%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL459+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 : 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 02:02:07 PM UTC 2026
% Result : Theorem 23.66s 8.49s
% Output : Proof 23.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 93 ( 18 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 76 ( 32 ~; 26 |; 13 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 52 ( 2 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(c34,plain,
( ~ is_a_theorem(implies(sk32,and(sk32,sk32)))
| kn1 ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t76,plain,
ifeq(is_a_theorem(implies(sk32,and(sk32,sk32))),true,kn1,true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
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(h29,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi66]) ).
fof(f8,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f8_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk17,implies(sk18,and(sk17,sk18))))
| and_3 )
& ( is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18])],[f8_nnf]) ).
cnf(c19,plain,
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi19,axiom,
ifeq(and_3,true,is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f41,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f41_nnf,plain,
and_3,
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c70,plain,
and_3,
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi70,axiom,
and_3 = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(h5,plain,
is_a_theorem(implies(V0,implies(V1,and(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi70]) ).
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(t34,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h5,h29]) ).
cnf(t248,plain,
is_a_theorem(implies(X1,and(X1,X1))) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t571,plain,
ifeq(true,true,kn1,true) = true,
inference(step,[status(thm)],[t76,t248]) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t209,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t31]) ).
cnf(t572,plain,
kn1 = true,
inference(step,[status(thm)],[t571,t209]) ).
cnf(t536,plain,
kn1 = true,
inference(orient,[status(thm)],[t572]) ).
fof(f52,conjecture,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f52_neg,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
~ kn1,
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
~ kn1,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c81,plain,
~ kn1,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != kn1,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t536]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n020.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 23:28:53 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.66/8.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.66/8.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------