%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL546+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 : n006.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 02:02:16 PM UTC 2026
% Result : Theorem 95.97s 12.54s
% Output : Proof 95.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 69 unt; 0 def)
% Number of atoms : 167 ( 49 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 118 ( 48 ~; 42 |; 19 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 90 ( 2 sgn 33 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f88,conjecture,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(f88_neg,negated_conjecture,
~ axiom_m6,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f88_nnf,plain,
~ axiom_m6,
inference(nnf_transformation,[status(thm)],[f88_neg]) ).
fof(f88_sk,plain,
~ axiom_m6,
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c146,plain,
~ axiom_m6,
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(t0,plain,
false = axiom_m6,
inference(equality_encoding,[status(esa)],[c146]) ).
cnf(t889,plain,
axiom_m6 = false,
inference(orient,[status(thm)],[t0]) ).
fof(f67,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m6) ).
fof(f67_nnf,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X)))
| axiom_m6 )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [X] :
( ( ~ is_a_theorem(strict_implies(sk87,possibly(sk87)))
| axiom_m6 )
& ( is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk87])],[f67_nnf]) ).
cnf(c121,plain,
( ~ is_a_theorem(strict_implies(sk87,possibly(sk87)))
| axiom_m6 ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t146,plain,
ifeq(is_a_theorem(strict_implies(sk87,possibly(sk87))),true,axiom_m6,true) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(t355,plain,
ifeq(is_a_theorem(strict_implies(sk87,possibly(sk87))),true,axiom_m6,true) = true,
inference(orient,[status(thm)],[t146]) ).
cnf(t8541,plain,
ifeq(is_a_theorem(strict_implies(sk87,possibly(sk87))),true,false,true) = true,
inference(step,[status(thm)],[t355,t889]) ).
cnf(t891,plain,
ifeq(is_a_theorem(strict_implies(sk87,possibly(sk87))),true,false,true) = true,
inference(rw,[status(thm)],[t8541]) ).
fof(f49,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f49_nnf,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X] :
( ( ( ~ is_a_theorem(necessarily(sk55))
& is_a_theorem(sk55) )
| necessitation )
& ( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X)
| ~ necessitation ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk55])],[f49_nnf]) ).
cnf(c78,plain,
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(t208,plain,
ifeq(necessitation,true,ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c78]) ).
cnf(t451,plain,
ifeq(necessitation,true,ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true),true) = true,
inference(orient,[status(thm)],[t208]) ).
fof(f77,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f77_nnf,plain,
necessitation,
inference(nnf_transformation,[status(thm)],[f77]) ).
cnf(c135,plain,
necessitation,
inference(cnf_transformation,[status(esa)],[f77_nnf]) ).
cnf(t19,plain,
true = necessitation,
inference(equality_encoding,[status(esa)],[c135]) ).
cnf(t895,plain,
necessitation = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t8546,plain,
ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true),true) = true,
inference(step,[status(thm)],[t451,t895]) ).
cnf(t46,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(t8547,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true) = true,
inference(step,[status(thm)],[t8546,t256]) ).
cnf(t897,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true) = true,
inference(rw,[status(thm)],[t8547]) ).
cnf(t3205,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(necessarily(X1)),true) = true,
inference(orient,[status(thm)],[t897]) ).
fof(f5,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
fof(f5_nnf,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( ( ~ is_a_theorem(implies(implies(sk10,sk11),implies(implies(sk11,sk12),implies(sk10,sk12))))
| implies_3 )
& ( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12])],[f5_nnf]) ).
cnf(c13,plain,
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi13,axiom,
ifeq(implies_3,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f38,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f38_nnf,plain,
implies_3,
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c67,plain,
implies_3,
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(hi67,axiom,
implies_3 = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h6,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V1,V2),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi67]) ).
fof(f56,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_B) ).
fof(f56_nnf,plain,
( ( ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X))))
| axiom_B )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [X] :
( ( ~ is_a_theorem(implies(sk66,necessarily(possibly(sk66))))
| axiom_B )
& ( is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk66])],[f56_nnf]) ).
cnf(c98,plain,
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi98,axiom,
ifeq(axiom_B,true,is_a_theorem(implies(X0,necessarily(possibly(X0)))),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
fof(f81,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
fof(f81_nnf,plain,
axiom_B,
inference(nnf_transformation,[status(thm)],[f81]) ).
cnf(c139,plain,
axiom_B,
inference(cnf_transformation,[status(esa)],[f81_nnf]) ).
cnf(hi139,axiom,
axiom_B = true,
inference(equality_encoding,[status(esa)],[c139]) ).
cnf(h20,plain,
is_a_theorem(implies(V0,necessarily(possibly(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi139]) ).
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(h197,plain,
is_a_theorem(implies(implies(necessarily(possibly(V0)),V1),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h20,h6]) ).
fof(f54,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f54_nnf,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [X] :
( ( ~ is_a_theorem(implies(necessarily(sk64),sk64))
| axiom_M )
& ( is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk64])],[f54_nnf]) ).
cnf(c94,plain,
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi94,axiom,
ifeq(axiom_M,true,is_a_theorem(implies(necessarily(X0),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c94]) ).
fof(f79,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f79_nnf,plain,
axiom_M,
inference(nnf_transformation,[status(thm)],[f79]) ).
cnf(c137,plain,
axiom_M,
inference(cnf_transformation,[status(esa)],[f79_nnf]) ).
cnf(hi137,axiom,
axiom_M = true,
inference(equality_encoding,[status(esa)],[c137]) ).
cnf(h18,plain,
is_a_theorem(implies(necessarily(V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi94,hi137]) ).
cnf(t49,plain,
is_a_theorem(implies(X1,possibly(X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi63,h18,h197]) ).
cnf(t278,plain,
is_a_theorem(implies(X1,possibly(X1))) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t3241,plain,
true = ifeq(true,true,is_a_theorem(necessarily(implies(X1,possibly(X1)))),true),
inference(cp,[status(thm)],[t3205,t278]) ).
cnf(t8654,plain,
true = is_a_theorem(necessarily(implies(X1,possibly(X1)))),
inference(step,[status(thm)],[t3241,t256]) ).
fof(f74,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f74_nnf,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [X,Y] :
( strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c132,plain,
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(hi132,axiom,
ifeq(op_strict_implies,true,strict_implies(X0,X1),necessarily(implies(X0,X1))) = necessarily(implies(X0,X1)),
inference(equality_encoding,[status(esa)],[c132]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f85_nnf,plain,
op_strict_implies,
inference(nnf_transformation,[status(thm)],[f85]) ).
cnf(c143,plain,
op_strict_implies,
inference(cnf_transformation,[status(esa)],[f85_nnf]) ).
cnf(hi143,axiom,
op_strict_implies = true,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t72,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(hyper_resolution,[status(thm)],[hi132,hi143]) ).
cnf(t862,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(orient,[status(thm)],[t72]) ).
cnf(t8655,plain,
true = is_a_theorem(strict_implies(X1,possibly(X1))),
inference(step,[status(thm)],[t8654,t862]) ).
cnf(t3270,plain,
is_a_theorem(strict_implies(X1,possibly(X1))) = true,
inference(orient,[status(thm)],[t8655]) ).
cnf(t8819,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t891,t3270]) ).
cnf(t8820,plain,
false = true,
inference(step,[status(thm)],[t8819,t256]) ).
cnf(t8460,plain,
false = true,
inference(orient,[status(thm)],[t8820]) ).
cnf(t8821,plain,
axiom_m6 = true,
inference(step,[status(thm)],[t889,t8460]) ).
cnf(t8461,plain,
axiom_m6 = true,
inference(orient,[status(thm)],[t8821]) ).
cnf(goal_0,negated_conjecture,
true != axiom_m6,
inference(equality_encoding,[status(esa)],[c146]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8461]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n006.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
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 23:42:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 95.97/12.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.97/12.54 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------