%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL498+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 : n007.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 02:02:11 PM UTC 2026
% Result : Theorem 232.82s 30.99s
% Output : Proof 232.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 23
% Syntax : Number of formulae : 241 ( 197 unt; 0 def)
% Number of atoms : 335 ( 179 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 158 ( 64 ~; 58 |; 23 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 18 con; 0-4 aty)
% Number of variables : 363 ( 12 sgn 66 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f44_neg,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
~ cn3,
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
~ cn3,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c73,plain,
~ cn3,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(t0,plain,
false = cn3,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t1155,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(t62,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,cn3,true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t796,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,cn3,true) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t164564,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,false,true) = true,
inference(step,[status(thm)],[t796,t1155]) ).
cnf(t1157,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,false,true) = true,
inference(rw,[status(thm)],[t164564]) ).
cnf(t3044,plain,
ifeq(is_a_theorem(implies(implies(not(sk43),sk43),sk43)),true,false,true) = true,
inference(orient,[status(thm)],[t1157]) ).
fof(f29,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f29_nnf,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y] :
( implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c58,plain,
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
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/sandbox2/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(t24,plain,
or(not(X1),X2) = implies(X1,X2),
inference(hyper_resolution,[status(thm)],[hi58,hi60]) ).
cnf(t264,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t24]) ).
fof(f1,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f1_nnf,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ( ( sk2 != sk3
& is_a_theorem(equiv(sk2,sk3)) )
| substitution_of_equivalents )
& ( X = Y
| ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f1_nnf]) ).
cnf(c4,plain,
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t72,plain,
ifeq(substitution_of_equivalents,true,ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t258,plain,
ifeq(substitution_of_equivalents,true,ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t72]) ).
fof(f40,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40_nnf,plain,
substitution_of_equivalents,
inference(nnf_transformation,[status(thm)],[f40]) ).
cnf(c69,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(esa)],[f40_nnf]) ).
cnf(t14,plain,
true = substitution_of_equivalents,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(t1171,plain,
substitution_of_equivalents = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t164575,plain,
ifeq(true,true,ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2),X2) = X2,
inference(step,[status(thm)],[t258,t1171]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t164576,plain,
ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2) = X2,
inference(step,[status(thm)],[t164575,t256]) ).
cnf(t1173,plain,
ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2) = X2,
inference(rw,[status(thm)],[t164576]) ).
cnf(t1255,plain,
ifeq(is_a_theorem(equiv(X1,X2)),true,X1,X2) = X2,
inference(orient,[status(thm)],[t1173]) ).
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(t253,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(t818,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)],[t253]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox2/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(t1151,plain,
modus_ponens = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t164561,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)],[t818,t1151]) ).
cnf(t164562,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)],[t164561,t256]) ).
cnf(t1153,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)],[t164562]) ).
cnf(t23428,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)],[t1153]) ).
fof(f23,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/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/sandbox2/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(t27,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi66]) ).
cnf(t758,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t759,plain,
true = is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(cp,[status(thm)],[t758,t264]) ).
cnf(t1310,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))) = true,
inference(orient,[status(thm)],[t759]) ).
cnf(t23858,plain,
true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(true,true,is_a_theorem(or(X2,not(X1))),true),true),
inference(cp,[status(thm)],[t23428,t1310]) ).
cnf(t164907,plain,
true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(or(X2,not(X1))),true),
inference(step,[status(thm)],[t23858,t256]) ).
cnf(t30604,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(or(X2,not(X1))),true) = true,
inference(orient,[status(thm)],[t164907]) ).
fof(f22,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/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(t49,plain,
ifeq(r2,true,is_a_theorem(implies(X1,or(X2,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t1078,plain,
ifeq(r2,true,is_a_theorem(implies(X1,or(X2,X1))),true) = true,
inference(orient,[status(thm)],[t49]) ).
fof(f36,axiom,
r2,
file('/export/starexec/sandbox2/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(t10,plain,
true = r2,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t1158,plain,
r2 = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t164565,plain,
ifeq(true,true,is_a_theorem(implies(X1,or(X2,X1))),true) = true,
inference(step,[status(thm)],[t1078,t1158]) ).
cnf(t164566,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(step,[status(thm)],[t164565,t256]) ).
cnf(t1159,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(rw,[status(thm)],[t164566]) ).
cnf(t1191,plain,
is_a_theorem(implies(X1,or(X2,X1))) = true,
inference(orient,[status(thm)],[t1159]) ).
cnf(t23629,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)],[t23428,t1191]) ).
cnf(t165216,plain,
true = ifeq(is_a_theorem(implies(implies(X1,or(X2,X1)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t23629,t256]) ).
cnf(t45908,plain,
ifeq(is_a_theorem(implies(implies(X1,or(X2,X1)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t165216]) ).
fof(f25,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox2/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/sandbox2/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(h7,plain,
is_a_theorem(implies(implies(V0,V1),implies(or(V2,V0),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi68]) ).
fof(f21,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f21_nnf,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [P] :
( ( ~ is_a_theorem(implies(or(sk44,sk44),sk44))
| r1 )
& ( is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk44])],[f21_nnf]) ).
cnf(c45,plain,
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi45,axiom,
ifeq(r1,true,is_a_theorem(implies(or(X0,X0),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f35,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f35_nnf,plain,
r1,
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c64,plain,
r1,
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(hi64,axiom,
r1 = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h3,plain,
is_a_theorem(implies(or(V0,V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi45,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(t51,plain,
is_a_theorem(implies(or(X1,or(X2,X2)),or(X1,X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h3,h7]) ).
cnf(t783,plain,
is_a_theorem(implies(or(X1,or(X2,X2)),or(X1,X2))) = true,
inference(orient,[status(thm)],[t51]) ).
cnf(t784,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X2)),or(not(X1),X2))),
inference(cp,[status(thm)],[t783,t264]) ).
cnf(t164585,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X2)),implies(X1,X2))),
inference(step,[status(thm)],[t784,t264]) ).
cnf(t1483,plain,
is_a_theorem(implies(implies(X1,or(X2,X2)),implies(X1,X2))) = true,
inference(orient,[status(thm)],[t164585]) ).
cnf(t45912,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true),
inference(cp,[status(thm)],[t45908,t1483]) ).
cnf(t165217,plain,
true = is_a_theorem(implies(X1,X1)),
inference(step,[status(thm)],[t45912,t256]) ).
cnf(t45957,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(orient,[status(thm)],[t165217]) ).
cnf(t45978,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(X1))),true),
inference(cp,[status(thm)],[t30604,t45957]) ).
cnf(t165222,plain,
true = is_a_theorem(or(X1,not(X1))),
inference(step,[status(thm)],[t45978,t256]) ).
cnf(t45988,plain,
is_a_theorem(or(X1,not(X1))) = true,
inference(orient,[status(thm)],[t165222]) ).
cnf(t45998,plain,
true = is_a_theorem(implies(X1,not(not(X1)))),
inference(cp,[status(thm)],[t45988,t264]) ).
cnf(t46176,plain,
is_a_theorem(implies(X1,not(not(X1)))) = true,
inference(orient,[status(thm)],[t45998]) ).
cnf(t46207,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t23428,t46176]) ).
cnf(t166808,plain,
true = ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t46207,t256]) ).
fof(f27,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).
fof(f27_nnf,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y] :
( and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c56,plain,
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(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/sandbox2/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(t29,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(hyper_resolution,[status(thm)],[hi56,hi61]) ).
cnf(t164555,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(step,[status(thm)],[t29,t264]) ).
cnf(t1124,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t164555]) ).
cnf(t1126,plain,
implies(implies(X1,not(X2)),X3) = or(and(X1,X2),X3),
inference(cp,[status(thm)],[t264,t1124]) ).
cnf(t1205,plain,
implies(implies(X1,not(X2)),X3) = or(and(X1,X2),X3),
inference(orient,[status(thm)],[t1126]) ).
cnf(t166809,plain,
true = ifeq(is_a_theorem(or(and(X1,not(X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t166808,t1205]) ).
cnf(t144696,plain,
ifeq(is_a_theorem(or(and(X1,not(X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t166809]) ).
cnf(t23871,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)],[t23428,t758]) ).
cnf(t164799,plain,
true = ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true),
inference(step,[status(thm)],[t23871,t256]) ).
cnf(t25992,plain,
ifeq(is_a_theorem(or(X1,X2)),true,is_a_theorem(or(X2,X1)),true) = true,
inference(orient,[status(thm)],[t164799]) ).
cnf(t45979,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t23428,t45957]) ).
cnf(t165767,plain,
true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t45979,t256]) ).
cnf(t68280,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t165767]) ).
fof(f24,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
fof(f24_nnf,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(or(sk49,or(sk50,sk51)),or(sk50,or(sk49,sk51))))
| r4 )
& ( is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk49,sk50,sk51])],[f24_nnf]) ).
cnf(c51,plain,
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi51,axiom,
ifeq(r4,true,is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
fof(f38,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(f38_nnf,plain,
r4,
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c67,plain,
r4,
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(hi67,axiom,
r4 = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t76,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi51,hi67]) ).
cnf(t767,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(t768,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,or(not(X1),X3)))),
inference(cp,[status(thm)],[t767,t264]) ).
cnf(t164607,plain,
true = is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))),
inference(step,[status(thm)],[t768,t264]) ).
cnf(t6445,plain,
is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t164607]) ).
cnf(t6452,plain,
true = is_a_theorem(implies(implies(X1,implies(X2,X3)),or(not(X2),implies(X1,X3)))),
inference(cp,[status(thm)],[t6445,t264]) ).
cnf(t164620,plain,
true = is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))),
inference(step,[status(thm)],[t6452,t264]) ).
cnf(t7051,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t164620]) ).
cnf(t68281,plain,
true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),true),
inference(cp,[status(thm)],[t68280,t7051]) ).
cnf(t165768,plain,
true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(step,[status(thm)],[t68281,t256]) ).
cnf(t68307,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t165768]) ).
cnf(t68356,plain,
true = ifeq(is_a_theorem(X1),true,ifeq(true,true,is_a_theorem(implies(implies(X1,X2),X2)),true),true),
inference(cp,[status(thm)],[t23428,t68307]) ).
cnf(t166302,plain,
true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true),
inference(step,[status(thm)],[t68356,t256]) ).
cnf(t103176,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true) = true,
inference(orient,[status(thm)],[t166302]) ).
cnf(t46032,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)],[t23428,t45988]) ).
cnf(t166614,plain,
true = ifeq(is_a_theorem(implies(or(X1,not(X1)),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t46032,t256]) ).
cnf(t126650,plain,
ifeq(is_a_theorem(implies(or(X1,not(X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t166614]) ).
cnf(t247,plain,
ifeq(r5,true,is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t1086,plain,
ifeq(r5,true,is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),true) = true,
inference(orient,[status(thm)],[t247]) ).
cnf(t13,plain,
true = r5,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t1164,plain,
r5 = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t164571,plain,
ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),true) = true,
inference(step,[status(thm)],[t1086,t1164]) ).
cnf(t164572,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) = true,
inference(step,[status(thm)],[t164571,t256]) ).
cnf(t1165,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) = true,
inference(rw,[status(thm)],[t164572]) ).
cnf(t6570,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) = true,
inference(orient,[status(thm)],[t1165]) ).
cnf(t6571,plain,
true = is_a_theorem(or(and(X1,X2),implies(or(X3,X1),or(X3,not(X2))))),
inference(cp,[status(thm)],[t6570,t1205]) ).
cnf(t13243,plain,
is_a_theorem(or(and(X1,X2),implies(or(X3,X1),or(X3,not(X2))))) = true,
inference(orient,[status(thm)],[t6571]) ).
cnf(t144698,plain,
true = ifeq(true,true,is_a_theorem(implies(or(X1,X2),or(X1,not(not(X2))))),true),
inference(cp,[status(thm)],[t144696,t13243]) ).
cnf(t166828,plain,
true = is_a_theorem(implies(or(X1,X2),or(X1,not(not(X2))))),
inference(step,[status(thm)],[t144698,t256]) ).
cnf(t145369,plain,
is_a_theorem(implies(or(X1,X2),or(X1,not(not(X2))))) = true,
inference(orient,[status(thm)],[t166828]) ).
cnf(t145438,plain,
true = ifeq(true,true,is_a_theorem(or(X1,not(not(not(X1))))),true),
inference(cp,[status(thm)],[t126650,t145369]) ).
cnf(t166829,plain,
true = is_a_theorem(or(X1,not(not(not(X1))))),
inference(step,[status(thm)],[t145438,t256]) ).
cnf(t145439,plain,
is_a_theorem(or(X1,not(not(not(X1))))) = true,
inference(orient,[status(thm)],[t166829]) ).
cnf(t145490,plain,
true = ifeq(true,true,is_a_theorem(or(not(not(not(X1))),X1)),true),
inference(cp,[status(thm)],[t25992,t145439]) ).
cnf(t166830,plain,
true = is_a_theorem(or(not(not(not(X1))),X1)),
inference(step,[status(thm)],[t145490,t256]) ).
cnf(t166831,plain,
true = is_a_theorem(implies(not(not(X1)),X1)),
inference(step,[status(thm)],[t166830,t264]) ).
cnf(t145505,plain,
is_a_theorem(implies(not(not(X1)),X1)) = true,
inference(orient,[status(thm)],[t166831]) ).
cnf(t145550,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(not(X1)),X1),X2),X2)),true),
inference(cp,[status(thm)],[t103176,t145505]) ).
cnf(t166884,plain,
true = is_a_theorem(implies(implies(implies(not(not(X1)),X1),X2),X2)),
inference(step,[status(thm)],[t145550,t256]) ).
cnf(t148206,plain,
is_a_theorem(implies(implies(implies(not(not(X1)),X1),X2),X2)) = true,
inference(orient,[status(thm)],[t166884]) ).
cnf(t1208,plain,
or(and(X1,implies(X2,not(X3))),Y3) = implies(implies(X1,and(X2,X3)),Y3),
inference(cp,[status(thm)],[t1205,t1124]) ).
cnf(t1922,plain,
or(and(X1,implies(X2,not(X3))),Y3) = implies(implies(X1,and(X2,X3)),Y3),
inference(orient,[status(thm)],[t1208]) ).
fof(f30,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f30_nnf,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c59,plain,
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi59,axiom,
ifeq(op_equiv,true,equiv(X0,X1),and(implies(X0,X1),implies(X1,X0))) = and(implies(X0,X1),implies(X1,X0)),
inference(equality_encoding,[status(esa)],[c59]) ).
fof(f33,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f33_nnf,plain,
op_equiv,
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c62,plain,
op_equiv,
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi62,axiom,
op_equiv = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(t31,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(hyper_resolution,[status(thm)],[hi59,hi62]) ).
cnf(t1136,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(orient,[status(thm)],[t31]) ).
cnf(t1923,plain,
implies(implies(implies(not(X1),X2),and(X2,X1)),X3) = or(equiv(not(X1),X2),X3),
inference(cp,[status(thm)],[t1922,t1136]) ).
cnf(t7199,plain,
implies(implies(implies(not(X1),X2),and(X2,X1)),X3) = or(equiv(not(X1),X2),X3),
inference(orient,[status(thm)],[t1923]) ).
cnf(t148207,plain,
true = is_a_theorem(or(equiv(not(not(X1)),X1),and(X1,not(X1)))),
inference(cp,[status(thm)],[t148206,t7199]) ).
cnf(t161536,plain,
is_a_theorem(or(equiv(not(not(X1)),X1),and(X1,not(X1)))) = true,
inference(orient,[status(thm)],[t148207]) ).
cnf(t161609,plain,
true = ifeq(true,true,is_a_theorem(or(and(X1,not(X1)),equiv(not(not(X1)),X1))),true),
inference(cp,[status(thm)],[t25992,t161536]) ).
cnf(t167012,plain,
true = is_a_theorem(or(and(X1,not(X1)),equiv(not(not(X1)),X1))),
inference(step,[status(thm)],[t161609,t256]) ).
cnf(t163208,plain,
is_a_theorem(or(and(X1,not(X1)),equiv(not(not(X1)),X1))) = true,
inference(orient,[status(thm)],[t167012]) ).
cnf(t163294,plain,
true = ifeq(true,true,is_a_theorem(equiv(not(not(X1)),X1)),true),
inference(cp,[status(thm)],[t144696,t163208]) ).
cnf(t167013,plain,
true = is_a_theorem(equiv(not(not(X1)),X1)),
inference(step,[status(thm)],[t163294,t256]) ).
cnf(t163298,plain,
is_a_theorem(equiv(not(not(X1)),X1)) = true,
inference(orient,[status(thm)],[t167013]) ).
cnf(t163340,plain,
X1 = ifeq(true,true,not(not(X1)),X1),
inference(cp,[status(thm)],[t1255,t163298]) ).
cnf(t167014,plain,
X1 = not(not(X1)),
inference(step,[status(thm)],[t163340,t256]) ).
cnf(t163355,plain,
not(not(X1)) = X1,
inference(orient,[status(thm)],[t167014]) ).
cnf(t163393,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cp,[status(thm)],[t264,t163355]) ).
cnf(t163994,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t163393]) ).
cnf(t167157,plain,
ifeq(is_a_theorem(implies(or(sk43,sk43),sk43)),true,false,true) = true,
inference(step,[status(thm)],[t3044,t163994]) ).
cnf(t23,plain,
is_a_theorem(implies(or(X1,X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi45,hi64]) ).
cnf(t765,plain,
is_a_theorem(implies(or(X1,X1),X1)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t167158,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t167157,t765]) ).
cnf(t167159,plain,
false = true,
inference(step,[status(thm)],[t167158,t256]) ).
cnf(t164517,plain,
false = true,
inference(rw,[status(thm)],[t167159]) ).
cnf(t164538,plain,
false = true,
inference(orient,[status(thm)],[t164517]) ).
cnf(t167183,plain,
cn3 = true,
inference(step,[status(thm)],[t1155,t164538]) ).
cnf(t164539,plain,
cn3 = true,
inference(orient,[status(thm)],[t167183]) ).
cnf(goal_0,negated_conjecture,
true != cn3,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t164539]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL498+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 : n007.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 23:32:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 232.82/30.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.82/30.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------