%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL516+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 : n017.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 215.52s 31.73s
% Output : Proof 215.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 15
% Syntax : Number of formulae : 198 ( 170 unt; 0 def)
% Number of atoms : 258 ( 154 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 : 17 ( 17 usr; 12 con; 0-4 aty)
% Number of variables : 321 ( 44 sgn 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,conjecture,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn2) ).
fof(f42_neg,negated_conjecture,
~ cn2,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ cn2,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ cn2,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ cn2,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t0,plain,
false = cn2,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t1148,plain,
cn2 = false,
inference(orient,[status(thm)],[t0]) ).
fof(f19,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
fof(f19_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(sk41,implies(not(sk41),sk42)))
| cn2 )
& ( is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk41,sk42])],[f19_nnf]) ).
cnf(c42,plain,
( ~ is_a_theorem(implies(sk41,implies(not(sk41),sk42)))
| cn2 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t49,plain,
ifeq(is_a_theorem(implies(sk41,implies(not(sk41),sk42))),true,cn2,true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
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(t45242,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)],[t45242]) ).
cnf(t45562,plain,
ifeq(is_a_theorem(implies(sk41,or(sk41,sk42))),true,cn2,true) = true,
inference(step,[status(thm)],[t49,t143]) ).
cnf(t976,plain,
ifeq(is_a_theorem(implies(sk41,or(sk41,sk42))),true,cn2,true) = true,
inference(orient,[status(thm)],[t45562]) ).
cnf(t45570,plain,
ifeq(is_a_theorem(implies(sk41,or(sk41,sk42))),true,false,true) = true,
inference(step,[status(thm)],[t976,t1148]) ).
cnf(t1150,plain,
ifeq(is_a_theorem(implies(sk41,or(sk41,sk42))),true,false,true) = true,
inference(rw,[status(thm)],[t45570]) ).
cnf(t2426,plain,
ifeq(is_a_theorem(implies(sk41,or(sk41,sk42))),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(t45567,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(t45568,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)],[t45567,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)],[t45568]) ).
cnf(t4170,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(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(t4199,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)],[t4170,t897]) ).
cnf(t45601,plain,
true = ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t4199,t131]) ).
cnf(t4687,plain,
ifeq(is_a_theorem(implies(implies(and(X1,X2),X1),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t45601]) ).
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]) ).
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(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(t45530,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)],[t45530]) ).
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(t1168,plain,
true = is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))),
inference(cp,[status(thm)],[t902,t1159]) ).
cnf(t3573,plain,
is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))) = true,
inference(orient,[status(thm)],[t1168]) ).
cnf(t4688,plain,
true = ifeq(true,true,is_a_theorem(not(and(not(X1),X1))),true),
inference(cp,[status(thm)],[t4687,t3573]) ).
cnf(t45603,plain,
true = is_a_theorem(not(and(not(X1),X1))),
inference(step,[status(thm)],[t4688,t131]) ).
cnf(t4779,plain,
is_a_theorem(not(and(not(X1),X1))) = true,
inference(orient,[status(thm)],[t45603]) ).
cnf(t4789,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)],[t4170,t4779]) ).
cnf(t45627,plain,
true = ifeq(is_a_theorem(implies(not(and(not(X1),X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t4789,t131]) ).
cnf(t45628,plain,
true = ifeq(is_a_theorem(or(and(not(X1),X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t45627,t143]) ).
cnf(t5525,plain,
ifeq(is_a_theorem(or(and(not(X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t45628]) ).
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(t3520,plain,
is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))) = true,
inference(orient,[status(thm)],[t904]) ).
cnf(t3521,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),implies(not(X2),X1))),
inference(cp,[status(thm)],[t3520,t1159]) ).
cnf(t45584,plain,
true = is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))),
inference(step,[status(thm)],[t3521,t143]) ).
cnf(t3596,plain,
is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t45584]) ).
cnf(t4689,plain,
true = ifeq(true,true,is_a_theorem(or(not(X1),X1)),true),
inference(cp,[status(thm)],[t4687,t3596]) ).
cnf(t45602,plain,
true = is_a_theorem(or(not(X1),X1)),
inference(step,[status(thm)],[t4689,t131]) ).
cnf(t4767,plain,
is_a_theorem(or(not(X1),X1)) = true,
inference(orient,[status(thm)],[t45602]) ).
cnf(t4775,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)],[t4170,t4767]) ).
cnf(t45606,plain,
true = ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t4775,t131]) ).
cnf(t4893,plain,
ifeq(is_a_theorem(implies(or(not(X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t45606]) ).
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(t45550,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)],[t45550]) ).
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(t45583,plain,
true = is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(step,[status(thm)],[t951,t138]) ).
cnf(t3535,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))) = true,
inference(orient,[status(thm)],[t45583]) ).
cnf(t3538,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),implies(not(X3),X1)))),
inference(cp,[status(thm)],[t3535,t1159]) ).
cnf(t45585,plain,
true = is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(step,[status(thm)],[t3538,t143]) ).
cnf(t3605,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))) = true,
inference(orient,[status(thm)],[t45585]) ).
cnf(t4896,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),true),
inference(cp,[status(thm)],[t4893,t3605]) ).
cnf(t45608,plain,
true = is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(step,[status(thm)],[t4896,t131]) ).
cnf(t5002,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))) = true,
inference(orient,[status(thm)],[t45608]) ).
cnf(t5022,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(and(X1,X2)))),true),
inference(cp,[status(thm)],[t4687,t5002]) ).
cnf(t45609,plain,
true = is_a_theorem(or(X1,not(and(X1,X2)))),
inference(step,[status(thm)],[t5022,t131]) ).
cnf(t5026,plain,
is_a_theorem(or(X1,not(and(X1,X2)))) = true,
inference(orient,[status(thm)],[t45609]) ).
cnf(t5030,plain,
true = is_a_theorem(or(X1,implies(X1,X2))),
inference(cp,[status(thm)],[t5026,t138]) ).
cnf(t5045,plain,
is_a_theorem(or(X1,implies(X1,X2))) = true,
inference(orient,[status(thm)],[t5030]) ).
cnf(t5057,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)],[t4170,t5045]) ).
cnf(t45809,plain,
true = ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t5057,t131]) ).
cnf(t8629,plain,
ifeq(is_a_theorem(implies(or(X1,implies(X1,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t45809]) ).
cnf(t8634,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),true),
inference(cp,[status(thm)],[t8629,t3605]) ).
cnf(t45816,plain,
true = is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(step,[status(thm)],[t8634,t131]) ).
cnf(t8757,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))) = true,
inference(orient,[status(thm)],[t45816]) ).
cnf(t8774,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)],[t4170,t8757]) ).
cnf(t46147,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true),
inference(step,[status(thm)],[t8774,t131]) ).
cnf(t13766,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(or(X3,X1)),true) = true,
inference(orient,[status(thm)],[t46147]) ).
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(t4198,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)],[t4170,t894]) ).
cnf(t45596,plain,
true = ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t4198,t131]) ).
cnf(t4537,plain,
ifeq(is_a_theorem(implies(implies(X1,and(X1,X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t45596]) ).
cnf(t5024,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,X1),not(X1))),true),
inference(cp,[status(thm)],[t4537,t5002]) ).
cnf(t45610,plain,
true = is_a_theorem(or(and(X1,X1),not(X1))),
inference(step,[status(thm)],[t5024,t131]) ).
cnf(t5064,plain,
is_a_theorem(or(and(X1,X1),not(X1))) = true,
inference(orient,[status(thm)],[t45610]) ).
cnf(t5065,plain,
true = is_a_theorem(implies(implies(not(X1),X1),not(not(X1)))),
inference(cp,[status(thm)],[t5064,t1159]) ).
cnf(t45611,plain,
true = is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(step,[status(thm)],[t5065,t143]) ).
cnf(t5093,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))) = true,
inference(orient,[status(thm)],[t45611]) ).
cnf(t5102,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)],[t4170,t5093]) ).
cnf(t45624,plain,
true = ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true),
inference(step,[status(thm)],[t5102,t131]) ).
cnf(t5404,plain,
ifeq(is_a_theorem(or(X1,X1)),true,is_a_theorem(not(not(X1))),true) = true,
inference(orient,[status(thm)],[t45624]) ).
cnf(t8768,plain,
true = is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))),
inference(cp,[status(thm)],[t8757,t143]) ).
cnf(t9273,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))) = true,
inference(orient,[status(thm)],[t8768]) ).
cnf(t13786,plain,
true = ifeq(true,true,is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),true),
inference(cp,[status(thm)],[t13766,t9273]) ).
cnf(t46159,plain,
true = is_a_theorem(or(or(X1,not(X2)),or(X2,X3))),
inference(step,[status(thm)],[t13786,t131]) ).
cnf(t13912,plain,
is_a_theorem(or(or(X1,not(X2)),or(X2,X3))) = true,
inference(orient,[status(thm)],[t46159]) ).
cnf(t13920,plain,
true = ifeq(true,true,is_a_theorem(not(not(or(X1,not(X1))))),true),
inference(cp,[status(thm)],[t5404,t13912]) ).
cnf(t46160,plain,
true = is_a_theorem(not(not(or(X1,not(X1))))),
inference(step,[status(thm)],[t13920,t131]) ).
cnf(t13923,plain,
is_a_theorem(not(not(or(X1,not(X1))))) = true,
inference(orient,[status(thm)],[t46160]) ).
cnf(t13932,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)],[t4170,t13923]) ).
cnf(t46605,plain,
true = ifeq(is_a_theorem(implies(not(not(or(X1,not(X1)))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t13932,t131]) ).
cnf(t46606,plain,
true = ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t46605,t143]) ).
cnf(t21718,plain,
ifeq(is_a_theorem(or(not(or(X1,not(X1))),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t46606]) ).
cnf(t21721,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(X1))),true),
inference(cp,[status(thm)],[t21718,t4767]) ).
cnf(t46630,plain,
true = is_a_theorem(or(X1,not(X1))),
inference(step,[status(thm)],[t21721,t131]) ).
cnf(t21929,plain,
is_a_theorem(or(X1,not(X1))) = true,
inference(orient,[status(thm)],[t46630]) ).
cnf(t21930,plain,
true = is_a_theorem(implies(implies(X1,X2),not(and(X1,not(X2))))),
inference(cp,[status(thm)],[t21929,t1159]) ).
cnf(t46638,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(X1,X2))),
inference(step,[status(thm)],[t21930,t138]) ).
cnf(t21998,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,X2))) = true,
inference(orient,[status(thm)],[t46638]) ).
cnf(t22011,plain,
true = ifeq(true,true,is_a_theorem(or(implies(X1,X2),X1)),true),
inference(cp,[status(thm)],[t13766,t21998]) ).
cnf(t46639,plain,
true = is_a_theorem(or(implies(X1,X2),X1)),
inference(step,[status(thm)],[t22011,t131]) ).
cnf(t22014,plain,
is_a_theorem(or(implies(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t46639]) ).
cnf(t22024,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)],[t4170,t22014]) ).
cnf(t48203,plain,
true = ifeq(is_a_theorem(implies(or(implies(X1,X2),X1),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t22024,t131]) ).
cnf(t44921,plain,
ifeq(is_a_theorem(implies(or(implies(X1,X2),X1),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t48203]) ).
cnf(t44935,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),true),
inference(cp,[status(thm)],[t44921,t3535]) ).
cnf(t48215,plain,
true = is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),
inference(step,[status(thm)],[t44935,t131]) ).
cnf(t45195,plain,
is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t48215]) ).
cnf(t45218,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(X1),X2))),true),
inference(cp,[status(thm)],[t5525,t45195]) ).
cnf(t48216,plain,
true = is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(step,[status(thm)],[t45218,t131]) ).
cnf(t48217,plain,
true = is_a_theorem(implies(X1,or(X1,X2))),
inference(step,[status(thm)],[t48216,t143]) ).
cnf(t45219,plain,
is_a_theorem(implies(X1,or(X1,X2))) = true,
inference(orient,[status(thm)],[t48217]) ).
cnf(t48218,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t2426,t45219]) ).
cnf(t48219,plain,
false = true,
inference(step,[status(thm)],[t48218,t131]) ).
cnf(t45229,plain,
false = true,
inference(rw,[status(thm)],[t48219]) ).
cnf(t45231,plain,
false = true,
inference(orient,[status(thm)],[t45229]) ).
cnf(t48222,plain,
cn2 = true,
inference(step,[status(thm)],[t1148,t45231]) ).
cnf(t45232,plain,
cn2 = true,
inference(orient,[status(thm)],[t48222]) ).
cnf(goal_0,negated_conjecture,
true != cn2,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t45232]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL516+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.45 % Computer : n017.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Wed Sep 23 23:33:01 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 215.52/31.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 215.52/31.73 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------