,U_6] :
( subset(U_8,U_6)
| ? [U_2] :
( ~ member(U_2,U_6)
& member(U_2,U_8) ) )
& ! [U_7,U_5] :
( ! [U_1] :
( member(U_1,U_5)
| ~ member(U_1,U_7) )
| ~ subset(U_7,U_5) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_8,U_6] :
( subset(U_8,U_6)
| ( ~ member(sK1(U_8,U_6),U_6)
& member(sK1(U_8,U_6),U_8) ) )
& ! [U_7,U_5] :
( ! [U_1] :
( member(U_1,U_5)
| ~ member(U_1,U_7) )
| ~ subset(U_7,U_5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1(U_8,U_6))],[f_2_3]) ).
cnf(f_2_6,plain,
( member(sK1(U_8,U_6),U_8)
| subset(U_8,U_6) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_5_1,negated_conjecture,
~ ! [B] : subset(empty_set,B),
inference(negate,[status(cth)],[prove_empty_set_subset]) ).
fof(f_5_2,negated_conjecture,
? [B] : ~ subset(empty_set,B),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_15] : ~ subset(empty_set,U_15),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
~ subset(empty_set,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
~ subset(empty_set,sK3),
inference(definitional_conversion,[status(esa)],[f_5_4]) ).
cnf(f_5_6,negated_conjecture,
~ subset(empty_set,sK3),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(t1,plain,
~ member(sK1(empty_set,sK3),empty_set),
inference(start,[status(thm),parent(0:0)],[f_1_3]) ).
cnf(t2,plain,
( subset(empty_set,sK3)
| member(sK1(empty_set,sK3),empty_set) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ subset(empty_set,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_5_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 21:36:10 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------