%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP021_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:53:50 PM UTC 2026
% Result : Theorem 2.92s 0.89s
% Output : CNFRefutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 58 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 184 ( 48 ~; 64 |; 41 &)
% ( 20 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 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 : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 91 :)
% 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_2Eextreal_2Eextreal: $tType ).
tff(decl_23,type,
tyop_2Eextreal_2Eextreal: d ).
tff(decl_24,type,
tyop_2Emin_2Ebool: d ).
tff(decl_26,type,
s: ( u * d ) > du ).
tff(decl_28,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(decl_43,type,
c_2Ebool_2ECOND_2E3: ( du * ( du * du ) ) > u ).
tff(decl_66,type,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Eextreal_2Eextreal * ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Emin_2Ebool ) ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(decl_67,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_68,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_72,type,
mono_2Ec_2Eextreal_2Eextreal__le_2E2: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_74,type,
mono_2Ec_2Eextreal_2Eextreal__max_2E2: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(decl_77,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(decl_78,type,
i_mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Eextreal_2Eextreal > u ).
tff(decl_87,type,
j_mono_2Etyop_2Eextreal_2Eextreal: du > mono_2Etyop_2Eextreal_2Eextreal ).
tff(decl_96,type,
esk1_0: mono_2Etyop_2Eextreal_2Eextreal ).
tff(decl_97,type,
esk2_0: mono_2Etyop_2Eextreal_2Eextreal ).
tff(decl_98,type,
esk3_0: mono_2Etyop_2Eextreal_2Eextreal ).
tff(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1: d,X64: u,X65: u] :
( ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X1,X64),s(X1,X65))) = s(X1,X65) )
& ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X1,X64),s(X1,X65))) = s(X1,X64) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X60: mono_2Etyop_2Eextreal_2Eextreal,X61: mono_2Etyop_2Eextreal_2Eextreal] : ( s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(X6,X60,X61))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X6)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X60)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X61)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal) ).
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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(ji_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X24: mono_2Etyop_2Eextreal_2Eextreal] : ( j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X24))) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Eextreal_2Eextreal) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( p(X6)
<=> p(X7) )
=> ( X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
tff(thm_2Eextreal_2Emax__le,conjecture,
! [X83: mono_2Etyop_2Eextreal_2Eextreal,X84: mono_2Etyop_2Eextreal_2Eextreal,X85: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(X84,X85),X83))
<=> ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X85,X83))
& p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X84,X83)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
tff(thm_2Eextreal_2Eextreal__max__def,axiom,
! [X74: mono_2Etyop_2Eextreal_2Eextreal,X75: mono_2Etyop_2Eextreal_2Eextreal] : ( mono_2Ec_2Eextreal_2Eextreal__max_2E2(X74,X75) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X74,X75),X75,X74) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
tff(thm_2Eextreal_2Ele__trans,axiom,
! [X69: mono_2Etyop_2Eextreal_2Eextreal,X70: mono_2Etyop_2Eextreal_2Eextreal,X71: mono_2Etyop_2Eextreal_2Eextreal] :
( ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X70,X71))
& p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X69,X70)) )
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X69,X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
tff(thm_2Eextreal_2Ele__total,axiom,
! [X72: mono_2Etyop_2Eextreal_2Eextreal,X73: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X73,X72))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X72,X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
tff(c_0_11,plain,
! [X135: d,X136: u,X137: u] :
( ( s(X135,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X135,X136),s(X135,X137))) = s(X135,X137) )
& ( s(X135,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X135,X136),s(X135,X137))) = s(X135,X136) ) ),
inference(variable_rename,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES]) ).
tff(c_0_12,plain,
! [X145: mono_2Etyop_2Emin_2Ebool,X146: mono_2Etyop_2Eextreal_2Eextreal,X147: mono_2Etyop_2Eextreal_2Eextreal] : ( s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(X145,X146,X147))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X145)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X146)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X147)))) ),
inference(variable_rename,[status(thm)],[monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal]) ).
tff(c_0_13,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_14,plain,
! [X173: mono_2Etyop_2Eextreal_2Eextreal] : ( j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X173))) = X173 ),
inference(variable_rename,[status(thm)],[ji_2Emono_2Etyop_2Eextreal_2Eextreal]) ).
tcf(c_0_15,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_11]) ).
tcf(c_0_16,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X24: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(X6,X24,X41))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X6)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X24)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X41)))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tff(c_0_17,plain,
! [X134: mono_2Etyop_2Emin_2Ebool] :
( ( ( X134 = mono_2Ec_2Ebool_2EF_2E0 )
| p(X134) )
& ( ~ p(X134)
| ( X134 != mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X134 )
| p(X134) )
& ( ~ p(X134)
| ( mono_2Ec_2Ebool_2EF_2E0 != X134 ) )
& ( ( X134 = mono_2Ec_2Ebool_2ET_2E0 )
| ~ p(X134) )
& ( p(X134)
| ( X134 != mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X134 )
| ~ p(X134) )
& ( p(X134)
| ( mono_2Ec_2Ebool_2ET_2E0 != X134 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
tff(c_0_18,plain,
! [X89: mono_2Etyop_2Emin_2Ebool,X90: mono_2Etyop_2Emin_2Ebool] :
( ( ( X89 = X90 )
| p(X90)
| p(X89) )
& ( ( X89 = X90 )
| ~ p(X90)
| ~ p(X89) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
tcf(c_0_19,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X24))) = X24,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_20,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ET_2E0,X24,X41))) = s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X24)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
tcf(c_0_21,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X6)
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_22,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = X7 )
| p(X7)
| p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tff(c_0_23,negated_conjecture,
~ ! [X83: mono_2Etyop_2Eextreal_2Eextreal,X84: mono_2Etyop_2Eextreal_2Eextreal,X85: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(X84,X85),X83))
<=> ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X85,X83))
& p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X84,X83)) ) ),
inference(assume_negation,[status(cth)],[thm_2Eextreal_2Emax__le]) ).
tff(c_0_24,plain,
! [X128: mono_2Etyop_2Eextreal_2Eextreal,X129: mono_2Etyop_2Eextreal_2Eextreal] : ( mono_2Ec_2Eextreal_2Eextreal__max_2E2(X128,X129) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X128,X129),X129,X128) ),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Eextreal__max__def]) ).
tcf(c_0_25,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ET_2E0,X24,X41) = X24,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_19]) ).
tcf(c_0_26,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_21,c_0_22]) ).
tcf(c_0_27,plain,
! [X1: d,X3: u,X4: u] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X1,X3),s(X1,X4))) = s(X1,X4),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tff(c_0_28,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
tff(c_0_29,negated_conjecture,
( ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0)) )
& ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0)) )
& ( ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])]) ).
tcf(c_0_30,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__max_2E2(X24,X41) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41),X41,X24),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_31,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal,X7: mono_2Etyop_2Emin_2Ebool] :
( p(X7)
| ( X7 = X6 )
| ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(X6,X24,X41) = X24 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
tcf(c_0_32,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2EF_2E0,X24,X41))) = s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(X41)),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
tff(c_0_33,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
tcf(c_0_34,negated_conjecture,
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_35,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| ( mono_2Ec_2Eextreal_2Eextreal__max_2E2(X24,X41) = X41 )
| ( X6 = mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
tff(c_0_36,plain,
! [X123: mono_2Etyop_2Eextreal_2Eextreal,X124: mono_2Etyop_2Eextreal_2Eextreal,X125: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X123,X125))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X124,X125))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X123,X124)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Eextreal_2Ele__trans])])]) ).
tff(c_0_37,plain,
! [X126: mono_2Etyop_2Eextreal_2Eextreal,X127: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X127,X126))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X126,X127)) ),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Ele__total]) ).
tcf(c_0_38,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Ebool_2EF_2E0,X24,X41) = X41,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_19]) ).
tcf(c_0_39,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X41,X24))
| ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal(X6,X24,X41) = mono_2Ec_2Eextreal_2Eextreal__max_2E2(X41,X24) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
tcf(c_0_40,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tcf(c_0_41,negated_conjecture,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0))
| ( X6 = mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
tcf(c_0_42,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal,X42: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X41,X42))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X42)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tcf(c_0_43,plain,
! [X41: mono_2Etyop_2Eextreal_2Eextreal,X24: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X41,X24))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_44,negated_conjecture,
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_45,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41))
| ( mono_2Ec_2Eextreal_2Eextreal__max_2E2(X24,X41) = X24 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
tcf(c_0_46,negated_conjecture,
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0))
| ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0) = mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0) ) ),
inference(ef,[status(thm)],[c_0_41]) ).
tcf(c_0_47,negated_conjecture,
( ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0))
| ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0),esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_48,plain,
! [X24: mono_2Etyop_2Eextreal_2Eextreal,X42: mono_2Etyop_2Eextreal_2Eextreal,X41: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X42,X41))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X42,X24))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,X41)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
tcf(c_0_49,negated_conjecture,
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
tcf(c_0_50,negated_conjecture,
( ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0) = mono_2Ec_2Ebool_2ET_2E0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0) = mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
tcf(c_0_51,negated_conjecture,
p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_48]),c_0_49]) ).
tff(c_0_52,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_53,negated_conjecture,
( ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0) != mono_2Ec_2Ebool_2ET_2E0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0) = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(ef,[status(thm)],[c_0_50]) ).
tcf(c_0_54,negated_conjecture,
mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk3_0) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
tff(c_0_55,plain,
! [X133: mono_2Etyop_2Emin_2Ebool] :
( ( p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(X133)
| p(X133) )
& ( ~ p(X133)
| ~ p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ~ p(X133)
| p(X133) )
& p(mono_2Ec_2Ebool_2ET_2E0)
& ( p(X133)
| ~ p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X133) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| p(mono_2Ec_2Ebool_2EF_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X133)
| ~ 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(X133) )
& ( p(X133)
| ~ p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X133) )
& ( p(X133)
| ~ p(X133) )
& ( p(X133)
| 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_52])])])]) ).
tcf(c_0_56,negated_conjecture,
mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk3_0,esk1_0) = mono_2Ec_2Ebool_2ET_2E0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
tcf(c_0_57,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
tcf(c_0_58,negated_conjecture,
! [X24: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,esk3_0))
| p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(X24,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_57])]) ).
tcf(c_0_59,negated_conjecture,
p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_57])]) ).
tcf(c_0_60,negated_conjecture,
mono_2Ec_2Eextreal_2Eextreal__max_2E2(esk2_0,esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_54]),c_0_25]) ).
tcf(c_0_61,negated_conjecture,
mono_2Ec_2Eextreal_2Eextreal__le_2E2(esk2_0,esk1_0) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_21,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_56]),c_0_57])]),c_0_60]),c_0_56]),c_0_57]),c_0_61]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP021_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 21:53:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.92/0.89 % Version: 3.5.1
% 2.92/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.92/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.92/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.92/0.89 % Starting new_bool_3 with 300s (1) cores
% 2.92/0.89 % Starting new_bool_1 with 300s (1) cores
% 2.92/0.89 % Starting sh5l with 300s (1) cores
% 2.92/0.89 % sh5l with pid 1311160 completed with status 0
% 2.92/0.89 % Result found by sh5l
% 2.92/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.92/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.92/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.92/0.89 % Starting new_bool_3 with 300s (1) cores
% 2.92/0.89 % Starting new_bool_1 with 300s (1) cores
% 2.92/0.89 % Starting sh5l with 300s (1) cores
% 2.92/0.89 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.92/0.89 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.92/0.89 % Search class: FGHSM-FFMM31-DFFFFFNN
% 2.92/0.89 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.92/0.89 % Starting SubtermCWHack with 31s (1) cores
% 2.92/0.89 % SubtermCWHack with pid 1311163 completed with status 0
% 2.92/0.89 % Result found by SubtermCWHack
% 2.92/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.92/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.92/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.92/0.89 % Starting new_bool_3 with 300s (1) cores
% 2.92/0.89 % Starting new_bool_1 with 300s (1) cores
% 2.92/0.89 % Starting sh5l with 300s (1) cores
% 2.92/0.89 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.92/0.89 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.92/0.89 % Search class: FGHSM-FFMM31-DFFFFFNN
% 2.92/0.89 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.92/0.89 % Starting SubtermCWHack with 31s (1) cores
% 2.92/0.89 % Preprocessing time : 0.003 s
% 2.92/0.89
% 2.92/0.89 % Proof found!
% 2.92/0.89 % SZS status Theorem
% 2.92/0.89 % SZS output start CNFRefutation
% See solution above
% 2.92/0.89 % Parsed axioms : 165
% 2.92/0.89 % Removed by relevancy pruning/SinE : 95
% 2.92/0.89 % Initial clauses : 318
% 2.92/0.89 % Removed in clause preprocessing : 212
% 2.92/0.89 % Initial clauses in saturation : 106
% 2.92/0.89 % Processed clauses : 1851
% 2.92/0.89 % ...of these trivial : 28
% 2.92/0.89 % ...subsumed : 1461
% 2.92/0.89 % ...remaining for further processing : 361
% 2.92/0.89 % Other redundant clauses eliminated : 1770
% 2.92/0.89 % Clauses deleted for lack of memory : 0
% 2.92/0.89 % Backward-subsumed : 44
% 2.92/0.89 % Backward-rewritten : 59
% 2.92/0.89 % Generated clauses : 36114
% 2.92/0.89 % ...of the previous two non-redundant : 30867
% 2.92/0.89 % ...aggressively subsumed : 0
% 2.92/0.89 % Contextual simplify-reflections : 19
% 2.92/0.89 % Paramodulations : 33762
% 2.92/0.89 % Factorizations : 581
% 2.92/0.89 % NegExts : 0
% 2.92/0.89 % Equation resolutions : 1771
% 2.92/0.89 % Disequality decompositions : 0
% 2.92/0.89 % Total rewrite steps : 4208
% 2.92/0.89 % ...of those cached : 3988
% 2.92/0.89 % Propositional unsat checks : 0
% 2.92/0.89 % Propositional check models : 0
% 2.92/0.89 % Propositional check unsatisfiable : 0
% 2.92/0.89 % Propositional clauses : 0
% 2.92/0.89 % Propositional clauses after purity: 0
% 2.92/0.89 % Propositional unsat core size : 0
% 2.92/0.89 % Propositional preprocessing time : 0.000
% 2.92/0.89 % Propositional encoding time : 0.000
% 2.92/0.89 % Propositional solver time : 0.000
% 2.92/0.89 % Success case prop preproc time : 0.000
% 2.92/0.89 % Success case prop encoding time : 0.000
% 2.92/0.89 % Success case prop solver time : 0.000
% 2.92/0.89 % Current number of processed clauses : 250
% 2.92/0.89 % Positive orientable unit clauses : 55
% 2.92/0.89 % Positive unorientable unit clauses: 0
% 2.92/0.89 % Negative unit clauses : 1
% 2.92/0.89 % Non-unit-clauses : 194
% 2.92/0.89 % Current number of unprocessed clauses: 28516
% 2.92/0.89 % ...number of literals in the above : 138079
% 2.92/0.89 % Current number of archived formulas : 0
% 2.92/0.89 % Current number of archived clauses : 103
% 2.92/0.89 % Clause-clause subsumption calls (NU) : 24260
% 2.92/0.89 % Rec. Clause-clause subsumption calls : 12415
% 2.92/0.89 % Non-unit clause-clause subsumptions : 1464
% 2.92/0.89 % Unit Clause-clause subsumption calls : 814
% 2.92/0.89 % Rewrite failures with RHS unbound : 0
% 2.92/0.89 % BW rewrite match attempts : 48
% 2.92/0.89 % BW rewrite match successes : 23
% 2.92/0.89 % Condensation attempts : 0
% 2.92/0.89 % Condensation successes : 0
% 2.92/0.89 % Termbank termtop insertions : 325166
% 2.92/0.89 % Search garbage collected termcells : 2076
% 2.92/0.89
% 2.92/0.89 % -------------------------------------------------
% 2.92/0.89 % User time : 0.387 s
% 2.92/0.89 % System time : 0.027 s
% 2.92/0.89 % Total time : 0.414 s
% 2.92/0.89 % Maximum resident set size: 4304 pages
% 2.92/0.89
% 2.92/0.89 % -------------------------------------------------
% 2.92/0.89 % User time : 0.392 s
% 2.92/0.89 % System time : 0.032 s
% 2.92/0.89 % Total time : 0.424 s
% 2.92/0.89 % Maximum resident set size: 4864 pages
% 2.92/0.89 % E exiting
%------------------------------------------------------------------------------