%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:00:44 PM UTC 2026
% Result : Unsatisfiable 23.44s 3.55s
% Output : Proof 23.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 47 unt; 0 def)
% Number of atoms : 59 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 93 ( 15 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
fof(f1_nnf,plain,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(X0,implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
fof(f3_nnf,plain,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h11,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),not(V2)),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi3]) ).
cnf(h2,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
fof(f2_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),implies(V0,V1)),implies(implies(V0,implies(V1,V2)),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi2]) ).
cnf(h34,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V0),V2)),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h2]) ).
cnf(h229,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,h11]) ).
cnf(h79,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),not(V2))),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h11]) ).
cnf(h713,plain,
is_a_theorem(implies(not(not(V0)),implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h79,h229]) ).
cnf(f5,axiom,
is_a_theorem(implies(necessary(X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
fof(f5_nnf,plain,
! [X] : is_a_theorem(implies(necessary(X),X)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : is_a_theorem(implies(necessary(X),X)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
is_a_theorem(implies(necessary(X0),X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
is_a_theorem(implies(necessary(X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h3,plain,
is_a_theorem(implies(V0,implies(necessary(V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi5]) ).
cnf(h26,plain,
is_a_theorem(implies(V0,implies(V1,implies(necessary(V2),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3]) ).
cnf(h166,plain,
is_a_theorem(implies(implies(V0,implies(implies(necessary(V1),V1),V2)),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h26]) ).
cnf(h2420,plain,
is_a_theorem(implies(not(not(V0)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h166,h713]) ).
cnf(h25,plain,
is_a_theorem(implies(implies(V0,necessary(V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h3]) ).
cnf(h2483,plain,
is_a_theorem(implies(not(not(necessary(V0))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h25,h2420]) ).
cnf(h22,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h2]) ).
cnf(h137,plain,
is_a_theorem(implies(implies(not(V0),not(V1)),implies(V2,implies(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h22,hi3]) ).
cnf(h2967,plain,
is_a_theorem(implies(V0,implies(V1,not(necessary(not(V1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h137,h2483]) ).
cnf(h33,plain,
is_a_theorem(implies(implies(necessary(V0),implies(V0,V1)),implies(necessary(V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h3]) ).
cnf(t26,plain,
is_a_theorem(implies(necessary(X1),not(necessary(not(X1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h33,h2967]) ).
cnf(t393,plain,
is_a_theorem(implies(necessary(X1),not(necessary(not(X1))))) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f7,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f7_nnf,plain,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(necessary(a),not(necessary(not(a))))) != true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t393]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 21:41:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.44/3.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.44/3.55 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------