%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP013_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:53:39 PM UTC 2026
% Result : Theorem 1.05s 0.59s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 145 ( 51 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 144 ( 37 ~; 38 |; 39 &)
% ( 18 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
d: $tType ).
tff(decl_sort2,type,
u: $tType ).
tff(decl_sort3,type,
du: $tType ).
tff(decl_sort4,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(decl_sort5,type,
mono_2Etyop_2Enum_2Enum: $tType ).
tff(decl_23,type,
tyop_2Efcp_2Ecart: ( d * d ) > d ).
tff(decl_24,type,
tyop_2Emin_2Ebool: d ).
tff(decl_26,type,
tyop_2Enum_2Enum: d ).
tff(decl_27,type,
s: ( u * d ) > du ).
tff(decl_29,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(decl_50,type,
c_2Ebool_2ECOND_2E3: ( du * ( du * du ) ) > u ).
tff(decl_56,type,
c_2Ewords_2En2w_2E1: du > u ).
tff(decl_58,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
tff(decl_60,type,
c_2Ewords_2Eword__add_2E2: ( du * du ) > u ).
tff(decl_62,type,
c_2Ewords_2Eword__sub_2E2: ( du * du ) > u ).
tff(decl_72,type,
mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_74,type,
mono_2Ec_2Earithmetic_2E_2D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_78,type,
mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_81,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_82,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_87,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(decl_94,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
tff(decl_103,type,
esk1_0: d ).
tff(decl_104,type,
esk2_0: mono_2Etyop_2Enum_2Enum ).
tff(decl_105,type,
esk3_0: mono_2Etyop_2Enum_2Enum ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(X8) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(X8) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
<=> p(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [X1: d,X2: d] :
( ! [X83: mono_2Etyop_2Enum_2Enum,X84: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X83)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X84)))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X84,X83))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X83,X84))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X84,X83))))))))) )
& ! [X81: mono_2Etyop_2Enum_2Enum,X82: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X81)))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X82)))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(X81,X82))))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
tff(thm_2Ewords_2Eword__sub__def,axiom,
! [X1: d,X79: u,X80: u] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X79),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X80))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X79),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X80))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( p(X6)
<=> p(X7) )
=> ( X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
tff(thm_2Ewords_2En2w__sub,conjecture,
! [X1: d,X85: mono_2Etyop_2Enum_2Enum,X86: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X86,X85))
=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X85,X86))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X85)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X86)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
tff(thm_2Ebool_2Ebool__case__thm,axiom,
! [X1: d] :
( ! [X77: u,X78: u] : ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X1,X77),s(X1,X78))) = s(X1,X78) )
& ! [X75: u,X76: u] : ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X1,X75),s(X1,X76))) = s(X1,X75) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
tff(reserved_2Eho_2Ebool__cases__ax,axiom,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
| ( X8 = mono_2Ec_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(X8)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ~ p(X8) )
& ( ( p(X8)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(X8)
=> p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2ET_2E0)
=> p(X8) )
<=> p(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
tff(c_0_9,plain,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(X8) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(X8) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
<=> p(X8) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES]) ).
tff(c_0_10,plain,
! [X96: d,X97: d,X98: mono_2Etyop_2Enum_2Enum,X99: mono_2Etyop_2Enum_2Enum,X100: mono_2Etyop_2Enum_2Enum,X101: mono_2Etyop_2Enum_2Enum] :
( ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X100)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X101)))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X101,X100))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X100,X101))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X97),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X101,X100))))))))) )
& ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X98)))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X99)))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X96),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(X98,X99))))))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ewords_2EWORD__LITERAL__ADD])]) ).
tff(c_0_11,plain,
! [X93: d,X94: u,X95: u] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),X94),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),X95))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),X94),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X93),X95))))) ),
inference(variable_rename,[status(thm)],[thm_2Ewords_2Eword__sub__def]) ).
tff(c_0_12,plain,
! [X127: mono_2Etyop_2Emin_2Ebool] :
( ( ( X127 = mono_2Ec_2Ebool_2EF_2E0 )
| p(X127) )
& ( ~ p(X127)
| ( X127 != mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X127 )
| p(X127) )
& ( ~ p(X127)
| ( mono_2Ec_2Ebool_2EF_2E0 != X127 ) )
& ( ( X127 = mono_2Ec_2Ebool_2ET_2E0 )
| ~ p(X127) )
& ( p(X127)
| ( X127 != mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X127 )
| ~ p(X127) )
& ( p(X127)
| ( mono_2Ec_2Ebool_2ET_2E0 != X127 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
tff(c_0_13,plain,
! [X102: mono_2Etyop_2Emin_2Ebool,X103: mono_2Etyop_2Emin_2Ebool] :
( ( ( X102 = X103 )
| p(X103)
| p(X102) )
& ( ( X102 = X103 )
| ~ p(X103)
| ~ p(X102) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
tff(c_0_14,negated_conjecture,
~ ! [X1: d,X85: mono_2Etyop_2Enum_2Enum,X86: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X86,X85))
=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X85,X86))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X85)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X86)))))) ) ),
inference(assume_negation,[status(cth)],[thm_2Ewords_2En2w__sub]) ).
tff(c_0_15,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
tcf(c_0_16,plain,
! [X1: d,X31: mono_2Etyop_2Enum_2Enum,X29: mono_2Etyop_2Enum_2Enum] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X29)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X31)))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X31,X29))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X29,X31))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X31,X29))))))))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_17,plain,
! [X1: d,X3: u,X4: u] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X3),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X4))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X3),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X4))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_18,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X6)
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_19,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = X7 )
| p(X7)
| p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tff(c_0_20,plain,
! [X118: d,X119: u,X120: u,X121: u,X122: u] :
( ( s(X118,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X118,X121),s(X118,X122))) = s(X118,X122) )
& ( s(X118,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X118,X119),s(X118,X120))) = s(X118,X119) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ebool_2Ebool__case__thm])]) ).
tff(c_0_21,negated_conjecture,
( ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(esk2_0,esk3_0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(esk2_0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(esk3_0)))))) )
& p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(esk3_0,esk2_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
tff(c_0_22,plain,
! [X125: mono_2Etyop_2Emin_2Ebool] :
( ( X125 = mono_2Ec_2Ebool_2EF_2E0 )
| ( X125 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
tff(c_0_23,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
tcf(c_0_24,plain,
! [X1: d,X31: mono_2Etyop_2Enum_2Enum,X29: mono_2Etyop_2Enum_2Enum] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X29,X31))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X31,X29))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X29,X31))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X31)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X29)))))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_25,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( p(X7)
| ( X7 = X6 )
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_26,plain,
! [X1: d,X4: u,X3: u] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X1,X3),s(X1,X4))) = s(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_27,negated_conjecture,
p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_28,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = mono_2Ec_2Ebool_2EF_2E0 )
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_29,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tff(c_0_30,plain,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(X8)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ~ p(X8) )
& p(mono_2Ec_2Ebool_2ET_2E0)
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(X8)
=> p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2ET_2E0)
=> p(X8) )
<=> p(X8) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EIMP__CLAUSES]) ).
tcf(c_0_31,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(esk2_0,esk3_0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(esk2_0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(esk3_0)))))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_32,plain,
! [X1: d,X31: mono_2Etyop_2Enum_2Enum,X29: mono_2Etyop_2Enum_2Enum,X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| ( X6 = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X31,X29) )
| ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X29)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X31)))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(X29,X31))))) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
tcf(c_0_33,negated_conjecture,
mono_2Ec_2Earithmetic_2E_3C_3D_2E2(esk3_0,esk2_0) = mono_2Ec_2Ebool_2ET_2E0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
tff(c_0_34,plain,
! [X126: mono_2Etyop_2Emin_2Ebool] :
( ( p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(X126)
| p(X126) )
& ( ~ p(X126)
| ~ p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ~ p(X126)
| p(X126) )
& p(mono_2Ec_2Ebool_2ET_2E0)
& ( p(X126)
| ~ p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X126) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| p(mono_2Ec_2Ebool_2EF_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X126)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| p(X126) )
& ( p(X126)
| ~ p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X126) )
& ( p(X126)
| ~ p(X126) )
& ( p(X126)
| p(mono_2Ec_2Ebool_2ET_2E0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
tcf(c_0_35,negated_conjecture,
! [X6: mono_2Etyop_2Emin_2Ebool] : X6 = mono_2Ec_2Ebool_2ET_2E0,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_18]) ).
tcf(c_0_36,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 21:46:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/0.59 % Version: 3.5.1
% 1.05/0.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.05/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.05/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.59 % Starting new_bool_1 with 300s (1) cores
% 1.05/0.59 % Starting sh5l with 300s (1) cores
% 1.05/0.59 % new_bool_3 with pid 3441247 completed with status 0
% 1.05/0.59 % Result found by new_bool_3
% 1.05/0.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.05/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.05/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.05/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.05/0.59 % Search class: FGHSM-FFMM31-DFFFFFNN
% 1.05/0.59 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.05/0.59 % Starting SubtermCWHack with 31s (1) cores
% 1.05/0.59 % SubtermCWHack with pid 3441252 completed with status 0
% 1.05/0.59 % Result found by SubtermCWHack
% 1.05/0.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.05/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.05/0.59 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.05/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.05/0.59 % Search class: FGHSM-FFMM31-DFFFFFNN
% 1.05/0.59 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.05/0.59 % Starting SubtermCWHack with 31s (1) cores
% 1.05/0.59 % Preprocessing time : 0.002 s
% 1.05/0.59
% 1.05/0.59 % Proof found!
% 1.05/0.59 % SZS status Theorem
% 1.05/0.59 % SZS output start CNFRefutation
% See solution above
% 1.05/0.60 % Parsed axioms : 159
% 1.05/0.60 % Removed by relevancy pruning/SinE : 141
% 1.05/0.60 % Initial clauses : 58
% 1.05/0.60 % Removed in clause preprocessing : 25
% 1.05/0.60 % Initial clauses in saturation : 33
% 1.05/0.60 % Processed clauses : 914
% 1.05/0.60 % ...of these trivial : 7
% 1.05/0.60 % ...subsumed : 819
% 1.05/0.60 % ...remaining for further processing : 88
% 1.05/0.60 % Other redundant clauses eliminated : 709
% 1.05/0.60 % Clauses deleted for lack of memory : 0
% 1.05/0.60 % Backward-subsumed : 18
% 1.05/0.60 % Backward-rewritten : 39
% 1.05/0.60 % Generated clauses : 11457
% 1.05/0.60 % ...of the previous two non-redundant : 9394
% 1.05/0.60 % ...aggressively subsumed : 0
% 1.05/0.60 % Contextual simplify-reflections : 4
% 1.05/0.60 % Paramodulations : 9325
% 1.05/0.60 % Factorizations : 1421
% 1.05/0.60 % NegExts : 0
% 1.05/0.60 % Equation resolutions : 711
% 1.05/0.60 % Disequality decompositions : 0
% 1.05/0.60 % Total rewrite steps : 2289
% 1.05/0.60 % ...of those cached : 2191
% 1.05/0.60 % Propositional unsat checks : 0
% 1.05/0.60 % Propositional check models : 0
% 1.05/0.60 % Propositional check unsatisfiable : 0
% 1.05/0.60 % Propositional clauses : 0
% 1.05/0.60 % Propositional clauses after purity: 0
% 1.05/0.60 % Propositional unsat core size : 0
% 1.05/0.60 % Propositional preprocessing time : 0.000
% 1.05/0.60 % Propositional encoding time : 0.000
% 1.05/0.60 % Propositional solver time : 0.000
% 1.05/0.60 % Success case prop preproc time : 0.000
% 1.05/0.60 % Success case prop encoding time : 0.000
% 1.05/0.60 % Success case prop solver time : 0.000
% 1.05/0.60 % Current number of processed clauses : 25
% 1.05/0.60 % Positive orientable unit clauses : 7
% 1.05/0.60 % Positive unorientable unit clauses: 1
% 1.05/0.60 % Negative unit clauses : 1
% 1.05/0.60 % Non-unit-clauses : 16
% 1.05/0.60 % Current number of unprocessed clauses: 8398
% 1.05/0.60 % ...number of literals in the above : 54416
% 1.05/0.60 % Current number of archived formulas : 0
% 1.05/0.60 % Current number of archived clauses : 57
% 1.05/0.60 % Clause-clause subsumption calls (NU) : 5469
% 1.05/0.60 % Rec. Clause-clause subsumption calls : 2562
% 1.05/0.60 % Non-unit clause-clause subsumptions : 819
% 1.05/0.60 % Unit Clause-clause subsumption calls : 35
% 1.05/0.60 % Rewrite failures with RHS unbound : 3
% 1.05/0.60 % BW rewrite match attempts : 72
% 1.05/0.60 % BW rewrite match successes : 8
% 1.05/0.60 % Condensation attempts : 0
% 1.05/0.60 % Condensation successes : 0
% 1.05/0.60 % Termbank termtop insertions : 116747
% 1.05/0.60 % Search garbage collected termcells : 1069
% 1.05/0.60
% 1.05/0.60 % -------------------------------------------------
% 1.05/0.60 % User time : 0.134 s
% 1.05/0.60 % System time : 0.010 s
% 1.05/0.60 % Total time : 0.144 s
% 1.05/0.60 % Maximum resident set size: 3792 pages
% 1.05/0.60
% 1.05/0.60 % -------------------------------------------------
% 1.05/0.60 % User time : 0.141 s
% 1.05/0.60 % System time : 0.014 s
% 1.05/0.60 % Total time : 0.154 s
% 1.05/0.60 % Maximum resident set size: 4864 pages
% 1.05/0.60 % E exiting
%------------------------------------------------------------------------------