%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET019+4 : 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 : n015.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 08:55:56 AM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 21 ~; 13 |; 19 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 14 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('SET006+0.ax',equal_set) ).
fof(thI02,conjecture,
! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
file('theBenchmark.p',thI02) ).
fof(f_2_1,plain,
! [A,B] :
( ( equal_set(A,B)
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(fof_nnf,[status(thm)],[equal_set]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ( equal_set(U_9,U_8)
| ~ subset(U_8,U_9)
| ~ subset(U_9,U_8) )
& ( ( subset(U_8,U_9)
& subset(U_9,U_8) )
| ~ equal_set(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( ( subset(U_10,U_12)
& subset(U_12,U_10) )
| ~ equal_set(U_12,U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_6,plain,
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
inference(negate,[status(cth)],[thI02]) ).
fof(f_12_2,negated_conjecture,
? [A,B] :
( ~ equal_set(A,B)
& subset(B,A)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_80,U_79] :
( ~ equal_set(U_80,U_79)
& subset(U_79,U_80)
& subset(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_79] :
( ~ equal_set(sK4,U_79)
& subset(U_79,sK4)
& subset(sK4,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ~ equal_set(sK4,sK5)
& subset(sK5,sK4)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_79,sK5)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
( ~ equal_set(sK4,sK5)
& subset(sK5,sK4)
& subset(sK4,sK5) ),
inference(definitional_conversion,[status(esa)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,negated_conjecture,
subset(sK5,sK4),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,negated_conjecture,
~ equal_set(sK4,sK5),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(t1,plain,
~ equal_set(sK4,sK5),
inference(start,[status(thm),parent(0:0)],[f_12_9]) ).
cnf(t2,plain,
( ~ subset(sK5,sK4)
| ~ subset(sK4,sK5)
| equal_set(sK4,sK5) ),
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(sK4,sK5),
inference(extension,[status(thm),parent(t2:2)],[f_12_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(sK5,sK4),
inference(extension,[status(thm),parent(t2:3)],[f_12_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019+4 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 21:30:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.42 % SZS status Theorem for theBenchmark
% 0.11/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------