%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW900+1 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:33:24 PM UTC 2026
% Result : Theorem 118.07s 53.13s
% Output : CNFRefutation 118.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 29 unt; 0 def)
% Number of atoms : 256 ( 185 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 252 ( 56 ~; 41 |; 134 &)
% ( 16 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 82 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 12 con; 0-3 aty)
% Number of variables : 249 ( 7 sgn 192 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('thm.bool.EQ_CLAUSES',axiom,
! [X8] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,X8)
<=> p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,X8) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,X8)
<=> ~ p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,X8) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.bool.EQ_CLAUSES') ).
fof(conjecture,conjecture,
! [X7,X20,X29,X18,X19,X21] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X7),X29),s__02(c_27type_2elist_2elist_27__01(X7),X18))),s__02(c_27type_2elist_2elist_27__01(X20),X19))))
=> ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),X29),s__02(c_27type_2elist_2elist_27__01(X20),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X29))),s__02(c_27type_2elist_2elist_27__01(X20),X19))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),X18),s__02(c_27type_2elist_2elist_27__01(X20),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X29))),s__02(c_27type_2elist_2elist_27__01(X20),X19)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture) ).
fof('thm.rich_list.LIST_REL_APPEND_IMP',axiom,
! [X7,X20,X24,X25,X26,X27,X28] :
( ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X24),s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X7),X25),s__02(c_27type_2elist_2elist_27__01(X7),X27))),s__02(c_27type_2elist_2elist_27__01(X20),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X20),X26),s__02(c_27type_2elist_2elist_27__01(X20),X28))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X25))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X20),X26))) )
=> ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X24),s__02(c_27type_2elist_2elist_27__01(X7),X25),s__02(c_27type_2elist_2elist_27__01(X20),X26))))
& p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X24),s__02(c_27type_2elist_2elist_27__01(X7),X27),s__02(c_27type_2elist_2elist_27__01(X20),X28)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.rich_list.LIST_REL_APPEND_IMP') ).
fof('thm.list.TAKE_DROP',axiom,
! [X7,X15,X23] : s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2elist_2elist_27__01(X7),X23))),s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2elist_2elist_27__01(X7),X23))))) = s__02(c_27type_2elist_2elist_27__01(X7),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.list.TAKE_DROP') ).
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HL_TRUTH') ).
fof('thm.list.LIST_REL_LENGTH',axiom,
! [X7,X20,X21,X9,X22] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),X9),s__02(c_27type_2elist_2elist_27__01(X20),X22))))
=> s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X9))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X20),X22))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.list.LIST_REL_LENGTH') ).
fof('HL_BOOL_CASES',axiom,
! [X1] :
( s__02(cbool__00,X1) = s__02(cbool__00,cT__00)
| s__02(cbool__00,X1) = s__02(cbool__00,cF__00) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HL_BOOL_CASES') ).
fof('thm.numeral.numeral_distrib',axiom,
( ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))))
& ! [X15] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [X15] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [X15,X16] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16)))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,X16) )
& ! [X15] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& ! [X15] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(cbool__00,cF__00)
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(cbool__00,cT__00)
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ! [X15] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.numeral.numeral_distrib') ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HL_FALSITY') ).
fof('thm.arithmetic.ADD_MONO_LESS_EQ',axiom,
! [X16,X15,X17] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X17))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.arithmetic.ADD_MONO_LESS_EQ') ).
fof('thm.arithmetic.ADD_CLAUSES',axiom,
! [X15,X16] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X16))) = s__02(c_27type_2enum_2enum_27__00,X16)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X16)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X16))),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.arithmetic.ADD_CLAUSES') ).
fof('thm.list.LENGTH_TAKE',axiom,
! [X7,X15,X23] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X23))))))
=> s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2elist_2elist_27__01(X7),X23))))) = s__02(c_27type_2enum_2enum_27__00,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.list.LENGTH_TAKE') ).
fof('thm.list.LENGTH_APPEND',axiom,
! [X7,X18,X19] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X7),X18),s__02(c_27type_2elist_2elist_27__01(X7),X19))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X18))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X19))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm.list.LENGTH_APPEND') ).
fof(c_0_13,plain,
! [X8] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,X8)
<=> p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,X8) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,X8)
<=> ~ p__01(s__02(cbool__00,X8)) )
& ( s__02(cbool__00,X8) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,X8)) ) ),
inference(fof_simplification,[status(thm)],['thm.bool.EQ_CLAUSES']) ).
fof(c_0_14,negated_conjecture,
~ ! [X7,X20,X29,X18,X19,X21] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X7),X29),s__02(c_27type_2elist_2elist_27__01(X7),X18))),s__02(c_27type_2elist_2elist_27__01(X20),X19))))
=> ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),X29),s__02(c_27type_2elist_2elist_27__01(X20),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X29))),s__02(c_27type_2elist_2elist_27__01(X20),X19))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X7,cfun__02(X20,cbool__00)),X21),s__02(c_27type_2elist_2elist_27__01(X7),X18),s__02(c_27type_2elist_2elist_27__01(X20),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X7),X29))),s__02(c_27type_2elist_2elist_27__01(X20),X19)))))) ) ),
inference(assume_negation,[status(cth)],[conjecture]) ).
fof(c_0_15,plain,
! [X234,X235,X236,X237,X238,X239,X240] :
( ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X234,cfun__02(X235,cbool__00)),X236),s__02(c_27type_2elist_2elist_27__01(X234),X237),s__02(c_27type_2elist_2elist_27__01(X235),X238))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X234,cfun__02(X235,cbool__00)),X236),s__02(c_27type_2elist_2elist_27__01(X234),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X234),X237),s__02(c_27type_2elist_2elist_27__01(X234),X239))),s__02(c_27type_2elist_2elist_27__01(X235),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X235),X238),s__02(c_27type_2elist_2elist_27__01(X235),X240))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X234),X237))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X235),X238))) )
& ( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X234,cfun__02(X235,cbool__00)),X236),s__02(c_27type_2elist_2elist_27__01(X234),X239),s__02(c_27type_2elist_2elist_27__01(X235),X240))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X234,cfun__02(X235,cbool__00)),X236),s__02(c_27type_2elist_2elist_27__01(X234),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X234),X237),s__02(c_27type_2elist_2elist_27__01(X234),X239))),s__02(c_27type_2elist_2elist_27__01(X235),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X235),X238),s__02(c_27type_2elist_2elist_27__01(X235),X240))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X234),X237))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X235),X238))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['thm.rich_list.LIST_REL_APPEND_IMP'])])]) ).
fof(c_0_16,plain,
! [X231,X232,X233] : s__02(c_27type_2elist_2elist_27__01(X231),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X231),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X232),s__02(c_27type_2elist_2elist_27__01(X231),X233))),s__02(c_27type_2elist_2elist_27__01(X231),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,X232),s__02(c_27type_2elist_2elist_27__01(X231),X233))))) = s__02(c_27type_2elist_2elist_27__01(X231),X233),
inference(variable_rename,[status(thm)],['thm.list.TAKE_DROP']) ).
fof(c_0_17,plain,
! [X150] :
( ( s__02(cbool__00,cT__00) != s__02(cbool__00,X150)
| p__01(s__02(cbool__00,X150)) )
& ( ~ p__01(s__02(cbool__00,X150))
| s__02(cbool__00,cT__00) = s__02(cbool__00,X150) )
& ( s__02(cbool__00,X150) != s__02(cbool__00,cT__00)
| p__01(s__02(cbool__00,X150)) )
& ( ~ p__01(s__02(cbool__00,X150))
| s__02(cbool__00,X150) = s__02(cbool__00,cT__00) )
& ( s__02(cbool__00,cF__00) != s__02(cbool__00,X150)
| ~ p__01(s__02(cbool__00,X150)) )
& ( p__01(s__02(cbool__00,X150))
| s__02(cbool__00,cF__00) = s__02(cbool__00,X150) )
& ( s__02(cbool__00,X150) != s__02(cbool__00,cF__00)
| ~ p__01(s__02(cbool__00,X150)) )
& ( p__01(s__02(cbool__00,X150))
| s__02(cbool__00,X150) = s__02(cbool__00,cF__00) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_18,negated_conjecture,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))
& ( ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0)))))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,plain,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X2),X5))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X6),s__02(c_27type_2elist_2elist_27__01(X1),X4))),s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X2),X7),s__02(c_27type_2elist_2elist_27__01(X2),X5))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X6))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),X7))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X2),s__02(c_27type_2elist_2elist_27__01(X1),X3))),s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,X2),s__02(c_27type_2elist_2elist_27__01(X1),X3))))) = s__02(c_27type_2elist_2elist_27__01(X1),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( s__02(cbool__00,X1) = s__02(cbool__00,cT__00)
| ~ p__01(s__02(cbool__00,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0)))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,X5),s__02(c_27type_2elist_2elist_27__01(X2),X6))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X7))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X5),s__02(c_27type_2elist_2elist_27__01(X2),X6)))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X7),s__02(c_27type_2elist_2elist_27__01(X1),X4))),s__02(c_27type_2elist_2elist_27__01(X2),X6)))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))) = s__02(cbool__00,cT__00),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
p__01(s__02(cbool__00,cT__00)),
inference(split_conjunct,[status(thm)],['HL_TRUTH']) ).
fof(c_0_26,plain,
! [X223,X224,X225,X226,X227] :
( ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X223,cfun__02(X224,cbool__00)),X225),s__02(c_27type_2elist_2elist_27__01(X223),X226),s__02(c_27type_2elist_2elist_27__01(X224),X227))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X223),X226))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X224),X227))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['thm.list.LIST_REL_LENGTH'])]) ).
cnf(c_0_27,plain,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X2),X5))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X1),X6))),s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X2),X5),s__02(c_27type_2elist_2elist_27__01(X2),X7))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X4))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0)))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eDROP_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X4))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),X5)))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X2),X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X142] :
( s__02(cbool__00,X142) = s__02(cbool__00,cT__00)
| s__02(cbool__00,X142) = s__02(cbool__00,cF__00) ),
inference(variable_rename,[status(thm)],['HL_BOOL_CASES']) ).
fof(c_0_32,plain,
( ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X15)
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [X15,X16] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [X15] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))))
& ! [X15] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [X15] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [X15,X16] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16)))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,X16) )
& ! [X15] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& ! [X15] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(cbool__00,cF__00)
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))) = s__02(cbool__00,cT__00)
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,X16)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X15),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ! [X15] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X15))))
<=> s__02(c_27type_2enum_2enum_27__00,X15) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ! [X15,X16] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X16))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X16),s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
& ! [X15] : s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X15))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,X15)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ),
inference(fof_simplification,[status(thm)],['thm.numeral.numeral_distrib']) ).
cnf(c_0_33,plain,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X5),s__02(c_27type_2elist_2elist_27__01(X2),X6))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X4))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X5),s__02(c_27type_2elist_2elist_27__01(X2),X6)))))
| ~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(X1,cfun__02(X2,cbool__00)),X3),s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X4),s__02(c_27type_2elist_2elist_27__01(X1),X7))),s__02(c_27type_2elist_2elist_27__01(X2),X6)))) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_34,negated_conjecture,
~ p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0)))))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
( s__02(cbool__00,X1) = s__02(cbool__00,cT__00)
| s__02(cbool__00,X1) = s__02(cbool__00,cF__00) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,plain,
~ p__01(s__02(cbool__00,cF__00)),
inference(fof_simplification,[status(thm)],['HL_FALSITY']) ).
fof(c_0_37,plain,
! [X171,X172,X173] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X171),s__02(c_27type_2enum_2enum_27__00,X172))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X171),s__02(c_27type_2enum_2enum_27__00,X173))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X172),s__02(c_27type_2enum_2enum_27__00,X173))),
inference(variable_rename,[status(thm)],['thm.arithmetic.ADD_MONO_LESS_EQ']) ).
fof(c_0_38,plain,
! [X177,X178,X179,X180,X181,X182,X183,X184,X185,X186,X187,X188,X189,X190,X191,X192,X193,X194,X195,X196,X197,X198,X199,X200,X201,X202,X203,X204,X205,X206,X207,X208,X209,X210,X211,X212,X213,X214,X215,X216,X217] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X177))) = s__02(c_27type_2enum_2enum_27__00,X177)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X178),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X178)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X179))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X180))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X179),s__02(c_27type_2enum_2enum_27__00,X180)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X181))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X182),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X183))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X184))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,X183),s__02(c_27type_2enum_2enum_27__00,X184)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X185))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X186),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X186)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X187))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X188))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,X187),s__02(c_27type_2enum_2enum_27__00,X188)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,X189))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,X190))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X191),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X192))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X193))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,X192),s__02(c_27type_2enum_2enum_27__00,X193)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X194))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X194)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X195))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,X195)))))
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X196))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
| s__02(c_27type_2enum_2enum_27__00,X196) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ( s__02(c_27type_2enum_2enum_27__00,X196) != s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
| s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X196))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) != s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X197)))
| s__02(c_27type_2enum_2enum_27__00,X197) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ( s__02(c_27type_2enum_2enum_27__00,X197) != s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
| s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X197))) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X198))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X199)))
| s__02(c_27type_2enum_2enum_27__00,X198) = s__02(c_27type_2enum_2enum_27__00,X199) )
& ( s__02(c_27type_2enum_2enum_27__00,X198) != s__02(c_27type_2enum_2enum_27__00,X199)
| s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X198))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X199))) )
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X200),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X201))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X201)))
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X202))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X203))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X202),s__02(c_27type_2enum_2enum_27__00,X203)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X204))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X205))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,X205)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X206))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X207))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,X207),s__02(c_27type_2enum_2enum_27__00,X206)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X208))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X209))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X209),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X210))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X211))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X210),s__02(c_27type_2enum_2enum_27__00,X211)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X212),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ( ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X213))))
| s__02(c_27type_2enum_2enum_27__00,X213) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ( s__02(c_27type_2enum_2enum_27__00,X213) != s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
| p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X213)))) )
& s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X214))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X215))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X215),s__02(c_27type_2enum_2enum_27__00,X214)))
& s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X216))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,X216)))
& s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,X217))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,X217)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
fof(c_0_39,plain,
! [X159,X160] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X160))) = s__02(c_27type_2enum_2enum_27__00,X160)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X160),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X160)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X160))),s__02(c_27type_2enum_2enum_27__00,X159))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X160),s__02(c_27type_2enum_2enum_27__00,X159)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X160),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,X159))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X160),s__02(c_27type_2enum_2enum_27__00,X159))))) ),
inference(variable_rename,[status(thm)],['thm.arithmetic.ADD_CLAUSES']) ).
cnf(c_0_40,negated_conjecture,
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_25])]) ).
cnf(c_0_41,negated_conjecture,
s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(esk2_0,cfun__02(esk3_0,cbool__00)),esk7_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))) = s__02(cbool__00,cF__00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25])]) ).
cnf(c_0_42,plain,
~ p__01(s__02(cbool__00,cF__00)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_43,plain,
! [X228,X229,X230] :
( ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X229),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X228),X230))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X228),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X229),s__02(c_27type_2elist_2elist_27__01(X228),X230))))) = s__02(c_27type_2enum_2enum_27__00,X229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['thm.list.LENGTH_TAKE'])]) ).
cnf(c_0_44,plain,
s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,X2))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,X3))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X2),s__02(c_27type_2enum_2enum_27__00,X3))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,X1))) = s__02(cbool__00,cT__00),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_48,plain,
! [X220,X221,X222] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X220),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X220),X221),s__02(c_27type_2elist_2elist_27__01(X220),X222))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X220),X221))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X220),X222))))),
inference(variable_rename,[status(thm)],['thm.list.LENGTH_APPEND']) ).
cnf(c_0_49,negated_conjecture,
s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))) != s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,plain,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),c_27const_2elist_2eTAKE_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2elist_2elist_27__01(X2),X3))))) = s__02(c_27type_2enum_2enum_27__00,X1)
| ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X2),X3)))))) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,X1),s__02(c_27type_2enum_2enum_27__00,X2))))) = s__02(cbool__00,cT__00),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X2),s__02(c_27type_2elist_2elist_27__01(X1),X3))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X2))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X3))))),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,negated_conjecture,
~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0)))))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( s__02(cbool__00,X1) != s__02(cbool__00,cF__00)
| ~ p__01(s__02(cbool__00,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_55,plain,
s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),X2))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(X1),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X1),X2),s__02(c_27type_2elist_2elist_27__01(X1),X3))))))) = s__02(cbool__00,cT__00),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0),s__02(c_27type_2elist_2elist_27__01(esk2_0),esk5_0))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_25])]) ).
cnf(c_0_57,negated_conjecture,
s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk2_0),esk4_0))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(esk3_0),esk6_0))))) = s__02(cbool__00,cF__00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_25])]) ).
cnf(c_0_58,plain,
s__02(cbool__00,cT__00) != s__02(cbool__00,cF__00),
inference(spm,[status(thm)],[c_0_54,c_0_25]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW900+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 07:33:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 118.07/53.13 % Version : CSE_E---1.7
% 118.07/53.13 % Problem : theBenchmark.p
% 118.07/53.13 % SZS status Theorem for theBenchmark.p
% 118.07/53.13 % SZS output start CNFRefutation
% See solution above
% 118.35/53.47 % Total time : 38.791s
%------------------------------------------------------------------------------