%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:05:25 PM UTC 2026
% Result : Unsatisfiable 128.50s 27.54s
% Output : CNFRefutation 128.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of formulae : 84 ( 35 unt; 0 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 130 ( 66 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 228 ( 0 sgn 228 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',um) ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_yqj) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X0,X2)),equivalent(X2,X1)))),
inference(superposition,[status(thm)],[c_53,c_72]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X0,X2)),equivalent(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_76,c_52]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_86,c_52]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_86,c_107]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_115,c_52]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X0,X2)),equivalent(X2,X1)))),
inference(superposition,[status(thm)],[c_53,c_170]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_110]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_176,c_110]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,equivalent(X2,equivalent(X0,X1))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_86,c_110]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X0))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_191,c_52]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,X0),X2),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_191,c_170]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X0)),X3),X3))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_140]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X2)),
inference(superposition,[status(thm)],[c_53,c_192]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0))) ),
inference(superposition,[status(thm)],[c_321,c_52]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X0,X2)),equivalent(X2,X1)))),
inference(superposition,[status(thm)],[c_53,c_315]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_86,c_315]) ).
tcf(c_363,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X1),X0)),
inference(superposition,[status(thm)],[c_343,c_325]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_225,c_110]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_193,c_325]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_363,c_52]) ).
tcf(c_515,plain,
! [X0: $i] : is_a_theorem(equivalent(X0,X0)),
inference(superposition,[status(thm)],[c_363,c_511]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_414,c_511]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X1,X0)))),
inference(superposition,[status(thm)],[c_363,c_535]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X0),X1))),
inference(superposition,[status(thm)],[c_515,c_535]) ).
tcf(c_596,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),X2),X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_344,c_535]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X1,equivalent(X2,X0))),X2))),
inference(superposition,[status(thm)],[c_545,c_535]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X1,X0),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_546,c_52]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X0,equivalent(X1,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_662,c_535]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
inference(superposition,[status(thm)],[c_678,c_511]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_224,c_52]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(X2,X0))),X2))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_545,c_374]) ).
tcf(c_97516,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_97532,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X0)),X1)),
inference(superposition,[status(thm)],[c_53,c_715]) ).
tcf(c_97534,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X0),X1),X1)),
inference(superposition,[status(thm)],[c_363,c_715]) ).
tcf(c_97537,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X0))) ),
inference(superposition,[status(thm)],[c_97532,c_52]) ).
tcf(c_97539,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_97534,c_52]) ).
tcf(c_97568,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X0,equivalent(X1,equivalent(X2,X2)))),X1)),
inference(superposition,[status(thm)],[c_654,c_97539]) ).
tcf(c_97700,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X1,X0)))),
inference(superposition,[status(thm)],[c_363,c_97516]) ).
tcf(c_97811,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X0,X1))) ),
inference(superposition,[status(thm)],[c_97700,c_523]) ).
tcf(c_97832,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X0)) ),
inference(superposition,[status(thm)],[c_224,c_97811]) ).
tcf(c_97846,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X2))),equivalent(X1,X0))),
inference(superposition,[status(thm)],[c_97568,c_97516]) ).
tcf(c_98036,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),equivalent(equivalent(X0,X2),X2))),
inference(superposition,[status(thm)],[c_97846,c_97516]) ).
tcf(c_98655,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(equivalent(equivalent(X1,X2),X2),X1))),
inference(superposition,[status(thm)],[c_98036,c_97516]) ).
tcf(c_100116,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X2),X1),X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_98655,c_97832]) ).
tcf(c_100508,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X1),X0),X2)) ),
inference(superposition,[status(thm)],[c_100116,c_97811]) ).
tcf(c_102738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_890]) ).
tcf(c_102989,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X0),X1))),X2)),
inference(superposition,[status(thm)],[c_97532,c_192]) ).
tcf(c_103168,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X0),X1)))) ),
inference(superposition,[status(thm)],[c_102989,c_52]) ).
tcf(c_105457,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X2))) ),
inference(superposition,[status(thm)],[c_596,c_103168]) ).
tcf(c_105809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_253,c_52]) ).
tcf(c_106376,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X0)),equivalent(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_938,c_97516]) ).
tcf(c_107853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X0)),X1))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),X3))) ),
inference(superposition,[status(thm)],[c_53,c_102738]) ).
tcf(c_109170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X2,equivalent(equivalent(X3,X0),X1)))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_105809]) ).
tcf(c_122644,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_106376,c_52]) ).
tcf(c_124024,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,equivalent(equivalent(X1,X2),X0)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_122644]) ).
tcf(c_124301,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_124024,c_97537]) ).
tcf(c_124379,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X2,X0),X1))),
inference(superposition,[status(thm)],[c_53,c_124301]) ).
tcf(c_124639,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(equivalent(X1,X2),X0),X2))),
inference(superposition,[status(thm)],[c_124379,c_97516]) ).
tcf(c_124641,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X0,X2))),equivalent(X2,X1))),
inference(superposition,[status(thm)],[c_124379,c_192]) ).
tcf(c_124687,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X1),X2))),
inference(superposition,[status(thm)],[c_124379,c_109170]) ).
tcf(c_125823,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),X2)),X1)),
inference(superposition,[status(thm)],[c_124639,c_100508]) ).
tcf(c_125875,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X0,X2)))) ),
inference(superposition,[status(thm)],[c_124641,c_52]) ).
tcf(c_128372,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X0)),X2))),
inference(superposition,[status(thm)],[c_124687,c_125875]) ).
tcf(c_136314,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X0,X1),X1),X2),X2))),
inference(superposition,[status(thm)],[c_125823,c_105457]) ).
tcf(c_140198,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))),
inference(superposition,[status(thm)],[c_128372,c_107853]) ).
tcf(c_158305,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))),
inference(superposition,[status(thm)],[c_140198,c_124301]) ).
tcf(c_158310,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X1))) ),
inference(superposition,[status(thm)],[c_140198,c_52]) ).
tcf(c_158679,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X2),X1))),
inference(superposition,[status(thm)],[c_136314,c_158310]) ).
tcf(c_182187,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X0)),equivalent(X2,X1))),
inference(superposition,[status(thm)],[c_158305,c_192]) ).
tcf(c_184199,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X2,X1),X0))),
inference(superposition,[status(thm)],[c_158679,c_107853]) ).
tcf(c_214784,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X1),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_184199,c_52]) ).
tcf(c_215513,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),equivalent(X1,X2)))),
inference(superposition,[status(thm)],[c_182187,c_214784]) ).
tcf(c_215520,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_215513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 21:37:09 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 128.50/27.54 % SZS status Started for theBenchmark.p
% 128.50/27.54 % SZS status Unsatisfiable for theBenchmark.p
% 128.50/27.54
% 128.50/27.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 128.50/27.54
% 128.50/27.54 % ------ iProver source info
% 128.50/27.54
% 128.50/27.54 % git: date: 2026-07-19 20:42:38 +0200
% 128.50/27.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 128.50/27.54 % git: non_committed_changes: false
% 128.50/27.54
% 128.50/27.54 % ------ Parsing...% successful
% 128.50/27.54
% 128.50/27.54
% 128.50/27.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 128.50/27.54
% 128.50/27.54 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 128.50/27.54
% 128.50/27.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 128.50/27.54 % ------ Proving...
% 128.50/27.54 % ------ Problem Properties
% 128.50/27.54
% 128.50/27.54 %
% 128.50/27.54 % clauses 3
% 128.50/27.54 % conjectures 1
% 128.50/27.54 % EPR 0
% 128.50/27.54 % Horn 3
% 128.50/27.54 % unary 2
% 128.50/27.54 % binary 0
% 128.50/27.54 % lits 5
% 128.50/27.54 % lits eq 0
% 128.50/27.54 % fd_pure 0
% 128.50/27.54 % fd_pseudo 0
% 128.50/27.54 % fd_cond 0
% 128.50/27.54 % fd_pseudo_cond 0
% 128.50/27.54 % AC symbols 0
% 128.50/27.54
% 128.50/27.54 % ------ Input Options Time Limit: Unbounded
% 128.50/27.54
% 128.50/27.54
% 128.50/27.54 % ------
% 128.50/27.54 % Current options:
% 128.50/27.54 % ------
% 128.50/27.54
% 128.50/27.54
% 128.50/27.54 %
% 128.50/27.54
% 128.50/27.54 % ------ Proving...
% 128.50/27.54 %
% 128.50/27.54
% 128.50/27.54 % SZS status Unsatisfiable for theBenchmark.p
% 128.50/27.54
% 128.50/27.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 128.50/27.54
% 128.50/27.54
%------------------------------------------------------------------------------