%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET583+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 : n008.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 08:57:01 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 57 ( 18 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 ( 1 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_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_extensionality,conjecture,
! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
file('theBenchmark.p',prove_extensionality) ).
fof(f_1_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_1_2,plain,
! [U_1,U_0] :
( ( U_1 = U_0
| ~ subset(U_0,U_1)
| ~ subset(U_1,U_0) )
& ( ( subset(U_0,U_1)
& subset(U_1,U_0) )
| U_1 != U_0 ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_5,U_3] :
( U_5 = U_3
| ~ subset(U_3,U_5)
| ~ subset(U_5,U_3) )
& ! [U_4,U_2] :
( ( subset(U_2,U_4)
& subset(U_4,U_2) )
| U_4 != U_2 ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_6,plain,
( U_5 = U_3
| ~ subset(U_3,U_5)
| ~ subset(U_5,U_3) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_4_1,negated_conjecture,
~ ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
inference(negate,[status(cth)],[prove_extensionality]) ).
fof(f_4_2,negated_conjecture,
? [B,C] :
( B != C
& subset(C,B)
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_16,U_15] :
( U_16 != U_15
& subset(U_15,U_16)
& subset(U_16,U_15) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_15] :
( sK2 != U_15
& subset(U_15,sK2)
& subset(sK2,U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( sK2 != sK3
& subset(sK3,sK2)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( sK2 != sK3
& subset(sK3,sK2)
& subset(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_4_5]) ).
cnf(f_4_7,negated_conjecture,
subset(sK2,sK3),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,negated_conjecture,
subset(sK3,sK2),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,negated_conjecture,
sK2 != sK3,
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(t1,plain,
sK2 != sK3,
inference(start,[status(thm),parent(0:0)],[f_4_9]) ).
cnf(t2,plain,
( ~ subset(sK3,sK2)
| ~ subset(sK2,sK3)
| sK2 = sK3 ),
inference(extension,[status(thm),parent(t1:1)],[f_1_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
subset(sK2,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_4_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(sK3,sK2),
inference(extension,[status(thm),parent(t2:3)],[f_4_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET583+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 22:41:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------