%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 02:02:09 PM UTC 2026
% Result : Theorem 30.15s 4.44s
% Output : Proof 30.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 25 unt; 0 def)
% Number of atoms : 75 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 24 ~; 20 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f26_nnf,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c55,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f41,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41_nnf,plain,
op_or,
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c70,plain,
op_or,
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(p152,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c55,c70]) ).
fof(f28,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f28_nnf,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c57,plain,
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f42,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42_nnf,plain,
op_implies_and,
inference(nnf_transformation,[status(thm)],[f42]) ).
cnf(c71,plain,
op_implies_and,
inference(cnf_transformation,[status(esa)],[f42_nnf]) ).
cnf(p86,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c57,c71]) ).
cnf(p161,plain,
implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[p152,p86]) ).
fof(f2,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f2_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y,X] :
( ( ~ is_a_theorem(implies(implies(not(sk5),not(sk4)),implies(sk4,sk5)))
| modus_tollens )
& ( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f2_nnf]) ).
cnf(c8,plain,
( ~ is_a_theorem(implies(implies(not(sk5),not(sk4)),implies(sk4,sk5)))
| modus_tollens ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p162,plain,
( ~ is_a_theorem(implies(or(sk5,not(sk4)),implies(sk4,sk5)))
| modus_tollens ),
inference(demodulation,[status(thm)],[p161,c8]) ).
fof(f29,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f29_nnf,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y] :
( implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c58,plain,
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f31,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f31_nnf,plain,
op_implies_or,
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c60,plain,
op_implies_or,
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(p79,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c58,c60]) ).
fof(f23,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f23_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(sk47,sk48),or(sk48,sk47)))
| r3 )
& ( is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48])],[f23_nnf]) ).
cnf(c49,plain,
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f37,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f37_nnf,plain,
r3,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
r3,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(p78,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c49,c66]) ).
cnf(p83,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(superposition,[status(thm)],[p79,p78]) ).
cnf(p403,plain,
modus_tollens,
inference(resolution,[status(thm)],[p162,p83]) ).
fof(f44,conjecture,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f44_neg,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
~ modus_tollens,
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
~ modus_tollens,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c73,plain,
~ modus_tollens,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p404,plain,
$false,
inference(resolution,[status(thm)],[p403,c73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Wed Sep 23 23:31:21 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 30.15/4.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.15/4.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------