%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 7.58s 1.41s
% Output : Proof 7.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% 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 : 166 ( 75 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/sandbox2/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/sandbox2/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(h9,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(h14,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,h9]) ).
cnf(h17,plain,
is_a_theorem(or(V0,or(not(or(not(V1),V2)),or(not(V2),or(V2,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h14]) ).
cnf(h27,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V1),or(V1,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h17,h17]) ).
cnf(h34,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V0),or(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h27]) ).
cnf(h38,plain,
is_a_theorem(or(not(or(not(V0),V0)),or(not(V0),or(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h34]) ).
cnf(h42,plain,
is_a_theorem(or(V0,or(not(or(not(V1),V2)),or(not(V2),or(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h38]) ).
cnf(h55,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V1),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h42,h42]) ).
cnf(h62,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V2),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h55]) ).
cnf(h70,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(not(V0),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h62]) ).
cnf(h105,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(V2,or(not(V1),or(V3,V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h70,h55]) ).
cnf(h133,plain,
is_a_theorem(or(not(or(not(not(V0)),V1)),or(V2,or(or(V3,V0),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h105]) ).
cnf(h147,plain,
is_a_theorem(or(not(or(not(or(V0,V1)),not(V1))),or(V2,or(V3,not(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h133]) ).
cnf(h61,plain,
is_a_theorem(or(not(or(not(V0),or(V1,V2))),or(V3,or(not(V2),or(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h55]) ).
cnf(h229,plain,
is_a_theorem(or(V0,or(not(or(V1,not(V2))),or(V3,or(V1,not(V2)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61,h147]) ).
cnf(h268,plain,
is_a_theorem(or(not(or(V0,not(V1))),or(V2,or(V0,not(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h229,h229]) ).
cnf(h275,plain,
is_a_theorem(or(not(or(not(not(V0)),V0)),or(V1,or(not(V2),V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h268]) ).
cnf(h286,plain,
is_a_theorem(or(V0,or(not(or(not(V1),V2)),or(V3,or(not(V1),V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61,h275]) ).
cnf(h308,plain,
is_a_theorem(or(not(or(not(V0),V1)),or(V2,or(not(V0),V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h286,h286]) ).
cnf(h316,plain,
is_a_theorem(or(not(or(not(not(V0)),V0)),or(V1,or(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h308]) ).
cnf(h339,plain,
is_a_theorem(or(V0,or(not(or(V1,V2)),or(V3,or(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61,h316]) ).
cnf(h353,plain,
is_a_theorem(or(not(or(V0,V1)),or(V2,or(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h339,h339]) ).
cnf(h358,plain,
is_a_theorem(or(not(or(V0,V1)),or(V2,or(V3,or(V0,V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h70,h353]) ).
cnf(h361,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,h358]) ).
cnf(h388,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,h361]) ).
cnf(h408,plain,
is_a_theorem(or(V0,or(V1,or(not(V2),or(V2,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h388,h62]) ).
cnf(h698,plain,
is_a_theorem(or(V0,or(not(V1),or(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h408,h408]) ).
cnf(h699,plain,
is_a_theorem(or(not(V0),or(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h698,h698]) ).
cnf(h717,plain,
is_a_theorem(or(V0,or(not(V1),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61,h699]) ).
cnf(t5,plain,
is_a_theorem(or(not(X1),or(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h717,h717]) ).
cnf(t306,plain,
is_a_theorem(or(not(X1),or(X2,X1))) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(or(not(a),or(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_3) ).
fof(f2_nnf,plain,
~ is_a_theorem(or(not(a),or(b,a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(or(not(a),or(b,a))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(or(not(a),or(b,a))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(or(not(a),or(b,a))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t306]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 21:38:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.58/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.58/1.41 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------