%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET063+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 : n001.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 08:56:09 AM UTC 2026
% Result : Theorem 0.07s 0.39s
% Output : Proof 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 51 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 20 ~; 13 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 1 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [B] : subset(empty_set,B),
file('theBenchmark.p',empty_set_subset) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_subset_of_empty_set_is_empty_set,conjecture,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
fof(f_1_1,plain,
! [B] : subset(empty_set,B),
inference(fof_nnf,[status(thm)],[empty_set_subset]) ).
fof(f_1_2,plain,
! [U_0] : subset(empty_set,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
subset(empty_set,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_4_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_4_2,plain,
! [U_11,U_10] :
( ( U_11 = U_10
| ~ subset(U_10,U_11)
| ~ subset(U_11,U_10) )
& ( ( subset(U_10,U_11)
& subset(U_11,U_10) )
| U_11 != U_10 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( ( subset(U_12,U_14)
& subset(U_14,U_12) )
| U_14 != U_12 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_6,plain,
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_7_1,negated_conjecture,
~ ! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(negate,[status(cth)],[prove_subset_of_empty_set_is_empty_set]) ).
fof(f_7_2,negated_conjecture,
? [B] :
( B != empty_set
& subset(B,empty_set) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_22] :
( U_22 != empty_set
& subset(U_22,empty_set) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( sK3 != empty_set
& subset(sK3,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( sK3 != empty_set
& subset(sK3,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_7_4]) ).
cnf(f_7_6,negated_conjecture,
subset(sK3,empty_set),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
sK3 != empty_set,
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(t1,plain,
sK3 != empty_set,
inference(start,[status(thm),parent(0:0)],[f_7_7]) ).
cnf(t2,plain,
( ~ subset(empty_set,sK3)
| ~ subset(sK3,empty_set)
| sK3 = empty_set ),
inference(extension,[status(thm),parent(t1:1)],[f_4_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
subset(sK3,empty_set),
inference(extension,[status(thm),parent(t2:2)],[f_7_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(empty_set,sK3),
inference(extension,[status(thm),parent(t2:3)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.07/0.36 % Computer : n001.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 21:41:40 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.39 % SZS status Theorem for theBenchmark
% 0.07/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------