%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP011+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Tue Sep 29 11:28:01 AM UTC 2026
% Result : Theorem 5.33s 2.03s
% Output : Refutation 9.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 20 unt; 7 def)
% Number of atoms : 470 ( 253 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 504 ( 162 ~; 212 |; 107 &)
% ( 19 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-5 aty)
% Number of variables : 240 ( 0 sgn 228 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
fof(f42,axiom,
! [X0,X1] :
( s(X0,X1) = s(X0,X1)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
fof(f43,axiom,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
<=> s(X0,X5) = s(X0,X6) )
& ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
& ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
& ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [X11] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
<=> s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
& ! [X12] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
<=> s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
& ! [X13] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
=> s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13) )
& ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
& ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
& ! [X16] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16))))
=> s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4) )
& ! [X17] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))
=> s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))) )
& ! [X18] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18))))
=> s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18) )
& ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
& ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
& ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
& ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).
fof(f45,axiom,
! [X0,X1,X2,X3,X4] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
<=> ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
| ? [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).
fof(f46,conjecture,
! [X0,X1,X2,X3] :
( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).
fof(f47,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1))) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
<=> s(X0,X5) = s(X0,X6) )
& ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
& ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
& ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [X11] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
<=> s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
& ! [X12] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
<=> s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
& ! [X13] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13)))) )
& ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
& ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
& ! [X16] :
( s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16)))) )
& ! [X17] :
( s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17)))) )
& ! [X18] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18)))) )
& ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
& ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
& ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
& ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27) ),
inference(ennf_transformation,[],[f44]) ).
fof(f57,plain,
? [X0,X1,X2,X3] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1)))))
| s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f90,plain,
! [X0,X1] :
( ( s(X0,X1) = s(X0,X1)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(X0,X1) != s(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f91,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f92,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
| s(X0,X5) != s(X0,X6) )
& ( s(X0,X5) = s(X0,X6)
| s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6))) ) )
& ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
& ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
& ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [X11] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
| s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X11) )
& ( s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11)))) ) )
& ! [X12] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
| s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X12) )
& ( s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12)))) ) )
& ! [X13] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13)))) )
& ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
& ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
& ! [X16] :
( s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16)))) )
& ! [X17] :
( s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17)))) )
& ! [X18] :
( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18)))) )
& ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
& ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
& ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
& ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27) ),
inference(nnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| ( ( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
& ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ) ) )
& ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
| ? [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| ( ( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
& ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ) ) )
& ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
| ? [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| ( ( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
& ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ) ) )
& ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
| ? [X7,X8] :
( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7)))
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X8)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X7))),s(X1,X8)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| ( ( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
& ! [X5,X6] :
( s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
| s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ) ) )
& ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
| ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK3(X0,X1,X2,X3,X4))))
& s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,sK4(X0,X1,X2,X3,X4))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,sK3(X0,X1,X2,X3,X4)))),s(X1,sK4(X0,X1,X2,X3,X4))))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X7,sK3(X0,X1,X2,X3,X4)),skolemize(X8,sK4(X0,X1,X2,X3,X4))],[f96]) ).
fof(f98,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f57]) ).
fof(f104,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f196,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(X0,X1) != s(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f198,plain,
! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f203,plain,
! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f217,plain,
! [X0,X13] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
| s(tyop_2Eoption_2Eoption(X0),X13) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) ),
inference(cnf_transformation,[],[f93]) ).
fof(f218,plain,
! [X0,X12] :
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
| s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(X0),X12) ),
inference(cnf_transformation,[],[f93]) ).
fof(f222,plain,
! [X0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))),
inference(cnf_transformation,[],[f93]) ).
fof(f223,plain,
! [X10,X0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))),
inference(cnf_transformation,[],[f93]) ).
fof(f224,plain,
! [X0,X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))),
inference(cnf_transformation,[],[f93]) ).
fof(f226,plain,
! [X0,X7] : s(X0,X7) = s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))),
inference(cnf_transformation,[],[f93]) ).
fof(f231,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK3(X0,X1,X2,X3,X4))))
| s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f232,plain,
! [X2,X3,X0,X1,X4] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,sK3(X0,X1,X2,X3,X4)))),s(X1,sK4(X0,X1,X2,X3,X4)))))
| s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f233,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,sK4(X0,X1,X2,X3,X4))))
| s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f234,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK3(X0,X1,X2,X3,X4))))
| s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f235,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
| s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f236,plain,
! [X2,X3,X0,X1,X4] :
( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
| s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f237,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f238,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(trivial_inequality_removal,[],[f196]) ).
fof(f242,definition,
( spl9_1
<=> s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f243,plain,
( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| spl9_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl9_2
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f246,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| spl9_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl9_3
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0))) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f249,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| spl9_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,definition,
( spl9_4
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0))) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f252,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| spl9_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f237,f251,f248,f245,f242]) ).
fof(f269,plain,
! [X0,X1] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(superposition,[],[f104,f104]) ).
fof(f275,definition,
( spl9_7
<=> ! [X0] : s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f276,plain,
( ! [X0] : s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f281,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| spl9_1 ),
inference(superposition,[],[f243,f104]) ).
fof(f283,definition,
( spl9_9
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f284,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,definition,
( spl9_10
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f287,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| spl9_10 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( spl9_9
| ~ spl9_10
| spl9_1 ),
inference(avatar_split_clause,[],[f281,f242,f286,f283]) ).
fof(f292,plain,
! [X2,X3,X0,X1,X4,X5] :
( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2)))
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool)),X4),s(tyop_2Eoption_2Eoption(X0),X1),s(tyop_2Eoption_2Eoption(X3),c_2Eoption_2ESOME_2E1(s(X3,X5))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool)),X4),s(X0,X2))),s(X3,X5)))) ),
inference(equality_resolution,[],[f235]) ).
fof(f296,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X3))),s(X1,X4))))
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X3))),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X4)))))) ),
inference(equality_resolution,[],[f292]) ).
fof(f303,plain,
! [X2,X3,X0,X1] :
( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),X1),s(tyop_2Eoption_2Eoption(X2),c_2Eoption_2ENONE_2E0)))) ),
inference(equality_resolution,[],[f236]) ).
fof(f304,plain,
! [X2,X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)))),
inference(equality_resolution,[],[f303]) ).
fof(f355,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0))),
inference(resolution,[],[f304,f203]) ).
fof(f453,plain,
! [X0,X1] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))
| s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
inference(resolution,[],[f218,f198]) ).
fof(f464,plain,
! [X0,X1] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
inference(superposition,[],[f453,f223]) ).
fof(f496,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| spl9_10 ),
inference(superposition,[],[f287,f104]) ).
fof(f497,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| spl9_10 ),
inference(trivial_inequality_removal,[],[f496]) ).
fof(f500,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| spl9_10 ),
inference(superposition,[],[f296,f497]) ).
fof(f509,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f500,f238]) ).
fof(f812,plain,
( ! [X0] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| spl9_1 ),
inference(superposition,[],[f243,f269]) ).
fof(f888,plain,
( ! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| spl9_1
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f812,f497]) ).
fof(f944,plain,
( ! [X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) )
| spl9_1
| spl9_10 ),
inference(superposition,[],[f217,f888]) ).
fof(f1006,plain,
( ! [X0,X1] :
( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) )
| spl9_1
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f944,f509]) ).
fof(f1025,plain,
( ! [X0,X1] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) )
| spl9_1
| spl9_10 ),
inference(superposition,[],[f223,f1006]) ).
fof(f1058,plain,
( ! [X0,X1] : s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))
| spl9_1
| spl9_10 ),
inference(duplicate_literal_removal,[],[f1025]) ).
fof(f1067,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| spl9_1
| spl9_10 ),
inference(superposition,[],[f1058,f222]) ).
fof(f1092,plain,
( $false
| spl9_4 ),
inference(forward_subsumption_resolution,[],[f252,f355]) ).
fof(f1093,plain,
spl9_4,
inference(avatar_contradiction_clause,[],[f1092]) ).
fof(f1098,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| spl9_2 ),
inference(superposition,[],[f246,f104]) ).
fof(f1099,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| spl9_2 ),
inference(trivial_inequality_removal,[],[f1098]) ).
fof(f1106,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))
| spl9_2 ),
inference(superposition,[],[f231,f1099]) ).
fof(f1117,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f1106,f238]) ).
fof(f1120,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f1117,f224]) ).
fof(f1124,plain,
( $false
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f1120,f224]) ).
fof(f1125,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f1124]) ).
fof(f1130,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| spl9_3 ),
inference(superposition,[],[f249,f104]) ).
fof(f1131,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0)))
| spl9_3 ),
inference(trivial_inequality_removal,[],[f1130]) ).
fof(f1137,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ENONE_2E0))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| spl9_3 ),
inference(superposition,[],[f233,f1131]) ).
fof(f1150,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ENONE_2E0))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f1137,f238]) ).
fof(f1153,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ENONE_2E0))))
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f1150,f224]) ).
fof(f1156,plain,
( $false
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f1153,f224]) ).
fof(f1157,plain,
spl9_3,
inference(avatar_contradiction_clause,[],[f1156]) ).
fof(f1177,plain,
( ! [X0,X1] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| spl9_1
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f464,f1067]) ).
fof(f1183,plain,
( $false
| spl9_1
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f1177,f224]) ).
fof(f1184,plain,
( spl9_1
| spl9_10 ),
inference(avatar_contradiction_clause,[],[f1183]) ).
fof(f1189,plain,
( ! [X0,X1] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f464,f276]) ).
fof(f1195,plain,
( $false
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f1189,f224]) ).
fof(f1196,plain,
~ spl9_7,
inference(avatar_contradiction_clause,[],[f1195]) ).
fof(f1198,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| spl9_1
| ~ spl9_9 ),
inference(forward_demodulation,[],[f243,f284]) ).
fof(f1208,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| ~ spl9_9 ),
inference(superposition,[],[f233,f284]) ).
fof(f1209,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| ~ spl9_9 ),
inference(superposition,[],[f234,f284]) ).
fof(f1220,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1209,f238]) ).
fof(f1221,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1208,f238]) ).
fof(f1224,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1220,f224]) ).
fof(f1225,plain,
( s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1221,f224]) ).
fof(f1228,plain,
( s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))) = s(sK5,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))))
| ~ spl9_9 ),
inference(superposition,[],[f226,f1224]) ).
fof(f1266,plain,
( s(sK5,sK7) = s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))
| ~ spl9_9 ),
inference(forward_demodulation,[],[f1228,f226]) ).
fof(f1267,plain,
( s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))) = s(sK5,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))
| ~ spl9_9 ),
inference(superposition,[],[f226,f1225]) ).
fof(f1305,plain,
( s(sK5,sK6) = s(sK5,sK4(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))
| ~ spl9_9 ),
inference(forward_demodulation,[],[f1267,f226]) ).
fof(f1307,plain,
( ! [X0] :
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| spl9_1
| ~ spl9_9 ),
inference(superposition,[],[f1198,f269]) ).
fof(f1311,plain,
( ! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6)))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| spl9_1
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f1307]) ).
fof(f1431,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))),s(sK5,sK6))))
| s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| ~ spl9_9 ),
inference(superposition,[],[f232,f1305]) ).
fof(f1438,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK3(sK5,sK5,sK8,c_2Eoption_2ESOME_2E1(s(sK5,sK7)),c_2Eoption_2ESOME_2E1(s(sK5,sK6)))))),s(sK5,sK6))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1431,f224]) ).
fof(f1440,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK7))),s(tyop_2Eoption_2Eoption(sK5),c_2Eoption_2ESOME_2E1(s(sK5,sK6))))))
| ~ spl9_9 ),
inference(forward_demodulation,[],[f1438,f1266]) ).
fof(f1450,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))))
| ~ spl9_9 ),
inference(forward_demodulation,[],[f1440,f284]) ).
fof(f1452,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool)),sK8),s(sK5,sK7))),s(sK5,sK6))))
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1450,f238]) ).
fof(f1458,plain,
( ! [X0] :
( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| spl9_1
| ~ spl9_9 ),
inference(superposition,[],[f1452,f1311]) ).
fof(f1468,plain,
( ! [X0] : s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| spl9_1
| ~ spl9_9 ),
inference(forward_subsumption_resolution,[],[f1458,f203]) ).
fof(f1477,plain,
( spl9_7
| spl9_1
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f1468,f283,f242,f275]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f253]) ).
cnf(s11,plain,
( spl9_1
| spl9_9
| ~ spl9_10 ),
inference(sat_conversion,[],[f288]) ).
cnf(s15,plain,
spl9_4,
inference(sat_conversion,[],[f1093]) ).
cnf(s17,plain,
spl9_2,
inference(sat_conversion,[],[f1125]) ).
cnf(s19,plain,
spl9_3,
inference(sat_conversion,[],[f1157]) ).
cnf(s24,plain,
( spl9_1
| spl9_10 ),
inference(sat_conversion,[],[f1184]) ).
cnf(s29,plain,
~ spl9_7,
inference(sat_conversion,[],[f1196]) ).
cnf(s45,plain,
( spl9_1
| spl9_7
| ~ spl9_9 ),
inference(sat_conversion,[],[f1477]) ).
cnf(s50,plain,
~ spl9_1,
inference(rat,[],[s1,s15,s19,s17]) ).
cnf(s51,plain,
~ spl9_9,
inference(rat,[],[s45,s29,s50]) ).
cnf(s52,plain,
spl9_10,
inference(rat,[],[s24,s50]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s11,s52,s51,s50]) ).
fof(f1478,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP011+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 11:59:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/2.03 % (2717853)Detected formulas, will run a generic FOF schedule.
% 5.33/2.03 % (2717862)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=131274128:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.33/2.03 % (2717862)Instruction limit reached!
% 5.33/2.03 % (2717862)------------------------------
% 5.33/2.03 % (2717862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717862)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717862)Termination reason: Instruction limit
% 5.33/2.03 % (2717862)Termination phase: Saturation
% 5.33/2.03 % (2717862)Time elapsed: 0.032 s
% 5.33/2.03 % (2717862)Peak memory usage: 88 MB
% 5.33/2.03 % (2717862)Instructions burned: 123 (million)
% 5.33/2.03 % (2717861)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2611488240:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.33/2.03 % (2717858)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=322782918:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.33/2.03 % (2717859)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1380000613:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.33/2.03 % (2717860)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2314669441:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.33/2.03 % (2717863)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2547400359:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.33/2.03 % (2717864)dis-21_1_sil=8000:lcm=predicate:random_seed=3329752739:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.33/2.03 % (2717861)Instruction limit reached!
% 5.33/2.03 % (2717861)------------------------------
% 5.33/2.03 % (2717861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717861)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717861)Termination reason: Instruction limit
% 5.33/2.03 % (2717861)Termination phase: Saturation
% 5.33/2.03 % (2717861)Time elapsed: 0.058 s
% 5.33/2.03 % (2717861)Peak memory usage: 88 MB
% 5.33/2.03 % (2717861)Instructions burned: 111 (million)
% 5.33/2.03 % (2717864)Instruction limit reached!
% 5.33/2.03 % (2717864)------------------------------
% 5.33/2.03 % (2717864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717864)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717864)Termination reason: Instruction limit
% 5.33/2.03 % (2717864)Termination phase: Saturation
% 5.33/2.03 % (2717864)Time elapsed: 0.080 s
% 5.33/2.03 % (2717864)Peak memory usage: 89 MB
% 5.33/2.03 % (2717864)Instructions burned: 129 (million)
% 5.33/2.03 % (2717863)Instruction limit reached!
% 5.33/2.03 % (2717863)------------------------------
% 5.33/2.03 % (2717863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717863)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717863)Termination reason: Instruction limit
% 5.33/2.03 % (2717863)Termination phase: Saturation
% 5.33/2.03 % (2717863)Time elapsed: 0.086 s
% 5.33/2.03 % (2717863)Peak memory usage: 89 MB
% 5.33/2.03 % (2717863)Instructions burned: 140 (million)
% 5.33/2.03 % (2717870)lrs+10_1_sil=8000:sp=occurrence:random_seed=3677376250:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.33/2.03 % (2717870)Instruction limit reached!
% 5.33/2.03 % (2717870)------------------------------
% 5.33/2.03 % (2717870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717870)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717870)Termination reason: Instruction limit
% 5.33/2.03 % (2717870)Termination phase: Saturation
% 5.33/2.03 % (2717870)Time elapsed: 0.082 s
% 5.33/2.03 % (2717870)Peak memory usage: 90 MB
% 5.33/2.03 % (2717870)Instructions burned: 285 (million)
% 5.33/2.03 % (2717873)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3022230366:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.33/2.03 % (2717874)lrs+1011_1_sil=32000:sp=occurrence:random_seed=617439090:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.33/2.03 % (2717876)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1821823520:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.33/2.03 % (2717877)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1515696503:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.33/2.03 % (2717873)Instruction limit reached!
% 5.33/2.03 % (2717873)------------------------------
% 5.33/2.03 % (2717873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717873)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717873)Termination reason: Instruction limit
% 5.33/2.03 % (2717873)Termination phase: Saturation
% 5.33/2.03 % (2717873)Time elapsed: 0.089 s
% 5.33/2.03 % (2717873)Peak memory usage: 89 MB
% 5.33/2.03 % (2717873)Instructions burned: 159 (million)
% 5.33/2.03 % (2717877)Instruction limit reached!
% 5.33/2.03 % (2717877)------------------------------
% 5.33/2.03 % (2717877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717877)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717877)Termination reason: Instruction limit
% 5.33/2.03 % (2717877)Termination phase: Saturation
% 5.33/2.03 % (2717877)Time elapsed: 0.085 s
% 5.33/2.03 % (2717877)Peak memory usage: 90 MB
% 5.33/2.03 % (2717877)Instructions burned: 296 (million)
% 5.33/2.03 % (2717876)Instruction limit reached!
% 5.33/2.03 % (2717876)------------------------------
% 5.33/2.03 % (2717876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717876)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717876)Termination reason: Instruction limit
% 5.33/2.03 % (2717876)Termination phase: Saturation
% 5.33/2.03 % (2717876)Time elapsed: 0.144 s
% 5.33/2.03 % (2717876)Peak memory usage: 90 MB
% 5.33/2.03 % (2717876)Instructions burned: 249 (million)
% 5.33/2.03 % (2717874)Instruction limit reached!
% 5.33/2.03 % (2717874)------------------------------
% 5.33/2.03 % (2717874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717874)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717874)Termination reason: Instruction limit
% 5.33/2.03 % (2717874)Termination phase: Saturation
% 5.33/2.03 % (2717874)Time elapsed: 0.183 s
% 5.33/2.03 % (2717874)Peak memory usage: 90 MB
% 5.33/2.03 % (2717874)Instructions burned: 325 (million)
% 5.33/2.03 % (2717882)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2125933794:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.33/2.03 % (2717883)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2495424457:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.33/2.03 % (2717884)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2178928152:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.33/2.03 % (2717884)Refutation not found, incomplete strategy
% 5.33/2.03 % (2717884)------------------------------
% 5.33/2.03 % (2717884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717884)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717884)Termination reason: Refutation not found, incomplete strategy
% 5.33/2.03 % (2717884)Time elapsed: 0.005 s
% 5.33/2.03 % (2717884)Peak memory usage: 88 MB
% 5.33/2.03 % (2717884)Instructions burned: 9 (million)
% 5.33/2.03 % (2717883)Instruction limit reached!
% 5.33/2.03 % (2717883)------------------------------
% 5.33/2.03 % (2717883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717883)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717883)Termination reason: Instruction limit
% 5.33/2.03 % (2717883)Termination phase: Saturation
% 5.33/2.03 % (2717883)Time elapsed: 0.030 s
% 5.33/2.03 % (2717883)Peak memory usage: 89 MB
% 5.33/2.03 % (2717883)Instructions burned: 115 (million)
% 5.33/2.03 % (2717885)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4276174668:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 5.33/2.03 % (2717889)lrs+10_1_sil=8000:sp=occurrence:random_seed=2088908709:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 5.33/2.03 % (2717885)Instruction limit reached!
% 5.33/2.03 % (2717885)------------------------------
% 5.33/2.03 % (2717885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717885)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717885)Termination reason: Instruction limit
% 5.33/2.03 % (2717885)Termination phase: Saturation
% 5.33/2.03 % (2717885)Time elapsed: 0.059 s
% 5.33/2.03 % (2717885)Peak memory usage: 88 MB
% 5.33/2.03 % (2717885)Instructions burned: 115 (million)
% 5.33/2.03 % (2717884)------------------------------
% 5.33/2.03 % (2717884)------------------------------
% 5.33/2.03 % (2717892)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2220842703:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.33/2.03 % (2717892)Refutation not found, incomplete strategy
% 5.33/2.03 % (2717892)------------------------------
% 5.33/2.03 % (2717892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717892)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717892)Termination reason: Refutation not found, incomplete strategy
% 5.33/2.03 % (2717892)Time elapsed: 0.014 s
% 5.33/2.03 % (2717892)Peak memory usage: 89 MB
% 5.33/2.03 % (2717892)Instructions burned: 24 (million)
% 5.33/2.03 % (2717859)First to succeed.
% 5.33/2.03 % (2717859)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2717853"
% 5.33/2.03 % (2717889)Instruction limit reached!
% 5.33/2.03 % (2717889)------------------------------
% 5.33/2.03 % (2717889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717889)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717889)Termination reason: Instruction limit
% 5.33/2.03 % (2717889)Termination phase: Saturation
% 5.33/2.03 % (2717889)Time elapsed: 0.253 s
% 5.33/2.03 % (2717889)Peak memory usage: 92 MB
% 5.33/2.03 % (2717889)Instructions burned: 910 (million)
% 5.33/2.03 % (2717894)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=211577997:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 5.33/2.03 % (2717895)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1976239412:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2990 on theBenchmark for (2990ds/134Mi)
% 5.33/2.03 % (2717892)------------------------------
% 5.33/2.03 % (2717892)------------------------------
% 5.33/2.03 % (2717895)Instruction limit reached!
% 5.33/2.03 % (2717895)------------------------------
% 5.33/2.03 % (2717895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/2.03 % (2717895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/2.03 % (2717895)CaDiCaL version: 2.1.3
% 5.33/2.03 % (2717895)Termination reason: Instruction limit
% 5.33/2.03 % (2717895)Termination phase: Saturation
% 5.33/2.03 % (2717895)Time elapsed: 0.039 s
% 5.33/2.03 % (2717895)Peak memory usage: 90 MB
% 5.33/2.03 % (2717895)Instructions burned: 134 (million)
% 5.33/2.03 % (2717859)Refutation found. Thanks to Tanya!
% 5.33/2.03 % SZS status Theorem for theBenchmark
% 5.33/2.03 % SZS output start Proof for theBenchmark
% See solution above
% 9.01/2.23 % (2717859)------------------------------
% 9.01/2.23 % (2717859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.01/2.23 % (2717859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.01/2.23 % (2717859)CaDiCaL version: 2.1.3
% 9.01/2.23 % (2717859)Termination reason: Refutation
% 9.01/2.23 % (2717859)Time elapsed: 0.771 s
% 9.01/2.23 % (2717859)Peak memory usage: 131 MB
% 9.01/2.23 % (2717859)Instructions burned: 1172 (million)
% 9.01/2.23 % (2717859)------------------------------
% 9.01/2.23 % (2717859)------------------------------
% 9.01/2.23 % (2717853)Success in time 1.195 s
% 9.01/2.23 % Vampire exiting
%------------------------------------------------------------------------------