%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 : Fri Sep 25 02:43:57 PM UTC 2026
% Result : Theorem 3.96s 1.08s
% Output : Proof 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 4 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 108 ( 32 ~; 54 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 37 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [X,Y] :
( ( equalish(Y,X)
& ~ equalish(X,Y) )
| ( ~ equalish(Y,X)
& equalish(X,Y) ) )
& ! [X,Y] :
( ( ? [Z] :
( ( a_member_of(Z,Y)
& ~ a_member_of(Z,X) )
| ( ~ a_member_of(Z,Y)
& a_member_of(Z,X) ) )
| equalish(X,Y) )
& ( ! [Z] :
( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ equalish(X,Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,Z] :
( ( ( equalish(sk2,sk1)
& ~ equalish(sk1,sk2) )
| ( ~ equalish(sk2,sk1)
& equalish(sk1,sk2) ) )
& ( ( a_member_of(sk0(X,Y),Y)
& ~ a_member_of(sk0(X,Y),X) )
| ( ~ a_member_of(sk0(X,Y),Y)
& a_member_of(sk0(X,Y),X) )
| equalish(X,Y) )
& ( ( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ equalish(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c7,plain,
( equalish(sk2,sk1)
| equalish(sk1,sk2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c1,plain,
( ~ a_member_of(X2,X1)
| a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p13,plain,
( ~ a_member_of(X0,sk1)
| a_member_of(X0,sk2)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(c3,plain,
( a_member_of(sk0(X0,X1),X1)
| a_member_of(sk0(X0,X1),X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( a_member_of(sk0(sk1,X0),X0)
| equalish(sk1,X0)
| a_member_of(sk0(sk1,X0),sk2)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[p13,c3]) ).
cnf(p24,plain,
( a_member_of(sk0(sk1,sk2),sk2)
| a_member_of(sk0(sk1,sk2),sk2)
| equalish(sk1,sk2) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(p27,plain,
( a_member_of(sk0(sk1,sk2),sk2)
| equalish(sk1,sk2) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(c4,plain,
( ~ a_member_of(sk0(X0,X1),X0)
| ~ a_member_of(sk0(X0,X1),X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p28,plain,
( ~ a_member_of(sk0(sk1,sk2),sk1)
| equalish(sk1,sk2)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(p29,plain,
( ~ a_member_of(sk0(sk1,sk2),sk1)
| equalish(sk1,sk2) ),
inference(factoring,[status(thm)],[p28]) ).
cnf(c0,plain,
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( a_member_of(X0,sk1)
| ~ a_member_of(X0,sk2)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(p16,plain,
( a_member_of(sk0(X0,sk2),X0)
| equalish(X0,sk2)
| a_member_of(sk0(X0,sk2),sk1)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[p12,c3]) ).
cnf(p22,plain,
( a_member_of(sk0(sk1,sk2),sk1)
| a_member_of(sk0(sk1,sk2),sk1)
| equalish(sk1,sk2) ),
inference(factoring,[status(thm)],[p16]) ).
cnf(p26,plain,
( a_member_of(sk0(sk1,sk2),sk1)
| equalish(sk1,sk2) ),
inference(factoring,[status(thm)],[p22]) ).
cnf(p30,plain,
( equalish(sk1,sk2)
| equalish(sk1,sk2) ),
inference(resolution,[status(thm)],[p29,p26]) ).
cnf(p31,plain,
equalish(sk1,sk2),
inference(factoring,[status(thm)],[p30]) ).
cnf(p33,plain,
( ~ a_member_of(X0,sk2)
| a_member_of(X0,sk1) ),
inference(resolution,[status(thm)],[p31,c1]) ).
cnf(p36,plain,
( a_member_of(sk0(sk2,X0),X0)
| equalish(sk2,X0)
| a_member_of(sk0(sk2,X0),sk1) ),
inference(resolution,[status(thm)],[p33,c3]) ).
cnf(p39,plain,
( equalish(sk2,sk1)
| a_member_of(sk0(sk2,sk1),sk1) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(p40,plain,
( ~ a_member_of(sk0(sk2,sk1),sk2)
| equalish(sk2,sk1)
| equalish(sk2,sk1) ),
inference(resolution,[status(thm)],[p39,c4]) ).
cnf(p41,plain,
( ~ a_member_of(sk0(sk2,sk1),sk2)
| equalish(sk2,sk1) ),
inference(factoring,[status(thm)],[p40]) ).
cnf(p32,plain,
( a_member_of(X0,sk2)
| ~ a_member_of(X0,sk1) ),
inference(resolution,[status(thm)],[p31,c0]) ).
cnf(p35,plain,
( a_member_of(sk0(X0,sk1),X0)
| equalish(X0,sk1)
| a_member_of(sk0(X0,sk1),sk2) ),
inference(resolution,[status(thm)],[p32,c3]) ).
cnf(p38,plain,
( equalish(sk2,sk1)
| a_member_of(sk0(sk2,sk1),sk2) ),
inference(factoring,[status(thm)],[p35]) ).
cnf(p42,plain,
( equalish(sk2,sk1)
| equalish(sk2,sk1) ),
inference(resolution,[status(thm)],[p41,p38]) ).
cnf(p43,plain,
equalish(sk2,sk1),
inference(factoring,[status(thm)],[p42]) ).
cnf(c8,plain,
( ~ equalish(sk1,sk2)
| ~ equalish(sk2,sk1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p44,plain,
~ equalish(sk1,sk2),
inference(resolution,[status(thm)],[p43,c8]) ).
cnf(p45,plain,
$false,
inference(resolution,[status(thm)],[p44,p31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:57:59 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.96/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.96/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------