%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 02:00:47 PM UTC 2026
% Result : Unsatisfiable 13.68s 2.12s
% Output : Proof 13.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 44 unt; 0 def)
% Number of atoms : 56 ( 27 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 : 12 ( 3 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 : 40 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(h0,plain,
is_a_theorem(implies(b,implies(not(b),a))) = true,
inference(hyper_resolution,[status(thm)],[hi3]) ).
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(h15,plain,
is_a_theorem(implies(implies(implies(not(b),a),a),implies(b,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
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(h14,plain,
is_a_theorem(implies(implies(implies(implies(not(b),a),a),implies(b,a)),implies(implies(not(implies(implies(not(b),a),a)),implies(implies(not(b),a),a)),implies(b,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h16,plain,
is_a_theorem(implies(implies(not(implies(implies(not(b),a),a)),implies(implies(not(b),a),a)),implies(b,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h14,h15]) ).
cnf(h12,plain,
is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(not(implies(implies(not(b),a),a)),implies(implies(not(b),a),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi3]) ).
cnf(h13,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(b),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h12]) ).
cnf(h17,plain,
is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h13,h16]) ).
cnf(h9,plain,
is_a_theorem(implies(not(implies(implies(not(a),a),a)),not(not(implies(implies(not(b),a),a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
cnf(h10,plain,
is_a_theorem(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h9]) ).
cnf(h7,plain,
is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a))),implies(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)))),implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a))),implies(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h8,plain,
is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a))),implies(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi1]) ).
cnf(h11,plain,
is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b),a),a))),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h8,h10]) ).
cnf(h18,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11,h17]) ).
cnf(h3,plain,
is_a_theorem(implies(implies(implies(implies(not(a),a),a),implies(implies(not(b),a),a)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h2,plain,
is_a_theorem(implies(implies(implies(implies(implies(not(a),a),a),implies(implies(not(b),a),a)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a))),implies(implies(implies(not(b),a),implies(not(a),a)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h4,plain,
is_a_theorem(implies(implies(implies(not(b),a),implies(not(a),a)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h3]) ).
cnf(h1,plain,
is_a_theorem(implies(implies(implies(implies(not(b),a),implies(not(a),a)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a))),implies(implies(not(a),not(b)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(not(a),not(b)),implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h4]) ).
cnf(h6,plain,
is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a),a),a)),implies(implies(not(a),a),a)),implies(implies(not(b),a),a)),implies(b,a)),implies(implies(not(a),not(b)),implies(b,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h5]) ).
cnf(t3,plain,
is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h18]) ).
cnf(t10,plain,
is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_49) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Wed Sep 23 21:45:27 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.68/2.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.68/2.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------