%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL487+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 02:02:09 PM UTC 2026
% Result : Theorem 182.00s 27.11s
% Output : Proof 182.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 19
% Syntax : Number of formulae : 149 ( 113 unt; 0 def)
% Number of atoms : 217 ( 99 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 117 ( 49 ~; 43 |; 15 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-4 aty)
% Number of variables : 215 ( 20 sgn 57 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f44_neg,negated_conjecture,
~ and_1,
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
~ and_1,
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
~ and_1,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c73,plain,
~ and_1,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(t0,plain,
false = and_1,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t1231,plain,
and_1 = false,
inference(orient,[status(thm)],[t0]) ).
fof(f6,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f6_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(and(sk13,sk14),sk13))
| and_1 )
& ( is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f6_nnf]) ).
cnf(c16,plain,
( ~ is_a_theorem(implies(and(sk13,sk14),sk13))
| and_1 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t40,plain,
ifeq(is_a_theorem(implies(and(sk13,sk14),sk13)),true,and_1,true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t872,plain,
ifeq(is_a_theorem(implies(and(sk13,sk14),sk13)),true,and_1,true) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t553977,plain,
ifeq(is_a_theorem(implies(and(sk13,sk14),sk13)),true,false,true) = true,
inference(step,[status(thm)],[t872,t1231]) ).
cnf(t1233,plain,
ifeq(is_a_theorem(implies(and(sk13,sk14),sk13)),true,false,true) = true,
inference(rw,[status(thm)],[t553977]) ).
cnf(t4361,plain,
ifeq(is_a_theorem(implies(and(sk13,sk14),sk13)),true,false,true) = true,
inference(orient,[status(thm)],[t1233]) ).
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f0_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(sk1)
& is_a_theorem(implies(sk0,sk1))
& is_a_theorem(sk0) )
| modus_ponens )
& ( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| ~ modus_ponens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t195,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(t885,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)],[t195]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f34_nnf,plain,
modus_ponens,
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c63,plain,
modus_ponens,
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(t1,plain,
true = modus_ponens,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t1227,plain,
modus_ponens = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t553974,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)],[t885,t1227]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t216,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t553975,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)],[t553974,t216]) ).
cnf(t1229,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)],[t553975]) ).
cnf(t197683,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)],[t1229]) ).
fof(f23,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f23_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(sk47,sk48),or(sk48,sk47)))
| r3 )
& ( is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48])],[f23_nnf]) ).
cnf(c49,plain,
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi49,axiom,
ifeq(r3,true,is_a_theorem(implies(or(X0,X1),or(X1,X0))),true) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
fof(f37,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f37_nnf,plain,
r3,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
r3,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(hi66,axiom,
r3 = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t29,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi66]) ).
cnf(t752,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t198748,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)],[t197683,t752]) ).
cnf(t554582,plain,
true = ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true),
inference(step,[status(thm)],[t198748,t216]) ).
cnf(t206532,plain,
ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true) = true,
inference(orient,[status(thm)],[t554582]) ).
fof(f22,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f22_nnf,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Q,P] :
( ( ~ is_a_theorem(implies(sk46,or(sk45,sk46)))
| r2 )
& ( is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk45,sk46])],[f22_nnf]) ).
cnf(c47,plain,
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi47,axiom,
ifeq(r2,true,is_a_theorem(implies(X0,or(X1,X0))),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
fof(f36,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f36_nnf,plain,
r2,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
r2,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(hi65,axiom,
r2 = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t23,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi47,hi65]) ).
cnf(t750,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t198274,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,or(X2,X1)),X3)),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t197683,t750]) ).
cnf(t556203,plain,
true = ifeq(is_a_theorem(implies(implies(X1,or(X2,X1)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t198274,t216]) ).
cnf(t551122,plain,
ifeq(is_a_theorem(implies(implies(X1,or(X2,X1)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t556203]) ).
fof(f25,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
fof(f25_nnf,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Q,R,P] :
( ( ~ is_a_theorem(implies(implies(sk53,sk54),implies(or(sk52,sk53),or(sk52,sk54))))
| r5 )
& ( is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk52,sk53,sk54])],[f25_nnf]) ).
cnf(c53,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi53,axiom,
ifeq(r5,true,is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
fof(f39,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f39_nnf,plain,
r5,
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c68,plain,
r5,
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(hi68,axiom,
r5 = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h14,plain,
is_a_theorem(implies(implies(V0,V1),implies(or(V2,V0),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi68]) ).
cnf(h4,plain,
is_a_theorem(implies(or(V0,V1),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi66]) ).
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(t81,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X1,or(X3,X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h4,h14]) ).
cnf(t766,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X1,or(X3,X2)))) = true,
inference(orient,[status(thm)],[t81]) ).
fof(f29,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f29_nnf,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y] :
( implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c58,plain,
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi58,axiom,
ifeq(op_implies_or,true,implies(X0,X1),or(not(X0),X1)) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c58]) ).
fof(f31,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f31_nnf,plain,
op_implies_or,
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c60,plain,
op_implies_or,
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi60,axiom,
op_implies_or = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t25,plain,
or(not(X1),X2) = implies(X1,X2),
inference(hyper_resolution,[status(thm)],[hi58,hi60]) ).
cnf(t223,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t25]) ).
cnf(t767,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X3)),or(not(X1),or(X3,X2)))),
inference(cp,[status(thm)],[t766,t223]) ).
cnf(t554178,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X3)),implies(X1,or(X3,X2)))),
inference(step,[status(thm)],[t767,t223]) ).
cnf(t33252,plain,
is_a_theorem(implies(implies(X1,or(X2,X3)),implies(X1,or(X3,X2)))) = true,
inference(orient,[status(thm)],[t554178]) ).
cnf(t551124,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,or(X1,X2))),true),
inference(cp,[status(thm)],[t551122,t33252]) ).
cnf(t556322,plain,
true = is_a_theorem(implies(X1,or(X1,X2))),
inference(step,[status(thm)],[t551124,t216]) ).
cnf(t553416,plain,
is_a_theorem(implies(X1,or(X1,X2))) = true,
inference(orient,[status(thm)],[t556322]) ).
fof(f26,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f26_nnf,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c55,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
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(f41,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41_nnf,plain,
op_or,
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c70,plain,
op_or,
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi70,axiom,
op_or = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(t34,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(hyper_resolution,[status(thm)],[hi55,hi70]) ).
cnf(t220,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(orient,[status(thm)],[t34]) ).
fof(f28,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f28_nnf,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c57,plain,
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
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(f42,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42_nnf,plain,
op_implies_and,
inference(nnf_transformation,[status(thm)],[f42]) ).
cnf(c71,plain,
op_implies_and,
inference(cnf_transformation,[status(esa)],[f42_nnf]) ).
cnf(hi71,axiom,
op_implies_and = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t28,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(hyper_resolution,[status(thm)],[hi57,hi71]) ).
cnf(t226,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t553949,plain,
implies(not(X1),X2) = or(X1,X2),
inference(step,[status(thm)],[t220,t226]) ).
cnf(t229,plain,
implies(not(X1),X2) = or(X1,X2),
inference(rw,[status(thm)],[t553949]) ).
cnf(t1242,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t229]) ).
cnf(t553462,plain,
true = is_a_theorem(or(X1,or(not(X1),X2))),
inference(cp,[status(thm)],[t553416,t1242]) ).
cnf(t556339,plain,
true = is_a_theorem(or(X1,implies(X1,X2))),
inference(step,[status(thm)],[t553462,t223]) ).
cnf(t553731,plain,
is_a_theorem(or(X1,implies(X1,X2))) = true,
inference(orient,[status(thm)],[t556339]) ).
cnf(t553773,plain,
true = ifeq(true,true,is_a_theorem(or(implies(X1,X2),X1)),true),
inference(cp,[status(thm)],[t206532,t553731]) ).
cnf(t556341,plain,
true = is_a_theorem(or(implies(X1,X2),X1)),
inference(step,[status(thm)],[t553773,t216]) ).
cnf(t553794,plain,
is_a_theorem(or(implies(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t556341]) ).
fof(f27,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f27_nnf,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y] :
( and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c56,plain,
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi56,axiom,
ifeq(op_and,true,and(X0,X1),not(or(not(X0),not(X1)))) = not(or(not(X0),not(X1))),
inference(equality_encoding,[status(esa)],[c56]) ).
fof(f32,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f32_nnf,plain,
op_and,
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c61,plain,
op_and,
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi61,axiom,
op_and = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(t35,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(hyper_resolution,[status(thm)],[hi56,hi61]) ).
cnf(t553968,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(step,[status(thm)],[t35,t223]) ).
cnf(t1202,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t553968]) ).
cnf(t1244,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(cp,[status(thm)],[t1242,t1202]) ).
cnf(t1974,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(orient,[status(thm)],[t1244]) ).
cnf(t553799,plain,
true = is_a_theorem(implies(and(X1,X2),X1)),
inference(cp,[status(thm)],[t553794,t1974]) ).
cnf(t553865,plain,
is_a_theorem(implies(and(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t553799]) ).
cnf(t556342,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t4361,t553865]) ).
cnf(t556343,plain,
false = true,
inference(step,[status(thm)],[t556342,t216]) ).
cnf(t553937,plain,
false = true,
inference(rw,[status(thm)],[t556343]) ).
cnf(t553939,plain,
false = true,
inference(orient,[status(thm)],[t553937]) ).
cnf(t556346,plain,
and_1 = true,
inference(step,[status(thm)],[t1231,t553939]) ).
cnf(t553940,plain,
and_1 = true,
inference(orient,[status(thm)],[t556346]) ).
cnf(goal_0,negated_conjecture,
true != and_1,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t553940]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL487+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 23:33:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 182.00/27.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 182.00/27.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------