%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL389-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:01:52 PM UTC 2026
% Result : Unsatisfiable 66.72s 9.01s
% Output : Proof 66.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 88 ( 84 unt; 0 def)
% Number of atoms : 96 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 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 : 207 ( 56 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(h25,plain,
is_a_theorem(implies(implies(not(implies(not(V0),V0)),implies(not(V0),V0)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi2]) ).
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(h31,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V1)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h14]) ).
cnf(h34,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h31]) ).
cnf(h38,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,hi2]) ).
cnf(h43,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h38]) ).
cnf(h46,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,h43]) ).
cnf(h80,plain,
is_a_theorem(implies(implies(implies(V0,V0),implies(not(V1),V1)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h46,h25]) ).
cnf(h203,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(h540,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),implies(not(V2),V2)),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h203,h80]) ).
cnf(h192,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(h695,plain,
is_a_theorem(implies(implies(not(V0),not(implies(V1,V1))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h540]) ).
cnf(h727,plain,
is_a_theorem(implies(implies(implies(not(not(V0)),V1),not(implies(V2,V2))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h203,h695]) ).
cnf(h48,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h43,h7]) ).
cnf(h54,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h48]) ).
cnf(h713,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h54]) ).
cnf(h953,plain,
is_a_theorem(implies(V0,implies(implies(V1,implies(not(V2),V2)),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h713,h713]) ).
cnf(h20,plain,
is_a_theorem(implies(V0,implies(implies(not(not(V0)),not(V0)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h7]) ).
cnf(h200,plain,
is_a_theorem(implies(implies(implies(implies(not(not(V0)),not(V0)),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h20]) ).
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(h201,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(h417,plain,
is_a_theorem(implies(V0,implies(V1,implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h201,h200]) ).
cnf(h438,plain,
is_a_theorem(implies(implies(implies(V0,implies(not(V1),V2)),V3),implies(V1,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h417]) ).
cnf(h956,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h438,h713]) ).
cnf(h983,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h713,h956]) ).
cnf(h549,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,h203,hi1]) ).
cnf(h1000,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h549,h983]) ).
cnf(h1295,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h713,h1000]) ).
cnf(h1364,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1295,h1295]) ).
cnf(h1675,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1364,h953]) ).
cnf(h1692,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h1675]) ).
cnf(h995,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h983,h983]) ).
cnf(h1025,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h995]) ).
cnf(h1749,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1025,h1692]) ).
cnf(h1925,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1749]) ).
cnf(h2830,plain,
is_a_theorem(implies(not(not(V0)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1925,h727]) ).
cnf(h2868,plain,
is_a_theorem(implies(implies(V0,not(V0)),not(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1692,h2830]) ).
cnf(h1378,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h1364]) ).
cnf(h3089,plain,
is_a_theorem(implies(implies(V0,not(V0)),implies(V1,not(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1378,h2868]) ).
cnf(h2852,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V2,V0),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1925,h192]) ).
cnf(h33443,plain,
is_a_theorem(implies(implies(V0,implies(V1,not(V1))),implies(V0,implies(V2,not(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2852,h3089]) ).
cnf(h33630,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),implies(V2,not(V2))),implies(V0,implies(V3,not(V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h203,h33443]) ).
cnf(h33729,plain,
is_a_theorem(implies(implies(V0,not(V1)),implies(V1,implies(V2,not(V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h33630]) ).
cnf(h2860,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1925,h6]) ).
cnf(h2958,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1692,h2860]) ).
cnf(h3682,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(implies(V0,V2),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2958]) ).
cnf(h72935,plain,
is_a_theorem(implies(implies(implies(implies(V0,not(V1)),V2),implies(V0,not(V1))),implies(V1,implies(V3,not(V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3682,h33729]) ).
cnf(h3136,plain,
is_a_theorem(implies(V0,not(not(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h2868]) ).
cnf(h3247,plain,
is_a_theorem(implies(V0,not(not(implies(V1,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1025,h3136]) ).
cnf(h720,plain,
is_a_theorem(implies(implies(V0,not(V1)),implies(V1,implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h6]) ).
cnf(h4136,plain,
is_a_theorem(implies(not(implies(V0,V1)),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h720,h3247]) ).
cnf(h5271,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(V2,V0)),implies(V2,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1692,h4136]) ).
cnf(h73122,plain,
is_a_theorem(implies(V0,implies(implies(V1,not(V0)),not(V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5271,h72935]) ).
cnf(h2804,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(V1,implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h192,h1925]) ).
cnf(h73390,plain,
is_a_theorem(implies(implies(V0,not(V1)),implies(V1,not(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2804,h73122]) ).
cnf(t76,plain,
is_a_theorem(implies(implies(X1,implies(X2,not(X3))),implies(X1,implies(X3,not(X2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2852,h73390]) ).
cnf(t275,plain,
is_a_theorem(implies(implies(X1,implies(X2,not(X3))),implies(X1,implies(X3,not(X2))))) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,not(z))),implies(x,implies(z,not(y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_52) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(x,implies(y,not(z))),implies(x,implies(z,not(y))))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(x,implies(y,not(z))),implies(x,implies(z,not(y))))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(x,implies(y,not(z))),implies(x,implies(z,not(y))))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(x,implies(y,not(z))),implies(x,implies(z,not(y))))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t275]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL389-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.43 % Computer : n020.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8046.5625MB
% 0.11/0.43 % OS : Linux 6.8.0-71-generic
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Wed Sep 23 23:09:03 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 66.72/9.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.72/9.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------