%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:00:39 PM UTC 2026
% Result : Unsatisfiable 10.39s 1.93s
% Output : Proof 10.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 3
% Syntax : Number of formulae : 54 ( 50 unt; 0 def)
% Number of atoms : 62 ( 41 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 : 8 ( 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 : 178 ( 83 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(or(not(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(or(not(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(or(not(X),Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(or(not(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(or(not(or(not(or(not(X),Y)),or(Z,or(U,V)))),or(not(or(not(U),X)),or(Z,or(V,X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_CAMeredith) ).
fof(f1_nnf,plain,
! [X,Y,Z,U,V] : is_a_theorem(or(not(or(not(or(not(X),Y)),or(Z,or(U,V)))),or(not(or(not(U),X)),or(Z,or(V,X))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U,V] : is_a_theorem(or(not(or(not(or(not(X),Y)),or(Z,or(U,V)))),or(not(or(not(U),X)),or(Z,or(V,X))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(or(not(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))),or(not(or(not(X3),X0)),or(X2,or(X4,X0))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(or(not(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))),or(not(or(not(X3),X0)),or(X2,or(X4,X0))))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(or(not(or(not(V0),or(not(V1),V2))),or(not(or(not(V3),V1)),or(or(V4,V1),or(not(V1),V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),V2)),or(not(or(not(V3),V1)),or(or(not(V1),V4),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h2,plain,
is_a_theorem(or(not(or(not(or(not(V0),V1)),or(V2,V0))),or(not(or(not(V3),V0)),or(V4,or(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h3,plain,
is_a_theorem(or(not(or(not(V0),or(not(V1),or(V2,V1)))),or(V3,or(not(or(not(V4),V1)),or(not(V1),or(V2,V1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h2]) ).
cnf(h5,plain,
is_a_theorem(or(not(or(not(not(or(not(V0),V1))),V2)),or(V3,or(or(not(V1),or(V4,V1)),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3]) ).
cnf(h7,plain,
is_a_theorem(or(V0,or(not(or(not(V1),V2)),or(not(V2),or(or(not(V3),or(V4,V3)),V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h5]) ).
cnf(h13,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V1),or(or(not(V2),or(V3,V2)),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h7]) ).
cnf(h19,plain,
is_a_theorem(or(not(or(not(or(not(V0),or(V1,V0))),V2)),or(not(V3),or(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h13]) ).
cnf(h25,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(or(V2,V1),or(not(V1),or(V1,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h19]) ).
cnf(h37,plain,
is_a_theorem(or(not(or(not(not(V0)),V1)),or(or(V2,V0),or(or(V0,V3),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h25]) ).
cnf(h41,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),not(V0))),or(or(V2,V0),or(V3,not(V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h37]) ).
cnf(h51,plain,
is_a_theorem(or(not(or(not(V0),or(V1,not(V1)))),or(V2,or(or(V3,V1),or(V1,not(V1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h41]) ).
cnf(h82,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),V2)),or(V3,or(or(V1,not(V1)),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h51]) ).
cnf(h89,plain,
is_a_theorem(or(not(or(not(V0),or(or(V1,not(V1)),V1))),or(V2,or(V3,or(or(V1,not(V1)),V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h82]) ).
cnf(h195,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(V2,or(or(or(V3,not(V3)),V3),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h89]) ).
cnf(h210,plain,
is_a_theorem(or(not(or(not(or(or(V0,not(V0)),V0)),V1)),or(V2,or(V3,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h195]) ).
cnf(h231,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(or(not(V1),V2),or(V3,or(V4,V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h210]) ).
cnf(h235,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(or(not(V2),V3),or(or(V4,V2),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h231]) ).
cnf(h241,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),V2)),or(or(not(V1),V3),or(V4,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h235]) ).
cnf(h245,plain,
is_a_theorem(or(not(or(not(V0),or(V1,V2))),or(V3,or(or(not(V2),V4),or(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h241]) ).
cnf(h253,plain,
is_a_theorem(or(not(or(not(or(not(V0),V1)),V2)),or(V3,or(or(V4,V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h245]) ).
cnf(h256,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),or(not(V1),V2))),or(V3,or(V4,or(not(V1),V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h253]) ).
cnf(h278,plain,
is_a_theorem(or(V0,or(V1,or(not(V2),or(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h256,h210]) ).
cnf(h486,plain,
is_a_theorem(or(V0,or(not(V1),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h278,h278]) ).
cnf(h493,plain,
is_a_theorem(or(not(V0),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h486,h486]) ).
cnf(h495,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V2),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h486]) ).
cnf(h506,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V0),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h495]) ).
cnf(h770,plain,
is_a_theorem(or(not(V0),or(V1,or(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h506,h493]) ).
cnf(h1072,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(V2,or(or(not(V1),V3),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h770]) ).
cnf(h1074,plain,
is_a_theorem(or(not(or(not(or(not(V0),V1)),V2)),or(V3,or(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1072]) ).
cnf(h1086,plain,
is_a_theorem(or(not(or(not(V0),or(not(V0),V1))),or(V2,or(V3,or(not(V0),V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1074]) ).
cnf(h1101,plain,
is_a_theorem(or(V0,or(V1,or(not(V2),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1086,h493]) ).
cnf(h1326,plain,
is_a_theorem(or(V0,or(not(V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1101,h1101]) ).
cnf(h1401,plain,
is_a_theorem(or(not(V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1326,h1326]) ).
cnf(h1405,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(or(V0,V2)),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1326]) ).
cnf(t2,plain,
is_a_theorem(or(not(or(X1,X2)),or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1405,h1401]) ).
cnf(t262,plain,
is_a_theorem(or(not(or(X1,X2)),or(X2,X1))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_2) ).
fof(f2_nnf,plain,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(or(not(or(a,b)),or(b,a))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t262]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 21:41:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.39/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.39/1.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------