%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:00:40 PM UTC 2026
% Result : Unsatisfiable 5.99s 11.28s
% Output : Proof 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 44 ( 23 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 : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(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(equivalent(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(equivalent(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(equivalent(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(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yql) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(b,c),a))),equivalent(equivalent(equivalent(b,c),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(b,c),a))),equivalent(equivalent(equivalent(b,c),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(b,c),a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(b,c),a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h13,h14]) ).
cnf(h12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)),equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(b,c),a)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h16,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h12,h15]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,c),equivalent(a,b)))) = true,
inference(hyper_resolution,[status(thm)],[hi1]) ).
cnf(h8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h7,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h9,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h8]) ).
cnf(h5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,h5]) ).
cnf(h10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h9]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2]) ).
cnf(h11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(b,c),a),equivalent(b,c))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h10]) ).
cnf(t2,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11,h16]) ).
cnf(t6,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ec_5) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.39 % Computer : n014.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Wed Sep 23 21:36:58 UTC 2026
% 0.10/10.40 % CPUTime :
% 0.10/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.99/11.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.99/11.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------