%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL454+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 : n015.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 02:02:06 PM UTC 2026
% Result : Theorem 24.16s 3.42s
% Output : Proof 24.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 41 unt; 0 def)
% Number of atoms : 113 ( 23 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 : 76 ( 5 sgn 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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(c46,plain,
( ~ is_a_theorem(implies(or(sk44,sk44),sk44))
| r1 ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t61,plain,
ifeq(is_a_theorem(implies(or(sk44,sk44),sk44)),true,r1,true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
fof(f11,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f11_nnf,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Z,Y] :
( ( ~ is_a_theorem(implies(implies(sk23,sk25),implies(implies(sk24,sk25),implies(or(sk23,sk24),sk25))))
| or_3 )
& ( is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk23,sk24,sk25])],[f11_nnf]) ).
cnf(c25,plain,
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi25,axiom,
ifeq(or_3,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
fof(f44,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f44_nnf,plain,
or_3,
inference(nnf_transformation,[status(thm)],[f44]) ).
cnf(c73,plain,
or_3,
inference(cnf_transformation,[status(esa)],[f44_nnf]) ).
cnf(hi73,axiom,
or_3 = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(h12,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V2,V1),implies(or(V0,V2),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi73]) ).
fof(f4,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/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(c11,plain,
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi11,axiom,
ifeq(implies_2,true,is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f37,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f37_nnf,plain,
implies_2,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
implies_2,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(hi66,axiom,
implies_2 = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi66]) ).
fof(f3,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f3_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk6,implies(sk7,sk6)))
| implies_1 )
& ( is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f3_nnf]) ).
cnf(c9,plain,
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi9,axiom,
ifeq(implies_1,true,is_a_theorem(implies(X0,implies(X1,X0))),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f36,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f36_nnf,plain,
implies_1,
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c65,plain,
implies_1,
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(hi65,axiom,
implies_1 = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h4,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi65]) ).
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(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/sandbox2/benchmark/theBenchmark.p',hilbert_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(h20,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h4,h5]) ).
cnf(h74,plain,
is_a_theorem(implies(implies(V0,V1),implies(or(V1,V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h20,h12]) ).
cnf(t38,plain,
is_a_theorem(implies(or(X1,X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h20,h74]) ).
cnf(t386,plain,
is_a_theorem(implies(or(X1,X1),X1)) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t856,plain,
ifeq(true,true,r1,true) = true,
inference(step,[status(thm)],[t61,t386]) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t33]) ).
cnf(t857,plain,
r1 = true,
inference(step,[status(thm)],[t856,t256]) ).
cnf(t806,plain,
r1 = true,
inference(orient,[status(thm)],[t857]) ).
fof(f52,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f52_neg,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ r1,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ r1,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ r1,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != r1,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t806]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 23:29:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.16/3.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.16/3.42 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------