%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:34:36 PM UTC 2026
% Result : Theorem 3.58s 0.94s
% Output : Proof 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 12 ~; 8 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,conjecture,
! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1] :
( ( join(X0,X1) != X1
& join(converse(X0),converse(X1)) = converse(X1) )
| ( join(converse(X0),converse(X1)) != converse(X1)
& join(X0,X1) = X1 ) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( ( join(sk0,sk1) != sk1
& join(converse(sk0),converse(sk1)) = converse(sk1) )
| ( join(converse(sk0),converse(sk1)) != converse(sk1)
& join(sk0,sk1) = sk1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f13_nnf]) ).
cnf(c13,plain,
( join(converse(sk0),converse(sk1)) = converse(sk1)
| join(sk0,sk1) = sk1 ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f8_nnf,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p59,plain,
( sk1 = join(sk0,sk1)
| join(sk0,sk1) = sk1 ),
inference(superposition,[status(thm)],[c13,c8]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p71,plain,
( sk1 = join(sk0,sk1)
| sk1 = join(sk0,sk1) ),
inference(superposition,[status(thm)],[p59,c0]) ).
cnf(p72,plain,
sk1 = join(sk0,sk1),
inference(factoring,[status(thm)],[p71]) ).
cnf(p74,plain,
join(sk0,sk1) = sk1,
inference(superposition,[status(thm)],[p72,c0]) ).
cnf(c16,plain,
( join(sk0,sk1) != sk1
| join(converse(sk0),converse(sk1)) != converse(sk1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p60,plain,
( join(sk0,sk1) != sk1
| converse(join(sk0,sk1)) != converse(sk1) ),
inference(superposition,[status(thm)],[c8,c16]) ).
cnf(p75,plain,
( sk1 != sk1
| converse(sk1) != converse(sk1) ),
inference(demodulation,[status(thm)],[p74,p60]) ).
cnf(p78,plain,
sk1 != sk1,
inference(equality_resolution,[status(thm)],[p75]) ).
cnf(p80,plain,
$false,
inference(equality_resolution,[status(thm)],[p78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:05:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.58/0.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/0.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------