%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:00:57 PM UTC 2026
% Result : Unsatisfiable 3.67s 0.92s
% Output : Proof 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 30 unt; 0 def)
% Number of atoms : 42 ( 17 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 45 ( 0 sgn 18 !; 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(f2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_3) ).
fof(f2_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X0),X2)),X2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X0),X2)),X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_4) ).
fof(f1_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h7,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,h5]) ).
cnf(h8,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h7]) ).
cnf(h2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,hi1]) ).
cnf(h9,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h8]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi1]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi2]) ).
cnf(t4,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h9]) ).
cnf(t8,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p_1) ).
fof(f3_nnf,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.38 % Computer : n020.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 21:56:20 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.67/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.67/0.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------