%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL119-1 : 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 : n015.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 02:05:43 PM UTC 2026
% Result : Unsatisfiable 83.81s 12.84s
% Output : CNFRefutation 83.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 99 ( 34 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 174 ( 88 ~; 86 |; 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 : 274 ( 0 sgn 274 !; 0 ?; 269 :)
% 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,equivalent(X2,X0)),equivalent(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xgj) ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(b,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wo) ).
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,equivalent(X2,X0)),equivalent(X1,X2)))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(b,a)))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X0)),equivalent(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_80,c_52]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,equivalent(X0,equivalent(X1,X2))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_84]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X1,X0)),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_80,c_84]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X0)),equivalent(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_121,c_52]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_86,c_52]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_124]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_52]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,X1)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_142]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_53,c_125]) ).
tcf(c_224,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_184,c_125]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,X0)))) ),
inference(superposition,[status(thm)],[c_53,c_222]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_222]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X0)),equivalent(X1,X2)))
| ~ 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(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_52]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),X0)),
inference(superposition,[status(thm)],[c_53,c_247]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,equivalent(X2,X2)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_281,c_224]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
inference(superposition,[status(thm)],[c_281,c_52]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_85,c_285]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(X1,X1))),
inference(superposition,[status(thm)],[c_281,c_285]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_277,c_52]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_278,c_285]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,X0),equivalent(X2,X2)),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_281,c_295]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X1)),equivalent(X2,X3)),X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_250]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,X2)))) ),
inference(superposition,[status(thm)],[c_281,c_250]) ).
tcf(c_370,plain,
! [X0: $i] : is_a_theorem(equivalent(X0,X0)),
inference(superposition,[status(thm)],[c_291,c_290]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_52]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,X1))) ),
inference(superposition,[status(thm)],[c_53,c_301]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X0,equivalent(X1,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_370,c_284]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X0,X1)),X1)),
inference(superposition,[status(thm)],[c_53,c_324]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : is_a_theorem(equivalent(X0,equivalent(X0,equivalent(X1,X1)))),
inference(superposition,[status(thm)],[c_370,c_324]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X0,X1))) ),
inference(superposition,[status(thm)],[c_429,c_52]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X1,equivalent(X0,equivalent(X2,X2)))))),
inference(superposition,[status(thm)],[c_429,c_324]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
inference(superposition,[status(thm)],[c_435,c_301]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_402,c_290]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(equivalent(X1,X1),X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_402,c_324]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_443]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X0),equivalent(X2,X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_306,c_450]) ).
tcf(c_583,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X2))),equivalent(X0,X1))),
inference(superposition,[status(thm)],[c_53,c_459]) ).
tcf(c_603,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,equivalent(X2,X2)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
inference(superposition,[status(thm)],[c_460,c_324]) ).
tcf(c_28772,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,X1)),X2)),
inference(superposition,[status(thm)],[c_53,c_476]) ).
tcf(c_28814,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,equivalent(X1,equivalent(X2,X2))))),
inference(superposition,[status(thm)],[c_583,c_476]) ).
tcf(c_28821,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_476]) ).
tcf(c_28834,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X0,equivalent(X2,X2)))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_446,c_52]) ).
tcf(c_29018,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X0,equivalent(X2,X2))),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_28834,c_476]) ).
tcf(c_29130,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_387,c_301]) ).
tcf(c_29216,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X0,equivalent(X1,X1))),equivalent(X2,X2))),
inference(superposition,[status(thm)],[c_583,c_603]) ).
tcf(c_29221,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X1)),X0),equivalent(X2,X2))),
inference(superposition,[status(thm)],[c_28814,c_603]) ).
tcf(c_29315,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X1,equivalent(X2,X2)))),X0)),
inference(superposition,[status(thm)],[c_29216,c_247]) ).
tcf(c_29326,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X2)),X1)),X0)),
inference(superposition,[status(thm)],[c_29221,c_247]) ).
tcf(c_29462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,X1)),X3)) ),
inference(superposition,[status(thm)],[c_53,c_29130]) ).
tcf(c_30028,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X2),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_562,c_187]) ).
tcf(c_30029,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X1),X2)),X0),X2)),
inference(superposition,[status(thm)],[c_583,c_187]) ).
tcf(c_30040,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X1),X2)),X2))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_29018,c_187]) ).
tcf(c_30043,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X1)),X2)),X2)),
inference(superposition,[status(thm)],[c_29315,c_187]) ).
tcf(c_30044,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X1)),equivalent(X0,X2)),X2)),
inference(superposition,[status(thm)],[c_29326,c_187]) ).
tcf(c_30110,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X0)),X1))),
inference(superposition,[status(thm)],[c_30029,c_476]) ).
tcf(c_30244,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X1)),X2))) ),
inference(superposition,[status(thm)],[c_30043,c_52]) ).
tcf(c_30263,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),equivalent(X0,X2))) ),
inference(superposition,[status(thm)],[c_30044,c_52]) ).
tcf(c_30306,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X2),X1)),X0)),
inference(superposition,[status(thm)],[c_30110,c_247]) ).
tcf(c_30356,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),X2)) ),
inference(superposition,[status(thm)],[c_85,c_30244]) ).
tcf(c_30428,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),X0),X2)) ),
inference(superposition,[status(thm)],[c_320,c_388]) ).
tcf(c_30431,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X2)) ),
inference(superposition,[status(thm)],[c_320,c_290]) ).
tcf(c_30442,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X0,X1)),X2),X1)) ),
inference(superposition,[status(thm)],[c_320,c_30263]) ).
tcf(c_30796,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X2),X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_30306,c_301]) ).
tcf(c_30798,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X2),X1))) ),
inference(superposition,[status(thm)],[c_30306,c_52]) ).
tcf(c_30947,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X2),equivalent(X0,X1))))),
inference(superposition,[status(thm)],[c_28772,c_30798]) ).
tcf(c_31169,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X1),equivalent(X2,X0))),X2)),
inference(superposition,[status(thm)],[c_30947,c_476]) ).
tcf(c_33917,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X0,equivalent(X2,equivalent(X2,X1))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_320,c_30356]) ).
tcf(c_34089,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X0),X1),equivalent(X2,X1))) ),
inference(superposition,[status(thm)],[c_30040,c_30428]) ).
tcf(c_34540,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X0,X1)),X2)) ),
inference(superposition,[status(thm)],[c_28821,c_30442]) ).
tcf(c_34570,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(X1,equivalent(X2,equivalent(X2,X1))))),
inference(superposition,[status(thm)],[c_31169,c_30442]) ).
tcf(c_34660,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X2,X1)))),X0)),
inference(superposition,[status(thm)],[c_34570,c_30431]) ).
tcf(c_34736,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X1,X0)),X2)),X2)),
inference(superposition,[status(thm)],[c_34660,c_187]) ).
tcf(c_34981,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(equivalent(X1,equivalent(X1,X2)),X2))),
inference(superposition,[status(thm)],[c_34736,c_30028]) ).
tcf(c_35416,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X1,X2)),X2)),X0)),
inference(superposition,[status(thm)],[c_34981,c_30431]) ).
tcf(c_35484,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X0,X1)),equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_35416,c_29462]) ).
tcf(c_36208,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(X0,X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_30796,c_476]) ).
tcf(c_39945,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X2,X0))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_35484]) ).
tcf(c_40346,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),X1)),X2)) ),
inference(superposition,[status(thm)],[c_320,c_34089]) ).
tcf(c_43853,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),X1)),X2))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_36208,c_187]) ).
tcf(c_45915,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X2,X0),equivalent(X2,X1)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(superposition,[status(thm)],[c_320,c_40346]) ).
tcf(c_46187,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X2))) ),
inference(superposition,[status(thm)],[c_43853,c_187]) ).
tcf(c_47523,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X2)) ),
inference(superposition,[status(thm)],[c_45915,c_30431]) ).
tcf(c_47546,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(equivalent(X0,X2),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_45915,c_34540]) ).
tcf(c_47597,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(superposition,[status(thm)],[c_39945,c_46187]) ).
tcf(c_47662,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(equivalent(X1,equivalent(X0,X2)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_33917,c_46187]) ).
tcf(c_49599,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),X2),equivalent(X0,X1))),
inference(superposition,[status(thm)],[c_28772,c_47546]) ).
tcf(c_49989,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X0,equivalent(X1,X2)))))),
inference(superposition,[status(thm)],[c_49599,c_47523]) ).
tcf(c_52349,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X0))),equivalent(X2,X1))),
inference(superposition,[status(thm)],[c_49989,c_47597]) ).
tcf(c_55200,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X1,X0)))),
inference(superposition,[status(thm)],[c_52349,c_47662]) ).
tcf(c_57226,plain,
$false,
inference(superposition,[status(thm)],[c_55200,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL119-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Sep 23 22:03:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 83.81/12.84 % SZS status Started for theBenchmark.p
% 83.81/12.84 % SZS status Unsatisfiable for theBenchmark.p
% 83.81/12.84
% 83.81/12.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 83.81/12.84
% 83.81/12.84 % ------ iProver source info
% 83.81/12.84
% 83.81/12.84 % git: date: 2026-07-19 20:42:38 +0200
% 83.81/12.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 83.81/12.84 % git: non_committed_changes: false
% 83.81/12.84
% 83.81/12.84 % ------ Parsing...% successful
% 83.81/12.84
% 83.81/12.84
% 83.81/12.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 83.81/12.84
% 83.81/12.84 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 83.81/12.84
% 83.81/12.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 83.81/12.84 % ------ Proving...
% 83.81/12.84 % ------ Problem Properties
% 83.81/12.84
% 83.81/12.84 %
% 83.81/12.84 % clauses 3
% 83.81/12.84 % conjectures 1
% 83.81/12.84 % EPR 0
% 83.81/12.84 % Horn 3
% 83.81/12.84 % unary 2
% 83.81/12.84 % binary 0
% 83.81/12.84 % lits 5
% 83.81/12.84 % lits eq 0
% 83.81/12.84 % fd_pure 0
% 83.81/12.84 % fd_pseudo 0
% 83.81/12.84 % fd_cond 0
% 83.81/12.84 % fd_pseudo_cond 0
% 83.81/12.84 % AC symbols 0
% 83.81/12.84
% 83.81/12.84 % ------ Input Options Time Limit: Unbounded
% 83.81/12.84
% 83.81/12.84
% 83.81/12.84 % ------
% 83.81/12.84 % Current options:
% 83.81/12.84 % ------
% 83.81/12.84
% 83.81/12.84
% 83.81/12.84 %
% 83.81/12.84
% 83.81/12.84 % ------ Proving...
% 83.81/12.84 %
% 83.81/12.84
% 83.81/12.84 % SZS status Unsatisfiable for theBenchmark.p
% 83.81/12.84
% 83.81/12.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 83.81/12.84
% 83.81/12.84
%------------------------------------------------------------------------------