%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL509+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 158.58s 23.31s
% Output : Proof 158.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 15
% Syntax : Number of formulae : 190 ( 162 unt; 0 def)
% Number of atoms : 250 ( 146 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 103 ( 43 ~; 37 |; 15 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 321 ( 44 sgn 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f9_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk19,or(sk19,sk20)))
| or_1 )
& ( is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20])],[f9_nnf]) ).
cnf(c22,plain,
( ~ is_a_theorem(implies(sk19,or(sk19,sk20)))
| or_1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t35,plain,
ifeq(is_a_theorem(implies(sk19,or(sk19,sk20))),true,or_1,true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t2403,plain,
ifeq(is_a_theorem(implies(sk19,or(sk19,sk20))),true,or_1,true) = true,
inference(orient,[status(thm)],[t35]) ).
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]) ).
cnf(t85,plain,
ifeq(modus_ponens,true,ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t2411,plain,
ifeq(modus_ponens,true,ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true),true) = true,
inference(orient,[status(thm)],[t85]) ).
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(t5,plain,
true = modus_ponens,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t2678,plain,
modus_ponens = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t51532,plain,
ifeq(true,true,ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true),true) = true,
inference(step,[status(thm)],[t2411,t2678]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t183,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t51533,plain,
ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true) = true,
inference(step,[status(thm)],[t51532,t183]) ).
cnf(t2680,plain,
ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true) = true,
inference(rw,[status(thm)],[t51533]) ).
cnf(t8511,plain,
ifeq(is_a_theorem(X1),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t2680]) ).
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]) ).
cnf(hi35,axiom,
ifeq(kn2,true,is_a_theorem(implies(and(X0,X1),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
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(hi65,axiom,
kn2 = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t22,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi35,hi65]) ).
cnf(t2006,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t8554,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t8511,t2006]) ).
cnf(t51572,plain,
true = ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t8554,t183]) ).
cnf(t9237,plain,
ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t51572]) ).
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(hi37,axiom,
ifeq(kn3,true,is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),true) = true,
inference(equality_encoding,[status(esa)],[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(hi66,axiom,
kn3 = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(V0,V1),implies(not(and(V1,V2)),not(and(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi66]) ).
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]) ).
cnf(hi33,axiom,
ifeq(kn1,true,is_a_theorem(implies(X0,and(X0,X0))),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
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(hi64,axiom,
kn1 = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h3,plain,
is_a_theorem(implies(V0,and(V0,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi64]) ).
cnf(hi0,axiom,
ifeq(modus_ponens,true,ifeq(is_a_theorem(X0),true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(hi63,axiom,
modus_ponens = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t62,plain,
is_a_theorem(implies(not(and(and(X1,X1),X2)),not(and(X2,X1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h3,h5]) ).
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]) ).
cnf(hi55,axiom,
ifeq(op_or,true,or(X0,X1),not(and(not(X0),not(X1)))) = not(and(not(X0),not(X1))),
inference(equality_encoding,[status(esa)],[c55]) ).
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(hi60,axiom,
op_or = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t26,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(hyper_resolution,[status(thm)],[hi55,hi60]) ).
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]) ).
cnf(hi57,axiom,
ifeq(op_implies_and,true,implies(X0,X1),not(and(X0,not(X1)))) = not(and(X0,not(X1))),
inference(equality_encoding,[status(esa)],[c57]) ).
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(hi61,axiom,
op_implies_and = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(t25,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(hyper_resolution,[status(thm)],[hi57,hi61]) ).
cnf(t190,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t25]) ).
cnf(t50525,plain,
implies(not(X1),X2) = or(X1,X2),
inference(step,[status(thm)],[t26,t190]) ).
cnf(t195,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t50525]) ).
cnf(t51341,plain,
is_a_theorem(or(and(and(X1,X1),X2),not(and(X2,X1)))) = true,
inference(step,[status(thm)],[t62,t195]) ).
cnf(t2011,plain,
is_a_theorem(or(and(and(X1,X1),X2),not(and(X2,X1)))) = true,
inference(orient,[status(thm)],[t51341]) ).
cnf(t196,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(cp,[status(thm)],[t195,t190]) ).
cnf(t2695,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(orient,[status(thm)],[t196]) ).
cnf(t2705,plain,
true = is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))),
inference(cp,[status(thm)],[t2011,t2695]) ).
cnf(t7439,plain,
is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))) = true,
inference(orient,[status(thm)],[t2705]) ).
cnf(t9238,plain,
true = ifeq(true,true,is_a_theorem(not(and(not(X1),X1))),true),
inference(cp,[status(thm)],[t9237,t7439]) ).
cnf(t51574,plain,
true = is_a_theorem(not(and(not(X1),X1))),
inference(step,[status(thm)],[t9238,t183]) ).
cnf(t9364,plain,
is_a_theorem(not(and(not(X1),X1))) = true,
inference(orient,[status(thm)],[t51574]) ).
cnf(t9374,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(not(and(not(X1),X1)),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t8511,t9364]) ).
cnf(t51598,plain,
true = ifeq(is_a_theorem(implies(not(and(not(X1),X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t9374,t183]) ).
cnf(t51599,plain,
true = ifeq(is_a_theorem(or(and(not(X1),X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t51598,t195]) ).
cnf(t10145,plain,
ifeq(is_a_theorem(or(and(not(X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t51599]) ).
cnf(t2013,plain,
true = is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))),
inference(cp,[status(thm)],[t2011,t190]) ).
cnf(t7386,plain,
is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))) = true,
inference(orient,[status(thm)],[t2013]) ).
cnf(t7387,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),implies(not(X2),X1))),
inference(cp,[status(thm)],[t7386,t2695]) ).
cnf(t51555,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))),
inference(step,[status(thm)],[t7387,t195]) ).
cnf(t7462,plain,
is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t51555]) ).
cnf(t9239,plain,
true = ifeq(true,true,is_a_theorem(or(not(X1),X1)),true),
inference(cp,[status(thm)],[t9237,t7462]) ).
cnf(t51573,plain,
true = is_a_theorem(or(not(X1),X1)),
inference(step,[status(thm)],[t9239,t183]) ).
cnf(t9352,plain,
is_a_theorem(or(not(X1),X1)) = true,
inference(orient,[status(thm)],[t51573]) ).
cnf(t9360,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t8511,t9352]) ).
cnf(t51577,plain,
true = ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t9360,t183]) ).
cnf(t9478,plain,
ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t51577]) ).
cnf(t68,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1))))) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi66]) ).
cnf(t51515,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))) = true,
inference(step,[status(thm)],[t68,t195]) ).
cnf(t2381,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))) = true,
inference(orient,[status(thm)],[t51515]) ).
cnf(t2382,plain,
true = is_a_theorem(implies(or(X1,X2),or(and(X2,X3),not(and(X3,not(X1)))))),
inference(cp,[status(thm)],[t2381,t195]) ).
cnf(t51554,plain,
true = is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(step,[status(thm)],[t2382,t190]) ).
cnf(t7401,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))) = true,
inference(orient,[status(thm)],[t51554]) ).
cnf(t7404,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),implies(not(X3),X1)))),
inference(cp,[status(thm)],[t7401,t2695]) ).
cnf(t51556,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(step,[status(thm)],[t7404,t195]) ).
cnf(t7471,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))) = true,
inference(orient,[status(thm)],[t51556]) ).
cnf(t9481,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),true),
inference(cp,[status(thm)],[t9478,t7471]) ).
cnf(t51579,plain,
true = is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(step,[status(thm)],[t9481,t183]) ).
cnf(t9622,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))) = true,
inference(orient,[status(thm)],[t51579]) ).
cnf(t9642,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(and(X1,X2)))),true),
inference(cp,[status(thm)],[t9237,t9622]) ).
cnf(t51580,plain,
true = is_a_theorem(or(X1,not(and(X1,X2)))),
inference(step,[status(thm)],[t9642,t183]) ).
cnf(t9646,plain,
is_a_theorem(or(X1,not(and(X1,X2)))) = true,
inference(orient,[status(thm)],[t51580]) ).
cnf(t9650,plain,
true = is_a_theorem(or(X1,implies(X1,X2))),
inference(cp,[status(thm)],[t9646,t190]) ).
cnf(t9665,plain,
is_a_theorem(or(X1,implies(X1,X2))) = true,
inference(orient,[status(thm)],[t9650]) ).
cnf(t9677,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t8511,t9665]) ).
cnf(t51780,plain,
true = ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t9677,t183]) ).
cnf(t13354,plain,
ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t51780]) ).
cnf(t13359,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),true),
inference(cp,[status(thm)],[t13354,t7471]) ).
cnf(t51787,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(step,[status(thm)],[t13359,t183]) ).
cnf(t13510,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))) = true,
inference(orient,[status(thm)],[t51787]) ).
cnf(t13527,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,ifeq(true,true,is_a_theorem(or(X3,X1)),true),true),
inference(cp,[status(thm)],[t8511,t13510]) ).
cnf(t52118,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true),
inference(step,[status(thm)],[t13527,t183]) ).
cnf(t18645,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true) = true,
inference(orient,[status(thm)],[t52118]) ).
cnf(t21,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi64]) ).
cnf(t2003,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t8553,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t8511,t2003]) ).
cnf(t51567,plain,
true = ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t8553,t183]) ).
cnf(t9052,plain,
ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t51567]) ).
cnf(t9644,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,X1),not(X1))),true),
inference(cp,[status(thm)],[t9052,t9622]) ).
cnf(t51581,plain,
true = is_a_theorem(or(and(X1,X1),not(X1))),
inference(step,[status(thm)],[t9644,t183]) ).
cnf(t9684,plain,
is_a_theorem(or(and(X1,X1),not(X1))) = true,
inference(orient,[status(thm)],[t51581]) ).
cnf(t9685,plain,
true = is_a_theorem(implies(implies(not(X1),X1),not(not(X1)))),
inference(cp,[status(thm)],[t9684,t2695]) ).
cnf(t51582,plain,
true = is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(step,[status(thm)],[t9685,t195]) ).
cnf(t9713,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))) = true,
inference(orient,[status(thm)],[t51582]) ).
cnf(t9722,plain,
true = ifeq(is_a_theorem(or(X1,X1)),true,ifeq(true,true,is_a_theorem(not(not(X1))),true),true),
inference(cp,[status(thm)],[t8511,t9713]) ).
cnf(t51595,plain,
true = ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true),
inference(step,[status(thm)],[t9722,t183]) ).
cnf(t10024,plain,
ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true) = true,
inference(orient,[status(thm)],[t51595]) ).
cnf(t13521,plain,
true = is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))),
inference(cp,[status(thm)],[t13510,t195]) ).
cnf(t14026,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))) = true,
inference(orient,[status(thm)],[t13521]) ).
cnf(t18665,plain,
true = ifeq(true,true,is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),true),
inference(cp,[status(thm)],[t18645,t14026]) ).
cnf(t52130,plain,
true = is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),
inference(step,[status(thm)],[t18665,t183]) ).
cnf(t18796,plain,
is_a_theorem(or(or(X1,not(X2)),or(X2,X3))) = true,
inference(orient,[status(thm)],[t52130]) ).
cnf(t18804,plain,
true = ifeq(true,true,is_a_theorem(not(not(or(X1,not(X1))))),true),
inference(cp,[status(thm)],[t10024,t18796]) ).
cnf(t52131,plain,
true = is_a_theorem(not(not(or(X1,not(X1))))),
inference(step,[status(thm)],[t18804,t183]) ).
cnf(t18807,plain,
is_a_theorem(not(not(or(X1,not(X1))))) = true,
inference(orient,[status(thm)],[t52131]) ).
cnf(t18816,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(not(not(or(X1,not(X1)))),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t8511,t18807]) ).
cnf(t52576,plain,
true = ifeq(is_a_theorem(implies(not(not(or(X1,not(X1)))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t18816,t183]) ).
cnf(t52577,plain,
true = ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t52576,t195]) ).
cnf(t26670,plain,
ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t52577]) ).
cnf(t26673,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(X1))),true),
inference(cp,[status(thm)],[t26670,t9352]) ).
cnf(t52601,plain,
true = is_a_theorem(or(X1,not(X1))),
inference(step,[status(thm)],[t26673,t183]) ).
cnf(t26909,plain,
is_a_theorem(or(X1,not(X1))) = true,
inference(orient,[status(thm)],[t52601]) ).
cnf(t26910,plain,
true = is_a_theorem(implies(implies(X1,X2),not(and(X1,not(X2))))),
inference(cp,[status(thm)],[t26909,t2695]) ).
cnf(t52609,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X1,X2))),
inference(step,[status(thm)],[t26910,t190]) ).
cnf(t26978,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,X2))) = true,
inference(orient,[status(thm)],[t52609]) ).
cnf(t26991,plain,
true = ifeq(true,true,is_a_theorem(or(implies(X1,X2),X1)),true),
inference(cp,[status(thm)],[t18645,t26978]) ).
cnf(t52610,plain,
true = is_a_theorem(or(implies(X1,X2),X1)),
inference(step,[status(thm)],[t26991,t183]) ).
cnf(t26994,plain,
is_a_theorem(or(implies(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t52610]) ).
cnf(t27004,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(or(implies(X1,X2),X1),X3)),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t8511,t26994]) ).
cnf(t54174,plain,
true = ifeq(is_a_theorem(implies(or(implies(X1,X2),X1),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t27004,t183]) ).
cnf(t50175,plain,
ifeq(is_a_theorem(implies(or(implies(X1,X2),X1),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t54174]) ).
cnf(t50189,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),true),
inference(cp,[status(thm)],[t50175,t7401]) ).
cnf(t54186,plain,
true = is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),
inference(step,[status(thm)],[t50189,t183]) ).
cnf(t50477,plain,
is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t54186]) ).
cnf(t50500,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(X1),X2))),true),
inference(cp,[status(thm)],[t10145,t50477]) ).
cnf(t54187,plain,
true = is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(step,[status(thm)],[t50500,t183]) ).
cnf(t54188,plain,
true = is_a_theorem(implies(X1,or(X1,X2))),
inference(step,[status(thm)],[t54187,t195]) ).
cnf(t50501,plain,
is_a_theorem(implies(X1,or(X1,X2))) = true,
inference(orient,[status(thm)],[t54188]) ).
cnf(t54191,plain,
ifeq(true,true,or_1,true) = true,
inference(step,[status(thm)],[t2403,t50501]) ).
cnf(t54192,plain,
or_1 = true,
inference(step,[status(thm)],[t54191,t183]) ).
cnf(t50512,plain,
or_1 = true,
inference(rw,[status(thm)],[t54192]) ).
cnf(t50514,plain,
or_1 = true,
inference(orient,[status(thm)],[t50512]) ).
fof(f42,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f42_neg,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ or_1,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ or_1,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ or_1,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
true != or_1,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t50514]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL509+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:38:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 158.58/23.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.58/23.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------