%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:00:41 PM UTC 2026
% Result : Unsatisfiable 112.79s 14.75s
% Output : Proof 112.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 40 unt; 0 def)
% Number of atoms : 52 ( 31 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 : 7 ( 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 : 111 ( 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,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wn) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(X,Y)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X0,X1)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X0,X1)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(equivalent(V0,equivalent(V1,V2)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h3,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(equivalent(V2,equivalent(V0,V1)),V3)),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi1]) ).
cnf(h1,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,V2),equivalent(V1,equivalent(V2,V0))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h4,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V1,V2),equivalent(V1,equivalent(V2,V0))),V3)),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h1]) ).
cnf(h5,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,h0]) ).
cnf(h2,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(equivalent(equivalent(V0,equivalent(V1,V2)),V2),V3)),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h7,plain,
is_a_theorem(equivalent(V0,equivalent(V1,equivalent(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h5]) ).
cnf(h6,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,equivalent(equivalent(V2,V1),V2))),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h5]) ).
cnf(h31,plain,
is_a_theorem(equivalent(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h7]) ).
cnf(h45,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V0,V1)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h31]) ).
cnf(h89,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(V0,V1)),equivalent(V1,V2)),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h45]) ).
cnf(h42,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,V1),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h31]) ).
cnf(h60,plain,
is_a_theorem(equivalent(equivalent(V0,V0),equivalent(equivalent(V1,equivalent(V2,V3)),equivalent(V3,equivalent(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h42,hi1]) ).
cnf(h61,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,V1)),equivalent(equivalent(V2,V0),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,h60]) ).
cnf(h18,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,equivalent(equivalent(V2,V1),V2)),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h5]) ).
cnf(h330,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,V0),V1)),equivalent(equivalent(V2,equivalent(V3,V3)),equivalent(equivalent(V4,V2),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h18,h61]) ).
cnf(h355,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),V0),equivalent(equivalent(V2,equivalent(equivalent(V3,V2),V3)),equivalent(V1,equivalent(V4,V4))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h330]) ).
cnf(h528,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,V0),V1)),equivalent(equivalent(V2,equivalent(V3,equivalent(V3,V2))),equivalent(V4,V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h355,h89]) ).
cnf(h543,plain,
is_a_theorem(equivalent(equivalent(V0,V0),equivalent(equivalent(V1,equivalent(equivalent(V2,V1),V2)),equivalent(V3,equivalent(V4,equivalent(V4,V3)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h528]) ).
cnf(h16,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(V1,equivalent(V0,V1)),V2)),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h7]) ).
cnf(h546,plain,
is_a_theorem(equivalent(V0,equivalent(V1,equivalent(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h16,h543]) ).
cnf(h581,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h546]) ).
cnf(h798,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(V1,equivalent(V2,V3)),equivalent(equivalent(V3,equivalent(V1,V2)),V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h581,h3]) ).
cnf(h767,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,V1),equivalent(equivalent(V1,V0),V2)),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h581]) ).
cnf(h2704,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(V1,V2)),equivalent(equivalent(V2,V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h767,h798]) ).
cnf(t3,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X3)),equivalent(X3,X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2704]) ).
cnf(t306,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,X3)),equivalent(X3,X2)))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xgf) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))) != 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
% 0.00/0.05 % Problem : LCL014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 % Computer : n002.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 21:39:03 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 112.79/14.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 112.79/14.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------