%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL371+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 02:01:48 PM UTC 2026
% Result : Theorem 78.76s 10.42s
% Output : Proof 78.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 75 unt; 0 def)
% Number of atoms : 87 ( 57 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 6 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 239 ( 37 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(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]) ).
fof(f1,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(f3_nnf,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h7,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi3]) ).
fof(f2,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(f2_nnf,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(not(X0),X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h21,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi2]) ).
cnf(h4,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,hi1,hi1]) ).
cnf(h9,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),V3),implies(implies(implies(implies(V1,V4),implies(V0,V4)),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h4]) ).
cnf(h11,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(V3,V4),implies(implies(V2,V0),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h9,hi1]) ).
cnf(h16,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V3),implies(implies(V1,not(V0)),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11,h7]) ).
cnf(h25,plain,
is_a_theorem(implies(implies(implies(implies(V0,not(V1)),V2),V3),implies(implies(implies(V1,implies(V0,V4)),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h16]) ).
cnf(h53,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V3),implies(implies(V3,V4),implies(implies(V1,not(V0)),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h25,hi1]) ).
cnf(h67,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(V0,not(not(implies(V0,V1)))),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h53,hi2]) ).
cnf(h81,plain,
is_a_theorem(implies(implies(implies(implies(V0,not(not(implies(V0,V1)))),V2),V3),implies(implies(implies(V0,V1),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h67]) ).
cnf(h19,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,hi1,h7]) ).
cnf(h31,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(implies(not(V2),V4),V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h9,h19]) ).
cnf(h159,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),implies(V2,not(not(implies(V2,V3))))),implies(implies(implies(V2,V3),V4),implies(V0,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h31,h81]) ).
cnf(h10,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),V2),implies(implies(V3,V1),V2)),V4),implies(implies(V0,V3),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h9,h4]) ).
cnf(h12,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(V0,V3),implies(implies(V2,V4),implies(implies(V3,V1),V4))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10,h10]) ).
cnf(h78,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(implies(V0,not(not(implies(V0,V1)))),V3),V4),implies(implies(V2,V3),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h12,h67]) ).
cnf(h609,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),not(not(implies(not(V0),V0)))),V1),V2),implies(implies(V0,V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h78,hi2]) ).
cnf(h635,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),implies(not(V2),not(not(implies(not(V2),V2))))),implies(implies(V2,V3),implies(V0,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h31,h609]) ).
cnf(h75,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(implies(V2,not(not(implies(V2,V3)))),implies(V0,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h31,h67]) ).
cnf(h129,plain,
is_a_theorem(implies(implies(implies(implies(V0,not(not(implies(V0,V1)))),implies(V2,V1)),V3),implies(implies(implies(not(V2),V4),V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h75]) ).
cnf(h650,plain,
is_a_theorem(implies(implies(implies(not(not(V0)),V1),not(V2)),implies(implies(V0,V3),implies(V2,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h129,h635]) ).
cnf(h667,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(implies(not(not(V0)),V4),not(V2)),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h650]) ).
cnf(h727,plain,
is_a_theorem(implies(implies(implies(not(not(not(V0))),V1),not(V2)),implies(implies(implies(V2,V3),V4),implies(V0,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h667,h159]) ).
cnf(h657,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(not(V0),not(V2)),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11,h635]) ).
cnf(h32,plain,
is_a_theorem(implies(implies(implies(implies(implies(not(V0),V1),V2),V3),V4),implies(implies(implies(V0,V2),V3),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h19]) ).
cnf(h676,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V3),implies(implies(not(not(V0)),not(V1)),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h32,h657]) ).
cnf(h695,plain,
is_a_theorem(implies(implies(implies(implies(not(not(V0)),not(V1)),V2),V3),implies(implies(implies(V0,implies(V1,V4)),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h676]) ).
cnf(h798,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V3),implies(implies(V3,V4),implies(implies(not(not(V0)),not(V1)),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h695,hi1]) ).
cnf(h844,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(not(not(not(implies(V0,V1)))),not(V0)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h798,hi2]) ).
cnf(h883,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(implies(V0,V1)))),not(V0)),V2),V3),implies(implies(implies(V0,V1),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h844]) ).
cnf(h1176,plain,
is_a_theorem(implies(implies(implies(V0,V1),not(V2)),implies(implies(implies(V2,V3),V4),implies(implies(V0,V1),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h883,h727]) ).
cnf(h1328,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(not(not(V0)),not(V0)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1176,hi2]) ).
cnf(h1364,plain,
is_a_theorem(implies(implies(implies(implies(not(not(V0)),not(V0)),implies(V1,V2)),V3),implies(implies(V1,V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11,h1328]) ).
cnf(h1493,plain,
is_a_theorem(implies(implies(implies(not(V0),implies(V1,V2)),V3),implies(implies(V1,V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h32,h1364]) ).
cnf(h1516,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1493,hi2]) ).
cnf(h37,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,h19,hi1]) ).
cnf(h681,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),not(V1)),V2),V3),implies(implies(implies(implies(V0,V4),implies(V1,V4)),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h657]) ).
cnf(h969,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(V3,V4),implies(V0,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h681,h37]) ).
cnf(h978,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),not(V1)),implies(V2,implies(V1,V3))),V4),implies(implies(V0,V3),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h969,h657]) ).
cnf(h1012,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,implies(V2,V3))),V4),implies(implies(V0,V3),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h32,h978]) ).
cnf(h2324,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1012,h1516]) ).
cnf(h2506,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2324,h21]) ).
cnf(h2570,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2506,hi2]) ).
cnf(h1365,plain,
is_a_theorem(implies(implies(implies(implies(not(not(V0)),not(V0)),V1),V2),implies(implies(implies(V0,V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1328]) ).
cnf(h1542,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(implies(implies(V0,V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h32,h1365]) ).
cnf(h1674,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1542,hi2]) ).
cnf(h2162,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10,h1674]) ).
cnf(h5453,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2162,h2570]) ).
cnf(h6067,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10,h5453]) ).
cnf(t4,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1542,h6067]) ).
cnf(t270,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),X1))) = true,
inference(orient,[status(thm)],[t4]) ).
fof(f4,conjecture,
is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_27) ).
fof(f4_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t270]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL371+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.43 % Computer : n008.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Wed Sep 23 23:01:09 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 78.76/10.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 78.76/10.42 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------