%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL517+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 : 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 02:02:12 PM UTC 2026
% Result : Theorem 56.18s 7.75s
% Output : Proof 56.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 15
% Syntax : Number of formulae : 191 ( 163 unt; 0 def)
% Number of atoms : 251 ( 147 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 : 295 ( 31 sgn 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f42_neg,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ cn3,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ cn3,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ cn3,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t0,plain,
false = cn3,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t1148,plain,
cn3 = false,
inference(orient,[status(thm)],[t0]) ).
fof(f20,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f20_nnf,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [P] :
( ( ~ is_a_theorem(implies(implies(not(sk43),sk43),sk43))
| cn3 )
& ( is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk43])],[f20_nnf]) ).
cnf(c44,plain,
( ~ is_a_theorem(implies(implies(not(sk43),sk43),sk43))
| cn3 ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t48,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,cn3,true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
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(t138,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t25]) ).
cnf(t24067,plain,
implies(not(X1),X2) = or(X1,X2),
inference(step,[status(thm)],[t26,t138]) ).
cnf(t143,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t24067]) ).
cnf(t24380,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,cn3,true) = true,
inference(step,[status(thm)],[t48,t143]) ).
cnf(t958,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,cn3,true) = true,
inference(orient,[status(thm)],[t24380]) ).
cnf(t24395,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,false,true) = true,
inference(step,[status(thm)],[t958,t1148]) ).
cnf(t1150,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,false,true) = true,
inference(rw,[status(thm)],[t24395]) ).
cnf(t2425,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,false,true) = true,
inference(orient,[status(thm)],[t1150]) ).
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(t980,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(t1143,plain,
modus_ponens = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t24392,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)],[t980,t1143]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t131,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t24393,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)],[t24392,t131]) ).
cnf(t1145,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)],[t24393]) ).
cnf(t4169,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)],[t1145]) ).
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(t21,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi64]) ).
cnf(t894,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t4197,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)],[t4169,t894]) ).
cnf(t24421,plain,
true = ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t4197,t131]) ).
cnf(t4536,plain,
ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t24421]) ).
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(t897,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t4198,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)],[t4169,t897]) ).
cnf(t24426,plain,
true = ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t4198,t131]) ).
cnf(t4686,plain,
ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t24426]) ).
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(h8,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]) ).
cnf(h2,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,h2,h8]) ).
cnf(t24355,plain,
is_a_theorem(or(and(and(X1,X1),X2),not(and(X2,X1)))) = true,
inference(step,[status(thm)],[t62,t143]) ).
cnf(t902,plain,
is_a_theorem(or(and(and(X1,X1),X2),not(and(X2,X1)))) = true,
inference(orient,[status(thm)],[t24355]) ).
cnf(t904,plain,
true = is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))),
inference(cp,[status(thm)],[t902,t138]) ).
cnf(t3519,plain,
is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))) = true,
inference(orient,[status(thm)],[t904]) ).
cnf(t144,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(cp,[status(thm)],[t143,t138]) ).
cnf(t1159,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(orient,[status(thm)],[t144]) ).
cnf(t3520,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),implies(not(X2),X1))),
inference(cp,[status(thm)],[t3519,t1159]) ).
cnf(t24409,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))),
inference(step,[status(thm)],[t3520,t143]) ).
cnf(t3595,plain,
is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t24409]) ).
cnf(t4688,plain,
true = ifeq(true,true,is_a_theorem(or(not(X1),X1)),true),
inference(cp,[status(thm)],[t4686,t3595]) ).
cnf(t24427,plain,
true = is_a_theorem(or(not(X1),X1)),
inference(step,[status(thm)],[t4688,t131]) ).
cnf(t4766,plain,
is_a_theorem(or(not(X1),X1)) = true,
inference(orient,[status(thm)],[t24427]) ).
cnf(t4774,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)],[t4169,t4766]) ).
cnf(t24431,plain,
true = ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t4774,t131]) ).
cnf(t4892,plain,
ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t24431]) ).
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(t24375,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))) = true,
inference(step,[status(thm)],[t68,t143]) ).
cnf(t950,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))) = true,
inference(orient,[status(thm)],[t24375]) ).
cnf(t951,plain,
true = is_a_theorem(implies(or(X1,X2),or(and(X2,X3),not(and(X3,not(X1)))))),
inference(cp,[status(thm)],[t950,t143]) ).
cnf(t24408,plain,
true = is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(step,[status(thm)],[t951,t138]) ).
cnf(t3534,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))) = true,
inference(orient,[status(thm)],[t24408]) ).
cnf(t3537,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),implies(not(X3),X1)))),
inference(cp,[status(thm)],[t3534,t1159]) ).
cnf(t24410,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(step,[status(thm)],[t3537,t143]) ).
cnf(t3604,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))) = true,
inference(orient,[status(thm)],[t24410]) ).
cnf(t4895,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),true),
inference(cp,[status(thm)],[t4892,t3604]) ).
cnf(t24433,plain,
true = is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(step,[status(thm)],[t4895,t131]) ).
cnf(t5001,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))) = true,
inference(orient,[status(thm)],[t24433]) ).
cnf(t5023,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,X1),not(X1))),true),
inference(cp,[status(thm)],[t4536,t5001]) ).
cnf(t24435,plain,
true = is_a_theorem(or(and(X1,X1),not(X1))),
inference(step,[status(thm)],[t5023,t131]) ).
cnf(t5063,plain,
is_a_theorem(or(and(X1,X1),not(X1))) = true,
inference(orient,[status(thm)],[t24435]) ).
cnf(t5064,plain,
true = is_a_theorem(implies(implies(not(X1),X1),not(not(X1)))),
inference(cp,[status(thm)],[t5063,t1159]) ).
cnf(t24436,plain,
true = is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(step,[status(thm)],[t5064,t143]) ).
cnf(t5092,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))) = true,
inference(orient,[status(thm)],[t24436]) ).
cnf(t5101,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)],[t4169,t5092]) ).
cnf(t24449,plain,
true = ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true),
inference(step,[status(thm)],[t5101,t131]) ).
cnf(t5403,plain,
ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true) = true,
inference(orient,[status(thm)],[t24449]) ).
cnf(t5021,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(and(X1,X2)))),true),
inference(cp,[status(thm)],[t4686,t5001]) ).
cnf(t24434,plain,
true = is_a_theorem(or(X1,not(and(X1,X2)))),
inference(step,[status(thm)],[t5021,t131]) ).
cnf(t5025,plain,
is_a_theorem(or(X1,not(and(X1,X2)))) = true,
inference(orient,[status(thm)],[t24434]) ).
cnf(t5029,plain,
true = is_a_theorem(or(X1,implies(X1,X2))),
inference(cp,[status(thm)],[t5025,t138]) ).
cnf(t5044,plain,
is_a_theorem(or(X1,implies(X1,X2))) = true,
inference(orient,[status(thm)],[t5029]) ).
cnf(t5056,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)],[t4169,t5044]) ).
cnf(t24634,plain,
true = ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t5056,t131]) ).
cnf(t8628,plain,
ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t24634]) ).
cnf(t8633,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),true),
inference(cp,[status(thm)],[t8628,t3604]) ).
cnf(t24641,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(step,[status(thm)],[t8633,t131]) ).
cnf(t8756,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))) = true,
inference(orient,[status(thm)],[t24641]) ).
cnf(t8773,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)],[t4169,t8756]) ).
cnf(t24972,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true),
inference(step,[status(thm)],[t8773,t131]) ).
cnf(t13765,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true) = true,
inference(orient,[status(thm)],[t24972]) ).
cnf(t8767,plain,
true = is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))),
inference(cp,[status(thm)],[t8756,t143]) ).
cnf(t9272,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))) = true,
inference(orient,[status(thm)],[t8767]) ).
cnf(t13785,plain,
true = ifeq(true,true,is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),true),
inference(cp,[status(thm)],[t13765,t9272]) ).
cnf(t24984,plain,
true = is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),
inference(step,[status(thm)],[t13785,t131]) ).
cnf(t13911,plain,
is_a_theorem(or(or(X1,not(X2)),or(X2,X3))) = true,
inference(orient,[status(thm)],[t24984]) ).
cnf(t13919,plain,
true = ifeq(true,true,is_a_theorem(not(not(or(X1,not(X1))))),true),
inference(cp,[status(thm)],[t5403,t13911]) ).
cnf(t24985,plain,
true = is_a_theorem(not(not(or(X1,not(X1))))),
inference(step,[status(thm)],[t13919,t131]) ).
cnf(t13922,plain,
is_a_theorem(not(not(or(X1,not(X1))))) = true,
inference(orient,[status(thm)],[t24985]) ).
cnf(t13931,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)],[t4169,t13922]) ).
cnf(t25430,plain,
true = ifeq(is_a_theorem(implies(not(not(or(X1,not(X1)))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t13931,t131]) ).
cnf(t25431,plain,
true = ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t25430,t143]) ).
cnf(t21717,plain,
ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t25431]) ).
cnf(t21720,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(X1))),true),
inference(cp,[status(thm)],[t21717,t4766]) ).
cnf(t25455,plain,
true = is_a_theorem(or(X1,not(X1))),
inference(step,[status(thm)],[t21720,t131]) ).
cnf(t21928,plain,
is_a_theorem(or(X1,not(X1))) = true,
inference(orient,[status(thm)],[t25455]) ).
cnf(t21937,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(or(X1,not(X1)),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t4169,t21928]) ).
cnf(t25566,plain,
true = ifeq(is_a_theorem(implies(or(X1,not(X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t21937,t131]) ).
cnf(t23381,plain,
ifeq(is_a_theorem(implies(or(X1,not(X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t25566]) ).
cnf(t3611,plain,
true = is_a_theorem(implies(or(X1,not(X2)),implies(or(X2,X3),or(X3,X1)))),
inference(cp,[status(thm)],[t3604,t143]) ).
cnf(t3712,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(or(X2,X3),or(X3,X1)))) = true,
inference(orient,[status(thm)],[t3611]) ).
cnf(t23382,plain,
true = ifeq(true,true,is_a_theorem(implies(or(X1,X2),or(X2,X1))),true),
inference(cp,[status(thm)],[t23381,t3712]) ).
cnf(t25567,plain,
true = is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(step,[status(thm)],[t23382,t131]) ).
cnf(t23441,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t25567]) ).
cnf(t23451,plain,
true = ifeq(is_a_theorem(or(X1,X2)),true,ifeq(true,true,is_a_theorem(or(X2,X1)),true),true),
inference(cp,[status(thm)],[t4169,t23441]) ).
cnf(t25604,plain,
true = ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true),
inference(step,[status(thm)],[t23451,t131]) ).
cnf(t23772,plain,
ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true) = true,
inference(orient,[status(thm)],[t25604]) ).
cnf(t895,plain,
true = is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(cp,[status(thm)],[t894,t143]) ).
cnf(t1364,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))) = true,
inference(orient,[status(thm)],[t895]) ).
cnf(t23806,plain,
true = ifeq(true,true,is_a_theorem(or(and(not(X1),not(X1)),X1)),true),
inference(cp,[status(thm)],[t23772,t1364]) ).
cnf(t25605,plain,
true = is_a_theorem(or(and(not(X1),not(X1)),X1)),
inference(step,[status(thm)],[t23806,t131]) ).
cnf(t25606,plain,
true = is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(step,[status(thm)],[t25605,t1159]) ).
cnf(t25607,plain,
true = is_a_theorem(implies(or(X1,X1),X1)),
inference(step,[status(thm)],[t25606,t143]) ).
cnf(t24044,plain,
is_a_theorem(implies(or(X1,X1),X1)) = true,
inference(orient,[status(thm)],[t25607]) ).
cnf(t25608,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t2425,t24044]) ).
cnf(t25609,plain,
false = true,
inference(step,[status(thm)],[t25608,t131]) ).
cnf(t24054,plain,
false = true,
inference(rw,[status(thm)],[t25609]) ).
cnf(t24056,plain,
false = true,
inference(orient,[status(thm)],[t24054]) ).
cnf(t25612,plain,
cn3 = true,
inference(step,[status(thm)],[t1148,t24056]) ).
cnf(t24057,plain,
cn3 = true,
inference(orient,[status(thm)],[t25612]) ).
cnf(goal_0,negated_conjecture,
true != cn3,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t24057]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL517+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n013.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 23:37:21 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 56.18/7.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.18/7.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------