%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL060-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 02:00:48 PM UTC 2026
% Result : Unsatisfiable 87.28s 11.47s
% Output : Proof 87.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 67 unt; 0 def)
% Number of atoms : 79 ( 50 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 : 6 ( 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 : 165 ( 43 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(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(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/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]) ).
cnf(f3,axiom,
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(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(f2,axiom,
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(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(h8,plain,
is_a_theorem(implies(implies(not(implies(V0,V1)),implies(V0,V1)),implies(implies(not(V0),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h7]) ).
cnf(h503,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi2]) ).
cnf(h505,plain,
is_a_theorem(implies(not(implies(V0,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h503]) ).
cnf(h508,plain,
is_a_theorem(implies(implies(V0,V1),implies(not(implies(V2,V2)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h505]) ).
cnf(h1623,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V1)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h508]) ).
cnf(h1626,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1623]) ).
cnf(h1894,plain,
is_a_theorem(implies(V0,implies(implies(not(V1),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1626,h8]) ).
cnf(h1902,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1894]) ).
cnf(h2203,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(h2664,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2203,h1902]) ).
cnf(h2904,plain,
is_a_theorem(implies(V0,implies(implies(V1,implies(not(V2),V2)),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2664,h2664]) ).
cnf(h10,plain,
is_a_theorem(implies(implies(not(V0),V0),implies(not(V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi3]) ).
cnf(h188,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(implies(not(V0),V0),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h10]) ).
cnf(h192,plain,
is_a_theorem(implies(implies(not(V0),V0),implies(implies(V1,V2),implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h188,hi1]) ).
cnf(h1934,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(not(V2),V1)),V3),implies(implies(not(V2),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h192]) ).
cnf(h1939,plain,
is_a_theorem(implies(implies(not(V0),V0),implies(V1,implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1934,h1902]) ).
cnf(h2079,plain,
is_a_theorem(implies(V0,implies(V1,implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h1939]) ).
cnf(h2087,plain,
is_a_theorem(implies(implies(implies(V0,implies(not(V1),V2)),V3),implies(V1,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2079]) ).
cnf(h2911,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2087,h2664]) ).
cnf(h2934,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2664,h2911]) ).
cnf(h2214,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(h2512,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,h2214,hi1]) ).
cnf(h2951,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2512,h2934]) ).
cnf(h3246,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2664,h2951]) ).
cnf(h3315,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3246,h3246]) ).
cnf(h3626,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3315,h2904]) ).
cnf(h3643,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2203,h3626]) ).
cnf(h2946,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2934,h2934]) ).
cnf(h2976,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2946]) ).
cnf(h3700,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2976,h3643]) ).
cnf(h3885,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3700]) ).
cnf(h4811,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3885,h6]) ).
cnf(h4909,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3643,h4811]) ).
cnf(h4800,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V2,V0),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3885,h2203]) ).
cnf(h35406,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V2),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4800,h4909]) ).
cnf(h72421,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(V2,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2203,h35406]) ).
cnf(h87706,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(implies(V0,V2),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2203,h72421]) ).
cnf(h4754,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(V1,implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2203,h3885]) ).
cnf(h100127,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(V0,V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4754,h87706]) ).
cnf(h2213,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(t4,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X2),X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2213,h100127]) ).
cnf(t259,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X2),X2))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_54) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))) != 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 : LCL060-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 21:51:00 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 87.28/11.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.28/11.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------