%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL494+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 : 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 02:02:10 PM UTC 2026
% Result : Theorem 43.36s 6.00s
% Output : Proof 43.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 104 ( 59 unt; 0 def)
% Number of atoms : 182 ( 32 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 134 ( 56 ~; 52 |; 15 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 145 ( 14 sgn 57 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',principia_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(p4290,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c59,c62]) ).
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(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]) ).
cnf(p187,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[p79,p161]) ).
fof(f27,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f27_nnf,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y] :
( and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c56,plain,
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p188,plain,
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(demodulation,[status(thm)],[p187,c56]) ).
fof(f32,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f32_nnf,plain,
op_and,
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c61,plain,
op_and,
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(p404,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(resolution,[status(thm)],[p188,c61]) ).
cnf(p427,plain,
and(not(X0),X1) = not(or(X0,not(X1))),
inference(superposition,[status(thm)],[p161,p404]) ).
cnf(p566,plain,
and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(superposition,[status(thm)],[p187,p427]) ).
cnf(p952,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(superposition,[status(thm)],[p404,p566]) ).
cnf(p4304,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(superposition,[status(thm)],[p4290,p952]) ).
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f0_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(sk1)
& is_a_theorem(implies(sk0,sk1))
& is_a_theorem(sk0) )
| modus_ponens )
& ( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| ~ modus_ponens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f34_nnf,plain,
modus_ponens,
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c63,plain,
modus_ponens,
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(p94,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c0,c63]) ).
fof(f22,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f22_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Q,P] :
( ( ~ is_a_theorem(implies(sk46,or(sk45,sk46)))
| r2 )
& ( is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk45,sk46])],[f22_nnf]) ).
cnf(c47,plain,
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f36,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f36_nnf,plain,
r2,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
r2,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(p75,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c47,c65]) ).
cnf(p96,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[p94,p75]) ).
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(p82,plain,
is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[p79,p78]) ).
cnf(p132,plain,
is_a_theorem(or(or(X0,X1),not(X1))),
inference(resolution,[status(thm)],[p96,p82]) ).
cnf(p137,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(or(or(X0,X1),not(X1)),X2)) ),
inference(resolution,[status(thm)],[p132,p94]) ).
cnf(p81,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[p79,p75]) ).
cnf(p189,plain,
is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[status(thm)],[p161,p81]) ).
cnf(p219,plain,
is_a_theorem(implies(X0,implies(X1,not(not(X0))))),
inference(superposition,[status(thm)],[p187,p189]) ).
cnf(p1272,plain,
is_a_theorem(implies(X0,not(and(not(or(X1,X2)),X2)))),
inference(resolution,[status(thm)],[p137,p219]) ).
fof(f21,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
fof(f21_nnf,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [P] :
( ( ~ is_a_theorem(implies(or(sk44,sk44),sk44))
| r1 )
& ( is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk44])],[f21_nnf]) ).
cnf(c45,plain,
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f35,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(f35_nnf,plain,
r1,
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c64,plain,
r1,
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(p74,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c45,c64]) ).
cnf(p95,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(or(X0,X0),X0),X1)) ),
inference(resolution,[status(thm)],[p94,p74]) ).
cnf(p1387,plain,
is_a_theorem(not(and(not(or(X0,X1)),X1))),
inference(resolution,[status(thm)],[p1272,p95]) ).
cnf(p1391,plain,
is_a_theorem(not(and(not(implies(X0,X1)),X1))),
inference(superposition,[status(thm)],[p187,p1387]) ).
cnf(p1394,plain,
is_a_theorem(not(and(and(X0,X1),not(X1)))),
inference(superposition,[status(thm)],[p952,p1391]) ).
cnf(p1395,plain,
is_a_theorem(implies(and(X0,X1),X1)),
inference(superposition,[status(thm)],[p86,p1394]) ).
cnf(p4341,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(superposition,[status(thm)],[p4304,p1395]) ).
fof(f13,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f13_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| equivalence_2 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(equiv(sk28,sk29),implies(sk29,sk28)))
| equivalence_2 )
& ( is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk28,sk29])],[f13_nnf]) ).
cnf(c30,plain,
( ~ is_a_theorem(implies(equiv(sk28,sk29),implies(sk29,sk28)))
| equivalence_2 ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p4456,plain,
equivalence_2,
inference(resolution,[status(thm)],[p4341,c30]) ).
fof(f44,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f44_neg,negated_conjecture,
~ equivalence_2,
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
~ equivalence_2,
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
~ equivalence_2,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c73,plain,
~ equivalence_2,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p4459,plain,
$false,
inference(resolution,[status(thm)],[p4456,c73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 23:33:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.36/6.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.36/6.00 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------