%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN966+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 : n017.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 03:36:25 PM UTC 2026
% Result : Theorem 4.35s 1.08s
% Output : Proof 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 72 ( 24 ~; 28 |; 12 &)
% ( 4 <=>; 4 =>; 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 : 32 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ( ? [Z] :
( ( a_member_of(Z,Y)
& ~ a_member_of(Z,X) )
| ( ~ a_member_of(Z,Y)
& a_member_of(Z,X) ) )
| eq(X,Y) )
& ( ! [Z] :
( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ eq(X,Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,Z] :
( ~ eq(sk2,sk1)
& eq(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) )
| eq(X,Y) )
& ( ( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ eq(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c3,plain,
( a_member_of(sk0(X0,X1),X1)
| a_member_of(sk0(X0,X1),X0)
| eq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c6,plain,
eq(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p8,plain,
( a_member_of(X0,sk2)
| ~ a_member_of(X0,sk1) ),
inference(resolution,[status(thm)],[c0,c6]) ).
cnf(p12,plain,
( a_member_of(sk0(X0,sk1),sk2)
| a_member_of(sk0(X0,sk1),X0)
| eq(X0,sk1) ),
inference(resolution,[status(thm)],[c3,p8]) ).
cnf(p20,plain,
( a_member_of(sk0(sk2,sk1),sk2)
| eq(sk2,sk1) ),
inference(factoring,[status(thm)],[p12]) ).
cnf(c1,plain,
( ~ a_member_of(X2,X1)
| a_member_of(X2,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( ~ a_member_of(X0,sk2)
| a_member_of(X0,sk1) ),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(p21,plain,
( a_member_of(sk0(sk2,sk1),sk1)
| eq(sk2,sk1) ),
inference(resolution,[status(thm)],[p20,p9]) ).
cnf(c4,plain,
( ~ a_member_of(sk0(X0,X1),X0)
| ~ a_member_of(sk0(X0,X1),X1)
| eq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
( ~ a_member_of(sk0(sk2,sk1),sk2)
| eq(sk2,sk1)
| eq(sk2,sk1) ),
inference(resolution,[status(thm)],[p21,c4]) ).
cnf(p23,plain,
( ~ a_member_of(sk0(sk2,sk1),sk2)
| eq(sk2,sk1) ),
inference(factoring,[status(thm)],[p22]) ).
cnf(p24,plain,
( eq(sk2,sk1)
| eq(sk2,sk1) ),
inference(resolution,[status(thm)],[p23,p20]) ).
cnf(p25,plain,
eq(sk2,sk1),
inference(factoring,[status(thm)],[p24]) ).
cnf(c7,plain,
~ eq(sk2,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
$false,
inference(resolution,[status(thm)],[p25,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 02:36:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.35/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.35/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------