%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:00:46 PM UTC 2026
% Result : Unsatisfiable 41.24s 15.65s
% Output : Proof 41.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 63 unt; 0 def)
% Number of atoms : 75 ( 46 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 : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 168 ( 30 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox/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(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox/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]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox/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(h7,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(not(V0),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h316,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V1),V2),implies(implies(V0,V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h7]) ).
cnf(h306,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(h1249,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(implies(V1,V2),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h306,h316]) ).
cnf(h1335,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(implies(V1,V2),implies(implies(not(V0),V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h316,h1249]) ).
cnf(f3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox/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(h6,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi3]) ).
cnf(h10,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi2]) ).
cnf(h12,plain,
is_a_theorem(implies(not(implies(V0,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h10]) ).
cnf(h14,plain,
is_a_theorem(implies(implies(V0,V1),implies(not(implies(V2,V2)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h12]) ).
cnf(h35,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V1)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h14]) ).
cnf(h38,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h35]) ).
cnf(h43,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38,hi2]) ).
cnf(h48,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h43]) ).
cnf(h51,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(V3,V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h48]) ).
cnf(h102,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h51,hi2]) ).
cnf(h175,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(implies(V2,V2),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h102]) ).
cnf(h1224,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(implies(V3,V1),implies(V0,implies(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h306,h306]) ).
cnf(h1516,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V1),V2)),implies(implies(V2,V3),implies(V0,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1224,h175]) ).
cnf(h1584,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(implies(V3,implies(implies(V4,V4),V1)),implies(V0,implies(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1224,h1516]) ).
cnf(h2748,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V1),implies(V2,V3))),implies(implies(V4,V2),implies(V0,implies(V4,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1584,hi1]) ).
cnf(h3007,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(implies(V1,implies(not(V2),V2)),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2748,h1335]) ).
cnf(h3204,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3007,hi3]) ).
cnf(h4160,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h306,h3204]) ).
cnf(h53,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h48,h7]) ).
cnf(h59,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h53]) ).
cnf(h379,plain,
is_a_theorem(implies(V0,implies(implies(not(implies(not(V1),V1)),implies(not(V1),V1)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h7]) ).
cnf(h103,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(implies(V1,V2),implies(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h51,hi1]) ).
cnf(h11,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi1]) ).
cnf(h315,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(not(V2),V1)),V3),implies(V2,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h11]) ).
cnf(h534,plain,
is_a_theorem(implies(V0,implies(implies(implies(not(V0),V1),V2),implies(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h315,h103]) ).
cnf(h1411,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(implies(V3,V1),implies(implies(not(V0),V0),implies(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h316,h1224]) ).
cnf(h2094,plain,
is_a_theorem(implies(implies(V0,implies(implies(not(V1),V2),V3)),implies(implies(not(V1),V1),implies(V0,implies(V4,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1411,h534]) ).
cnf(h2835,plain,
is_a_theorem(implies(implies(not(implies(not(V0),V0)),implies(not(V0),V0)),implies(V1,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2094,h379]) ).
cnf(h317,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,h6]) ).
cnf(h1334,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),implies(not(V2),V2)),implies(implies(V2,V3),implies(V0,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h317,h1249]) ).
cnf(h1782,plain,
is_a_theorem(implies(implies(implies(not(implies(not(V0),V1)),V2),implies(not(V3),V3)),implies(implies(V3,V4),implies(V0,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h317,h1334]) ).
cnf(h3363,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1782,h2835]) ).
cnf(h4395,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3363,h4160]) ).
cnf(t4,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1224,h4395]) ).
cnf(t259,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_21) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t259]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n013.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Wed Sep 23 21:43:48 UTC 2026
% 0.16/10.40 % CPUTime :
% 0.16/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 41.24/15.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.24/15.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------