%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL166-1 : 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 : n013.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 02:05:48 PM UTC 2026
% Result : Unsatisfiable 80.38s 11.80s
% Output : CNFRefutation 80.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 3
% Syntax : Number of formulae : 117 ( 16 unt; 0 def)
% Number of atoms : 294 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 356 ( 179 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 7 ( 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 : 337 ( 0 sgn 337 !; 0 ?; 332 :)
% 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(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xhn) ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_um) ).
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(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_82,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_52]) ).
tcf(c_83,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_82,c_52]) ).
tcf(c_84,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_83,c_52]) ).
tcf(c_124,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_52]) ).
tcf(c_125,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_124,c_52]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_84]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_124,c_84]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(X4)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X4),X2))),X0))) ),
inference(superposition,[status(thm)],[c_53,c_149]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X3,equivalent(X2,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_125,c_149]) ).
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_52]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(equivalent(X4,X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X4)),X0))) ),
inference(superposition,[status(thm)],[c_53,c_150]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X3))) ),
inference(superposition,[status(thm)],[c_191,c_150]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(X4)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X4)),X1)),X3))) ),
inference(superposition,[status(thm)],[c_53,c_155]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X3),X3))) ),
inference(superposition,[status(thm)],[c_191,c_155]) ).
tcf(c_254,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_52]) ).
tcf(c_278,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_254,c_153]) ).
tcf(c_280,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_254,c_215]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X1,equivalent(X3,X0)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_216]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_254,c_216]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_254,c_221]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X0)),X1)),X3))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_280]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_287,c_52]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_287,c_278]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_337]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_411,c_308]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_340]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X0)),equivalent(X3,equivalent(X1,X2))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_317,c_286]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_317,c_447]) ).
tcf(c_5327,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_52]) ).
tcf(c_5328,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_337,c_411]) ).
tcf(c_5329,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(renaming,[status(thm)],[c_5328]) ).
tcf(c_5337,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_5327,c_52]) ).
tcf(c_5401,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_431,c_994]) ).
tcf(c_5402,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(renaming,[status(thm)],[c_5401]) ).
tcf(c_5403,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_53,c_5402]) ).
tcf(c_5404,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_5327,c_5402]) ).
tcf(c_5415,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_5329,c_5403]) ).
tcf(c_5590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X3)),X0)),X2)) ),
inference(superposition,[status(thm)],[c_53,c_5415]) ).
tcf(c_5593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X0,X3)),X1))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_317,c_5415]) ).
tcf(c_5650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,equivalent(X3,X0)))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_5337,c_5590]) ).
tcf(c_5699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X2,equivalent(X0,X3)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_5593,c_52]) ).
tcf(c_5727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X1,equivalent(X3,X0)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_5329,c_5650]) ).
tcf(c_6707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,X3))) ),
inference(superposition,[status(thm)],[c_53,c_5699]) ).
tcf(c_6730,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_5327,c_6707]) ).
tcf(c_6843,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_6730]) ).
tcf(c_6844,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),equivalent(X1,X2)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_5327,c_6730]) ).
tcf(c_6928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X3)),X0)),X2),X3)),
inference(superposition,[status(thm)],[c_53,c_6843]) ).
tcf(c_7117,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_6844,c_5404]) ).
tcf(c_7519,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_6928,c_7117]) ).
tcf(c_7552,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X1,X0),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_7519,c_6843]) ).
tcf(c_7605,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X1,X1),X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_7552,c_6843]) ).
tcf(c_7610,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_7552,c_5404]) ).
tcf(c_7655,plain,
! [X0: $i] : is_a_theorem(equivalent(X0,X0)),
inference(superposition,[status(thm)],[c_6928,c_7610]) ).
tcf(c_7696,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X0),X1)),
inference(superposition,[status(thm)],[c_7655,c_6843]) ).
tcf(c_7753,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X0))) ),
inference(superposition,[status(thm)],[c_7696,c_5415]) ).
tcf(c_8489,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
inference(superposition,[status(thm)],[c_7605,c_7753]) ).
tcf(c_8603,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X1))
| ~ is_a_theorem(equivalent(X0,X0)) ),
inference(superposition,[status(thm)],[c_7605,c_8489]) ).
tcf(c_9017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X1,X3),X0))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X3))) ),
inference(superposition,[status(thm)],[c_53,c_5727]) ).
tcf(c_9460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X1,equivalent(X3,X2)),X0)),X3))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_9017]) ).
tcf(c_9546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X0)),X3))) ),
inference(superposition,[status(thm)],[c_9460,c_52]) ).
tcf(c_9608,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X1),X2),X2)) ),
inference(superposition,[status(thm)],[c_53,c_9546]) ).
tcf(c_10258,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_7519,c_9608]) ).
tcf(c_10777,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_52]) ).
tcf(c_10787,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_10777,c_52]) ).
tcf(c_10812,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_431,c_994]) ).
tcf(c_10813,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(renaming,[status(thm)],[c_10812]) ).
tcf(c_10815,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_10777,c_10813]) ).
tcf(c_12270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X2,equivalent(equivalent(X2,equivalent(X1,X3)),X3)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_515,c_286]) ).
tcf(c_12276,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X0,X2)),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_12270]) ).
tcf(c_12333,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X2)) ),
inference(superposition,[status(thm)],[c_12276,c_10813]) ).
tcf(c_12360,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_12276,c_220]) ).
tcf(c_12690,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_317,c_12333]) ).
tcf(c_12703,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X0))) ),
inference(superposition,[status(thm)],[c_10777,c_12360]) ).
tcf(c_12880,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_12690]) ).
tcf(c_12911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X3)),X0)),X2),X3)),
inference(superposition,[status(thm)],[c_53,c_12880]) ).
tcf(c_12969,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_10787,c_12703]) ).
tcf(c_13216,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X1)) ),
inference(global_subsumption_just,[status(thm)],[c_12969,c_10258]) ).
tcf(c_13237,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X2)),X0))),
inference(superposition,[status(thm)],[c_12911,c_13216]) ).
tcf(c_14942,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_13237,c_12690]) ).
tcf(c_20956,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X0)) ),
inference(superposition,[status(thm)],[c_14942,c_10815]) ).
tcf(c_25896,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_52]) ).
tcf(c_25897,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_337,c_411]) ).
tcf(c_25898,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(renaming,[status(thm)],[c_25897]) ).
tcf(c_25920,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_25896,c_153]) ).
tcf(c_25923,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_431,c_994]) ).
tcf(c_25924,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(renaming,[status(thm)],[c_25923]) ).
tcf(c_25926,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_25896,c_25924]) ).
tcf(c_25933,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_25898,c_25920]) ).
tcf(c_25973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X0,X3)),X1))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_317,c_25933]) ).
tcf(c_25995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X2,equivalent(X0,X3)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_25973,c_52]) ).
tcf(c_26549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,X3))) ),
inference(superposition,[status(thm)],[c_53,c_25995]) ).
tcf(c_26567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X0)),X3)),X2)) ),
inference(superposition,[status(thm)],[c_53,c_26549]) ).
tcf(c_26568,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_25896,c_26549]) ).
tcf(c_26680,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_53,c_26568]) ).
tcf(c_26681,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),equivalent(X1,X2)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_25896,c_26568]) ).
tcf(c_26794,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_26681,c_25926]) ).
tcf(c_26821,plain,
! [X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_26794,c_7655,c_20956]) ).
tcf(c_26822,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(renaming,[status(thm)],[c_26821]) ).
tcf(c_26831,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X1,X0),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_26822,c_26680]) ).
tcf(c_26866,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_26831,c_25926]) ).
tcf(c_26901,plain,
! [X1: $i] : is_a_theorem(equivalent(X1,X1)),
inference(global_subsumption_just,[status(thm)],[c_26866,c_7655,c_8603]) ).
tcf(c_26902,plain,
! [X0: $i] : is_a_theorem(equivalent(X0,X0)),
inference(renaming,[status(thm)],[c_26901]) ).
tcf(c_26911,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X0),X1)),
inference(superposition,[status(thm)],[c_26902,c_26680]) ).
tcf(c_27122,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,equivalent(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_26911,c_25926]) ).
tcf(c_27305,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),X1),X2))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_27122,c_26680]) ).
tcf(c_32106,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X0,equivalent(X2,X1))),X2))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_27305,c_26680]) ).
tcf(c_41312,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,X2),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_32106,c_26567]) ).
tcf(c_46181,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_41312]) ).
tcf(c_46391,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_46181,c_26680]) ).
tcf(c_47572,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
inference(superposition,[status(thm)],[c_46391,c_41312]) ).
tcf(c_48822,plain,
$false,
inference(superposition,[status(thm)],[c_47572,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL166-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 22:07:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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...
% 80.38/11.80 % SZS status Started for theBenchmark.p
% 80.38/11.80 % SZS status Unsatisfiable for theBenchmark.p
% 80.38/11.80
% 80.38/11.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 80.38/11.80
% 80.38/11.80 % ------ iProver source info
% 80.38/11.80
% 80.38/11.80 % git: date: 2026-07-19 20:42:38 +0200
% 80.38/11.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 80.38/11.80 % git: non_committed_changes: false
% 80.38/11.80
% 80.38/11.80 % ------ Parsing...% successful
% 80.38/11.80
% 80.38/11.80
% 80.38/11.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 80.38/11.80
% 80.38/11.80 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 80.38/11.80
% 80.38/11.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 80.38/11.80 % ------ Proving...
% 80.38/11.80 % ------ Problem Properties
% 80.38/11.80
% 80.38/11.80 %
% 80.38/11.80 % clauses 3
% 80.38/11.80 % conjectures 1
% 80.38/11.80 % EPR 0
% 80.38/11.80 % Horn 3
% 80.38/11.80 % unary 2
% 80.38/11.80 % binary 0
% 80.38/11.80 % lits 5
% 80.38/11.80 % lits eq 0
% 80.38/11.80 % fd_pure 0
% 80.38/11.80 % fd_pseudo 0
% 80.38/11.80 % fd_cond 0
% 80.38/11.80 % fd_pseudo_cond 0
% 80.38/11.80 % AC symbols 0
% 80.38/11.80
% 80.38/11.80 % ------ Input Options Time Limit: Unbounded
% 80.38/11.80
% 80.38/11.80
% 80.38/11.80 % ------
% 80.38/11.80 % Current options:
% 80.38/11.80 % ------
% 80.38/11.80
% 80.38/11.80
% 80.38/11.80 %
% 80.38/11.80
% 80.38/11.80 % ------ Proving...
% 80.38/11.80 %
% 80.38/11.80
% 80.38/11.80 % SZS status Unsatisfiable for theBenchmark.p
% 80.38/11.80
% 80.38/11.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.38/11.80
% 80.38/11.80
%------------------------------------------------------------------------------