%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL518+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 : n002.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 02:02:13 PM UTC 2026
% Result : Theorem 12.66s 11.51s
% Output : Proof 12.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 49 unt; 0 def)
% Number of atoms : 172 ( 27 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 135 ( 57 ~; 53 |; 15 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 134 ( 4 sgn 51 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/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(f31,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f31_nnf,plain,
op_or,
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c60,plain,
op_or,
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(p84,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c55,c60]) ).
fof(f28,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox2/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(f32,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f32_nnf,plain,
op_implies_and,
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c61,plain,
op_implies_and,
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(p80,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c57,c61]) ).
cnf(p87,plain,
implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[p84,p80]) ).
fof(f17,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3) ).
fof(f17_nnf,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| kn3 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(sk35,sk36),implies(not(and(sk36,sk37)),not(and(sk37,sk35)))))
| kn3 )
& ( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk35,sk36,sk37])],[f17_nnf]) ).
cnf(c37,plain,
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p90,plain,
( is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))
| ~ kn3 ),
inference(demodulation,[status(thm)],[p87,c37]) ).
fof(f37,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f37_nnf,plain,
kn3,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
kn3,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(p457,plain,
is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(resolution,[status(thm)],[p90,c66]) ).
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rosser_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(p72,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c0,c63]) ).
fof(f15,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f15_nnf,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [P] :
( ( ~ is_a_theorem(implies(sk32,and(sk32,sk32)))
| kn1 )
& ( is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk32])],[f15_nnf]) ).
cnf(c33,plain,
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f35,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f35_nnf,plain,
kn1,
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c64,plain,
kn1,
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(p74,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[c33,c64]) ).
cnf(p78,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,and(X0,X0)),X1)) ),
inference(resolution,[status(thm)],[p72,p74]) ).
cnf(p3668,plain,
is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[p457,p78]) ).
fof(f29,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/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(f39,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f39_nnf,plain,
op_implies_or,
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c68,plain,
op_implies_or,
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(p77,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c58,c68]) ).
cnf(p101,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[p77,p87]) ).
fof(f27,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox2/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(p102,plain,
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(demodulation,[status(thm)],[p101,c56]) ).
fof(f40,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f40_nnf,plain,
op_and,
inference(nnf_transformation,[status(thm)],[f40]) ).
cnf(c69,plain,
op_and,
inference(cnf_transformation,[status(esa)],[f40_nnf]) ).
cnf(p152,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(resolution,[status(thm)],[p102,c69]) ).
cnf(p163,plain,
or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[p152,p101]) ).
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(p75,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c35,c65]) ).
cnf(p79,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(and(X0,X1),X0),X2)) ),
inference(resolution,[status(thm)],[p72,p75]) ).
cnf(p732,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(or(and(and(not(X0),X1),X0),X2)) ),
inference(superposition,[status(thm)],[p163,p79]) ).
cnf(p3741,plain,
is_a_theorem(not(and(X0,not(X0)))),
inference(resolution,[status(thm)],[p3668,p732]) ).
cnf(p3761,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[p3741,p72]) ).
cnf(p4006,plain,
is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[p3761,p457]) ).
cnf(p4127,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(superposition,[status(thm)],[p84,p4006]) ).
cnf(p159,plain,
and(not(X0),X1) = not(or(X0,not(X1))),
inference(superposition,[status(thm)],[p87,p152]) ).
cnf(p181,plain,
or(and(not(X0),X1),X2) = implies(or(X0,not(X1)),X2),
inference(superposition,[status(thm)],[p159,p101]) ).
cnf(p95,plain,
implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[p84,p80]) ).
cnf(p493,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X0),or(X0,X0)),X1)) ),
inference(superposition,[status(thm)],[p95,p78]) ).
cnf(p2207,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X0,not(or(X0,X0))),X1)) ),
inference(superposition,[status(thm)],[p181,p493]) ).
cnf(p4166,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[p4127,p2207]) ).
fof(f21,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/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(c46,plain,
( ~ is_a_theorem(implies(or(sk44,sk44),sk44))
| r1 ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p4203,plain,
r1,
inference(resolution,[status(thm)],[p4166,c46]) ).
fof(f42,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f42_neg,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ r1,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ r1,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ r1,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p4212,plain,
$false,
inference(resolution,[status(thm)],[p4203,c71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n002.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 : Wed Sep 23 23:40:33 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.66/11.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.66/11.51 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------