%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET602+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 : n013.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 08:57:04 AM UTC 2026
% Result : Theorem 0.13s 6.23s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 33 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 8 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('theBenchmark.p',difference_empty_set) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(prove_self_difference_is_empty_set,conjecture,
! [B] : difference(B,B) = empty_set,
file('theBenchmark.p',prove_self_difference_is_empty_set) ).
fof(f_1_1,plain,
! [B,C] :
( ( difference(B,C) = empty_set
| ~ subset(B,C) )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(fof_nnf,[status(thm)],[difference_empty_set]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ( difference(U_1,U_0) = empty_set
| ~ subset(U_1,U_0) )
& ( subset(U_1,U_0)
| difference(U_1,U_0) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_5,U_3] :
( difference(U_5,U_3) = empty_set
| ~ subset(U_5,U_3) )
& ! [U_4,U_2] :
( subset(U_4,U_2)
| difference(U_4,U_2) != empty_set ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_5,plain,
( difference(U_5,U_3) = empty_set
| ~ subset(U_5,U_3) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_6_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_6_2,plain,
! [U_30] : subset(U_30,U_30),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
subset(U_30,U_30),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_8_1,negated_conjecture,
~ ! [B] : difference(B,B) = empty_set,
inference(negate,[status(cth)],[prove_self_difference_is_empty_set]) ).
fof(f_8_2,negated_conjecture,
? [B] : difference(B,B) != empty_set,
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_36] : difference(U_36,U_36) != empty_set,
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
difference(sK3,sK3) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_36,sK3)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
difference(sK3,sK3) != empty_set,
inference(definitional_conversion,[status(esa)],[f_8_4]) ).
cnf(f_8_6,negated_conjecture,
difference(sK3,sK3) != empty_set,
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(t1,plain,
difference(sK3,sK3) != empty_set,
inference(start,[status(thm),parent(0:0)],[f_8_6]) ).
cnf(t2,plain,
( ~ subset(sK3,sK3)
| difference(sK3,sK3) = empty_set ),
inference(extension,[status(thm),parent(t1:1)],[f_1_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
subset(sK3,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_6_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET602+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.10/6.19 % Computer : n013.cluster.edu
% 0.10/6.19 % Model : x86_64 x86_64
% 0.10/6.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.19 % Memory : 8046.5625MB
% 0.10/6.19 % OS : Linux 6.8.0-71-generic
% 0.10/6.19 % CPULimit : 300
% 0.10/6.19 % WCLimit : 300
% 0.10/6.19 % DateTime : Sat Sep 19 22:41:55 UTC 2026
% 0.10/6.20 % CPUTime :
% 0.13/6.23 % SZS status Theorem for theBenchmark
% 0.13/6.23 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------