%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL464+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 : n002.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 02:02:07 PM UTC 2026
% Result : Theorem 27.00s 3.85s
% Output : Proof 27.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 77 unt; 0 def)
% Number of atoms : 149 ( 59 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 89 ( 37 ~; 31 |; 15 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-4 aty)
% Number of variables : 185 ( 45 sgn 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f4_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(sk8,implies(sk8,sk9)),implies(sk8,sk9)))
| implies_2 )
& ( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f4_nnf]) ).
cnf(c12,plain,
( ~ is_a_theorem(implies(implies(sk8,implies(sk8,sk9)),implies(sk8,sk9)))
| implies_2 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t235,plain,
ifeq(is_a_theorem(implies(implies(sk8,implies(sk8,sk9)),implies(sk8,sk9))),true,implies_2,true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f18,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
fof(f18_nnf,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(sk38,sk39),implies(implies(sk39,sk40),implies(sk38,sk40))))
| cn1 )
& ( is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk38,sk39,sk40])],[f18_nnf]) ).
cnf(c39,plain,
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi39,axiom,
ifeq(cn1,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
fof(f35,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f35_nnf,plain,
cn1,
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c64,plain,
cn1,
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(hi64,axiom,
cn1 = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V1,V2),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi64]) ).
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(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]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_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(hi63,axiom,
modus_ponens = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h56,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(V2,V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h5,h5]) ).
fof(f19,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox/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(c41,plain,
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi41,axiom,
ifeq(cn2,true,is_a_theorem(implies(X0,implies(not(X0),X1))),true) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
fof(f36,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
fof(f36_nnf,plain,
cn2,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
cn2,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(hi65,axiom,
cn2 = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h1,plain,
is_a_theorem(implies(V0,implies(not(V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi41,hi65]) ).
cnf(h10,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h1,h5]) ).
fof(f20,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/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(c43,plain,
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi43,axiom,
ifeq(cn3,true,is_a_theorem(implies(implies(not(X0),X0),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
fof(f37,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(f37_nnf,plain,
cn3,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
cn3,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(hi66,axiom,
cn3 = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h2,plain,
is_a_theorem(implies(implies(not(V0),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi43,hi66]) ).
cnf(h14,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h2,h10]) ).
cnf(h16,plain,
is_a_theorem(implies(not(implies(V0,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h14,h1]) ).
cnf(h17,plain,
is_a_theorem(implies(implies(V0,V1),implies(not(implies(V2,V2)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h16,h5]) ).
cnf(h19,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V1)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h17,h10]) ).
cnf(h49,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h19,h5]) ).
cnf(h69,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h2,h49]) ).
cnf(h74,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h69,h5]) ).
cnf(h9,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(not(V0),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h2,h5]) ).
cnf(h80,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h9,h74]) ).
cnf(h94,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h80,h5]) ).
cnf(h383,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h94,h56]) ).
cnf(h516,plain,
is_a_theorem(implies(V0,implies(implies(V1,implies(not(V2),V2)),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h383,h383]) ).
cnf(h13,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h5,h10]) ).
cnf(h51,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(not(V2),V1)),V3),implies(V2,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h13,h5]) ).
cnf(h82,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(V3,V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h74,h5]) ).
cnf(h157,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V1),V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h82,h94]) ).
cnf(h165,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V0),V1),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h157,h5]) ).
cnf(h231,plain,
is_a_theorem(implies(V0,implies(V1,implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h165,h51]) ).
cnf(h261,plain,
is_a_theorem(implies(implies(implies(V0,implies(not(V1),V2)),V3),implies(V1,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h231,h5]) ).
cnf(h532,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h383,h261]) ).
cnf(h540,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h532,h383]) ).
cnf(h551,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h540,h540]) ).
cnf(h54,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(not(V0),V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h10,h5]) ).
cnf(h307,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(implies(V2,V3),implies(V0,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h5,h54]) ).
cnf(h558,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h540,h307]) ).
cnf(h766,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h558,h383]) ).
cnf(h798,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h766,h766]) ).
cnf(h809,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h798,h56]) ).
cnf(h844,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(V1,implies(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h809,h551]) ).
cnf(h978,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h844,h516]) ).
cnf(h1008,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h978,h56]) ).
cnf(h580,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h551,h5]) ).
cnf(h1221,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h1008,h580]) ).
cnf(h1332,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h1221,h5]) ).
cnf(h1664,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h10,h1332]) ).
cnf(h1763,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h1664,h1008]) ).
cnf(t71,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h1763,h56]) ).
cnf(t373,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) = true,
inference(orient,[status(thm)],[t71]) ).
cnf(t879,plain,
ifeq(true,true,implies_2,true) = true,
inference(step,[status(thm)],[t235,t373]) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t880,plain,
implies_2 = true,
inference(step,[status(thm)],[t879,t256]) ).
cnf(t719,plain,
implies_2 = true,
inference(orient,[status(thm)],[t880]) ).
fof(f42,conjecture,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f42_neg,negated_conjecture,
~ implies_2,
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
~ implies_2,
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
~ implies_2,
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c71,plain,
~ implies_2,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
true != implies_2,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t719]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL464+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:30:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.00/3.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.00/3.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------