%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:02:12 PM UTC 2026
% Result : Theorem 4.74s 1.13s
% Output : Proof 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 48 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 13 |; 4 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 2 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f30_nnf,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c59,plain,
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f33,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f33_nnf,plain,
op_equiv,
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c62,plain,
op_equiv,
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(p113,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c59,c62]) ).
fof(f16,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
fof(f16_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(sk33,sk34),sk33))
| kn2 )
& ( is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk33,sk34])],[f16_nnf]) ).
cnf(c35,plain,
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f36,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f36_nnf,plain,
kn2,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
kn2,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(p73,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c35,c65]) ).
cnf(p115,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[p113,p73]) ).
fof(f12,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
fof(f12_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| equivalence_1 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(equiv(sk26,sk27),implies(sk26,sk27)))
| equivalence_1 )
& ( is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f12_nnf]) ).
cnf(c28,plain,
( ~ is_a_theorem(implies(equiv(sk26,sk27),implies(sk26,sk27)))
| equivalence_1 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p125,plain,
equivalence_1,
inference(resolution,[status(thm)],[p115,c28]) ).
fof(f42,conjecture,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f42_neg,negated_conjecture,
~ equivalence_1,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ equivalence_1,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ equivalence_1,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ equivalence_1,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p127,plain,
$false,
inference(resolution,[status(thm)],[p125,c71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 23:39:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.74/1.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.74/1.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------