%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEG008^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Wed Sep 30 07:49:19 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 24 equ; 0 cnn)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 961 ( 107 ~; 79 |; 86 &; 627 @)
% ( 0 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 10 con; 0-3 aty)
% Number of variables : 188 ( 52 ^; 110 !; 26 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
c: reg > reg > $o ).
thf(decl_56,type,
p: reg > reg > $o ).
thf(decl_57,type,
eq: reg > reg > $o ).
thf(decl_58,type,
o: reg > reg > $o ).
thf(decl_60,type,
ec: reg > reg > $o ).
thf(decl_61,type,
pp: reg > reg > $o ).
thf(decl_62,type,
tpp: reg > reg > $o ).
thf(decl_63,type,
ntpp: reg > reg > $o ).
thf(decl_64,type,
catalunya: reg ).
thf(decl_65,type,
france: reg ).
thf(decl_66,type,
spain: reg ).
thf(decl_67,type,
paris: reg ).
thf(decl_68,type,
a: $i > $i > $o ).
thf(decl_73,type,
esk4_0: reg ).
thf(decl_74,type,
esk5_0: reg ).
thf(decl_75,type,
esk6_1: reg > reg ).
thf(decl_76,type,
esk7_1: reg > reg ).
thf(decl_77,type,
esk8_1: reg > reg ).
thf(decl_78,type,
esk9_1: reg > reg ).
thf(decl_81,type,
esk12_0: reg ).
thf(decl_82,type,
esk13_1: reg > reg ).
thf(decl_83,type,
esk14_1: reg > reg ).
thf(decl_84,type,
esk15_0: $i ).
thf(decl_85,type,
esk16_0: $i ).
thf(decl_86,type,
esk17_1: reg > reg ).
thf(decl_87,type,
esk18_1: reg > reg ).
thf(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',p) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',ec) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',pp) ).
thf(tpp,axiom,
( tpp
= ( ^ [X36: reg,X37: reg] :
( ( pp @ X36 @ X37 )
& ? [X25: reg] :
( ( ec @ X25 @ X36 )
& ( ec @ X25 @ X37 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',tpp) ).
thf(eq,axiom,
( eq
= ( ^ [X26: reg,X27: reg] :
( ( p @ X26 @ X27 )
& ( p @ X27 @ X26 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',eq) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',mvalid) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',con) ).
thf(ax1,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X41: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',ax1) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X38: reg,X39: reg] :
( ( pp @ X38 @ X39 )
& ~ ? [X25: reg] :
( ( ec @ X25 @ X38 )
& ( ec @ X25 @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',ntpp) ).
thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X43: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',ax3) ).
thf(c_symmetric,axiom,
! [X19: reg,X20: reg] :
( ( c @ X19 @ X20 )
=> ( c @ X20 @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p',c_symmetric) ).
thf(c_0_13,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X53: reg] :
( ( c @ X53 @ X25 )
=> ( c @ X53 @ Z0 ) )
& ! [X54: reg] :
( ( c @ X54 @ X25 )
=> ( c @ X54 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[o]) ).
thf(c_0_14,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X25: reg] :
( ( c @ X25 @ Z0 )
=> ( c @ X25 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_15,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X60: reg] :
( ! [X61: reg] :
( ( c @ X61 @ X60 )
=> ( c @ X61 @ Z0 ) )
& ! [X62: reg] :
( ( c @ X62 @ X60 )
=> ( c @ X62 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_16,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X53: reg] :
( ( c @ X53 @ X25 )
=> ( c @ X53 @ Z0 ) )
& ! [X54: reg] :
( ( c @ X54 @ X25 )
=> ( c @ X54 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X63: reg] :
( ( c @ X63 @ Z0 )
=> ( c @ X63 @ Z1 ) )
& ~ ! [X64: reg] :
( ( c @ X64 @ Z1 )
=> ( c @ X64 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_18,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X65: reg] :
( ( c @ X65 @ Z0 )
=> ( c @ X65 @ Z1 ) )
& ~ ! [X66: reg] :
( ( c @ X66 @ Z1 )
=> ( c @ X66 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X67: reg] :
( ! [X68: reg] :
( ( c @ X68 @ X67 )
=> ( c @ X68 @ X25 ) )
& ! [X69: reg] :
( ( c @ X69 @ X67 )
=> ( c @ X69 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X70: reg] :
( ! [X71: reg] :
( ( c @ X71 @ X70 )
=> ( c @ X71 @ X25 ) )
& ! [X72: reg] :
( ( c @ X72 @ X70 )
=> ( c @ X72 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[tpp]) ).
thf(c_0_19,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X60: reg] :
( ! [X61: reg] :
( ( c @ X61 @ X60 )
=> ( c @ X61 @ Z0 ) )
& ! [X62: reg] :
( ( c @ X62 @ X60 )
=> ( c @ X62 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X63: reg] :
( ( c @ X63 @ Z0 )
=> ( c @ X63 @ Z1 ) )
& ~ ! [X64: reg] :
( ( c @ X64 @ Z1 )
=> ( c @ X64 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_14]) ).
thf(c_0_21,plain,
( eq
= ( ^ [Z0: reg,Z1: reg] :
( ! [X51: reg] :
( ( c @ X51 @ Z0 )
=> ( c @ X51 @ Z1 ) )
& ! [X52: reg] :
( ( c @ X52 @ Z1 )
=> ( c @ X52 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[eq]) ).
thf(c_0_22,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_23,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_24,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X65: reg] :
( ( c @ X65 @ Z0 )
=> ( c @ X65 @ Z1 ) )
& ~ ! [X66: reg] :
( ( c @ X66 @ Z1 )
=> ( c @ X66 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X67: reg] :
( ! [X68: reg] :
( ( c @ X68 @ X67 )
=> ( c @ X68 @ X25 ) )
& ! [X69: reg] :
( ( c @ X69 @ X67 )
=> ( c @ X69 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X70: reg] :
( ! [X71: reg] :
( ( c @ X71 @ X70 )
=> ( c @ X71 @ X25 ) )
& ! [X72: reg] :
( ( c @ X72 @ X70 )
=> ( c @ X72 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_25,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_26,plain,
( eq
= ( ^ [Z0: reg,Z1: reg] :
( ! [X51: reg] :
( ( c @ X51 @ Z0 )
=> ( c @ X51 @ Z1 ) )
& ! [X52: reg] :
( ( c @ X52 @ Z1 )
=> ( c @ X52 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_14]) ).
thf(c_0_27,plain,
! [X103: $i,X102: $i] :
( ~ ( a @ X103 @ X102 )
| ( ! [X93: reg] :
( ( c @ X93 @ catalunya )
=> ( c @ X93 @ spain ) )
& ~ ! [X94: reg] :
( ( c @ X94 @ spain )
=> ( c @ X94 @ catalunya ) )
& ? [X95: reg] :
( ( c @ X95 @ catalunya )
& ~ ? [X96: reg] :
( ! [X97: reg] :
( ( c @ X97 @ X96 )
=> ( c @ X97 @ X95 ) )
& ! [X98: reg] :
( ( c @ X98 @ X96 )
=> ( c @ X98 @ catalunya ) ) )
& ( c @ X95 @ spain )
& ~ ? [X99: reg] :
( ! [X100: reg] :
( ( c @ X100 @ X99 )
=> ( c @ X100 @ X95 ) )
& ! [X101: reg] :
( ( c @ X101 @ X99 )
=> ( c @ X101 @ spain ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax1]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_28,negated_conjecture,
~ ! [X126: $i,X125: $i] :
( ~ ( a @ X126 @ X125 )
| ( ( ! [X120: reg] :
( ( c @ X120 @ catalunya )
=> ( c @ X120 @ paris ) )
& ! [X121: reg] :
( ( c @ X121 @ paris )
=> ( c @ X121 @ catalunya ) ) )
=> ? [X122: reg] :
( ! [X123: reg] :
( ( c @ X123 @ X122 )
=> ( c @ X123 @ france ) )
& ! [X124: reg] :
( ( c @ X124 @ X122 )
=> ( c @ X124 @ spain ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_25]),c_0_22]),c_0_23]),c_0_26]),c_0_16])]) ).
thf(c_0_29,plain,
! [X142: $i,X143: $i,X144: reg,X147: reg,X150: reg] :
( ( ~ ( c @ X144 @ catalunya )
| ( c @ X144 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk4_0 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ esk4_0 @ catalunya )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk5_0 @ catalunya )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk7_1 @ X147 ) @ X147 )
| ( c @ ( esk6_1 @ X147 ) @ X147 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk7_1 @ X147 ) @ catalunya )
| ( c @ ( esk6_1 @ X147 ) @ X147 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk7_1 @ X147 ) @ X147 )
| ~ ( c @ ( esk6_1 @ X147 ) @ esk5_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk7_1 @ X147 ) @ catalunya )
| ~ ( c @ ( esk6_1 @ X147 ) @ esk5_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk5_0 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk9_1 @ X150 ) @ X150 )
| ( c @ ( esk8_1 @ X150 ) @ X150 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk9_1 @ X150 ) @ spain )
| ( c @ ( esk8_1 @ X150 ) @ X150 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk9_1 @ X150 ) @ X150 )
| ~ ( c @ ( esk8_1 @ X150 ) @ esk5_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk9_1 @ X150 ) @ spain )
| ~ ( c @ ( esk8_1 @ X150 ) @ esk5_0 )
| ~ ( a @ X142 @ X143 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])])])]) ).
thf(c_0_30,negated_conjecture,
! [X171: reg,X172: reg,X173: reg] :
( ( a @ esk15_0 @ esk16_0 )
& ( ~ ( c @ X171 @ catalunya )
| ( c @ X171 @ paris ) )
& ( ~ ( c @ X172 @ paris )
| ( c @ X172 @ catalunya ) )
& ( ( c @ ( esk18_1 @ X173 ) @ X173 )
| ( c @ ( esk17_1 @ X173 ) @ X173 ) )
& ( ~ ( c @ ( esk18_1 @ X173 ) @ spain )
| ( c @ ( esk17_1 @ X173 ) @ X173 ) )
& ( ( c @ ( esk18_1 @ X173 ) @ X173 )
| ~ ( c @ ( esk17_1 @ X173 ) @ france ) )
& ( ~ ( c @ ( esk18_1 @ X173 ) @ spain )
| ~ ( c @ ( esk17_1 @ X173 ) @ france ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).
thf(c_0_31,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X73: reg] :
( ( c @ X73 @ Z0 )
=> ( c @ X73 @ Z1 ) )
& ~ ! [X74: reg] :
( ( c @ X74 @ Z1 )
=> ( c @ X74 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X75: reg] :
( ! [X76: reg] :
( ( c @ X76 @ X75 )
=> ( c @ X76 @ X25 ) )
& ! [X77: reg] :
( ( c @ X77 @ X75 )
=> ( c @ X77 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X78: reg] :
( ! [X79: reg] :
( ( c @ X79 @ X78 )
=> ( c @ X79 @ X25 ) )
& ! [X80: reg] :
( ( c @ X80 @ X78 )
=> ( c @ X80 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ntpp]) ).
thf(c_0_32,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ spain )
| ~ ( c @ X18 @ catalunya )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X18: reg] :
( ( c @ X18 @ catalunya )
| ~ ( c @ X18 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X73: reg] :
( ( c @ X73 @ Z0 )
=> ( c @ X73 @ Z1 ) )
& ~ ! [X74: reg] :
( ( c @ X74 @ Z1 )
=> ( c @ X74 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X75: reg] :
( ! [X76: reg] :
( ( c @ X76 @ X75 )
=> ( c @ X76 @ X25 ) )
& ! [X77: reg] :
( ( c @ X77 @ X75 )
=> ( c @ X77 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X78: reg] :
( ! [X79: reg] :
( ( c @ X79 @ X78 )
=> ( c @ X79 @ X25 ) )
& ! [X80: reg] :
( ( c @ X80 @ X78 )
=> ( c @ X80 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_19]),c_0_20]) ).
thf(c_0_35,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ spain )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,negated_conjecture,
a @ esk15_0 @ esk16_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,plain,
! [X119: $i,X118: $i] :
( ~ ( a @ X119 @ X118 )
| ( ! [X109: reg] :
( ( c @ X109 @ paris )
=> ( c @ X109 @ france ) )
& ~ ! [X110: reg] :
( ( c @ X110 @ france )
=> ( c @ X110 @ paris ) )
& ~ ? [X111: reg] :
( ( c @ X111 @ paris )
& ~ ? [X112: reg] :
( ! [X113: reg] :
( ( c @ X113 @ X112 )
=> ( c @ X113 @ X111 ) )
& ! [X114: reg] :
( ( c @ X114 @ X112 )
=> ( c @ X114 @ paris ) ) )
& ( c @ X111 @ france )
& ~ ? [X115: reg] :
( ! [X116: reg] :
( ( c @ X116 @ X115 )
=> ( c @ X116 @ X111 ) )
& ! [X117: reg] :
( ( c @ X117 @ X115 )
=> ( c @ X117 @ france ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax3]),c_0_22]),c_0_23]),c_0_34])]) ).
thf(c_0_38,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk17_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk18_1 @ X18 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,negated_conjecture,
! [X18: reg] :
( ( c @ X18 @ spain )
| ~ ( c @ X18 @ paris ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,plain,
! [X158: $i,X159: $i,X160: reg,X162: reg,X164: reg,X165: reg,X167: reg,X168: reg] :
( ( ~ ( c @ X160 @ paris )
| ( c @ X160 @ france )
| ~ ( a @ X158 @ X159 ) )
& ( ( c @ esk12_0 @ france )
| ~ ( a @ X158 @ X159 ) )
& ( ~ ( c @ esk12_0 @ paris )
| ~ ( a @ X158 @ X159 ) )
& ( ~ ( c @ X167 @ ( esk14_1 @ X162 ) )
| ( c @ X167 @ X162 )
| ~ ( c @ X162 @ france )
| ~ ( c @ X164 @ ( esk13_1 @ X162 ) )
| ( c @ X164 @ X162 )
| ~ ( c @ X162 @ paris )
| ~ ( a @ X158 @ X159 ) )
& ( ~ ( c @ X168 @ ( esk14_1 @ X162 ) )
| ( c @ X168 @ france )
| ~ ( c @ X162 @ france )
| ~ ( c @ X164 @ ( esk13_1 @ X162 ) )
| ( c @ X164 @ X162 )
| ~ ( c @ X162 @ paris )
| ~ ( a @ X158 @ X159 ) )
& ( ~ ( c @ X167 @ ( esk14_1 @ X162 ) )
| ( c @ X167 @ X162 )
| ~ ( c @ X162 @ france )
| ~ ( c @ X165 @ ( esk13_1 @ X162 ) )
| ( c @ X165 @ paris )
| ~ ( c @ X162 @ paris )
| ~ ( a @ X158 @ X159 ) )
& ( ~ ( c @ X168 @ ( esk14_1 @ X162 ) )
| ( c @ X168 @ france )
| ~ ( c @ X162 @ france )
| ~ ( c @ X165 @ ( esk13_1 @ X162 ) )
| ( c @ X165 @ paris )
| ~ ( c @ X162 @ paris )
| ~ ( a @ X158 @ X159 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])])]) ).
thf(c_0_41,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk17_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk18_1 @ X18 ) @ paris ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_42,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk18_1 @ X18 ) @ X18 )
| ( c @ ( esk17_1 @ X18 ) @ X18 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_43,plain,
! [X128: reg,X129: reg] :
( ~ ( c @ X128 @ X129 )
| ( c @ X129 @ X128 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])])]) ).
thf(c_0_44,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_45,negated_conjecture,
c @ ( esk17_1 @ paris ) @ paris,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_46,plain,
! [X18: reg,X19: reg] :
( ( c @ X19 @ X18 )
| ~ ( c @ X18 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_47,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk18_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk17_1 @ X18 ) @ france ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk17_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_49,negated_conjecture,
! [X18: reg] :
( ( c @ X18 @ ( esk18_1 @ X18 ) )
| ~ ( c @ ( esk17_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_50,negated_conjecture,
c @ ( esk17_1 @ paris ) @ france,
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
thf(c_0_51,negated_conjecture,
c @ paris @ ( esk18_1 @ paris ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_52,negated_conjecture,
! [X18: reg] :
( ( c @ spain @ X18 )
| ~ ( c @ X18 @ paris ) ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
thf(c_0_53,negated_conjecture,
c @ ( esk18_1 @ paris ) @ paris,
inference(spm,[status(thm)],[c_0_46,c_0_51]) ).
thf(c_0_54,negated_conjecture,
c @ spain @ ( esk18_1 @ paris ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_55,negated_conjecture,
! [X18: reg] :
( ~ ( c @ ( esk18_1 @ X18 ) @ spain )
| ~ ( c @ ( esk17_1 @ X18 ) @ france ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_56,negated_conjecture,
c @ ( esk18_1 @ paris ) @ spain,
inference(spm,[status(thm)],[c_0_46,c_0_54]) ).
thf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG008^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n004.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 18:33:52 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.H7Y3yToTlF/E---3.1_1670972.p
% 0.23/0.32 % Version: 3.5.1-ho
% 0.23/0.32 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.32 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.32 % Starting new_ho_12 with 300s (1) cores
% 0.23/0.32 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.32 % new_ho_10_cnf2 with pid 1671008 completed with status 0
% 0.23/0.32 % Result found by new_ho_10_cnf2
% 0.23/0.32 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHNF-FFMF21-SHSSMSBN
% 0.23/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.32 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.23/0.32 % Starting post_as_ho11 with 136s (1) cores
% 0.23/0.32 % Starting pre_casc_8 with 136s (1) cores
% 0.23/0.32 % Starting post_as_ho2 with 136s (1) cores
% 0.23/0.32 % SubtermCWHack with pid 1671014 completed with status 0
% 0.23/0.32 % Result found by SubtermCWHack
% 0.23/0.32 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHNF-FFMF21-SHSSMSBN
% 0.23/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.32 % Preprocessing time : 0.002 s
% 0.23/0.32
% 0.23/0.32 % Proof found!
% 0.23/0.32 % SZS status Theorem
% 0.23/0.32 % SZS output start CNFRefutation
% See solution above
% 0.23/0.32 % Parsed axioms : 98
% 0.23/0.32 % Removed by relevancy pruning/SinE : 0
% 0.23/0.32 % Initial clauses : 89
% 0.23/0.32 % Removed in clause preprocessing : 49
% 0.23/0.32 % Initial clauses in saturation : 40
% 0.23/0.32 % Processed clauses : 305
% 0.23/0.32 % ...of these trivial : 5
% 0.23/0.32 % ...subsumed : 70
% 0.23/0.32 % ...remaining for further processing : 230
% 0.23/0.32 % Other redundant clauses eliminated : 0
% 0.23/0.32 % Clauses deleted for lack of memory : 0
% 0.23/0.32 % Backward-subsumed : 16
% 0.23/0.32 % Backward-rewritten : 28
% 0.23/0.32 % Generated clauses : 562
% 0.23/0.32 % ...of the previous two non-redundant : 484
% 0.23/0.32 % ...aggressively subsumed : 0
% 0.23/0.32 % Contextual simplify-reflections : 4
% 0.23/0.32 % Paramodulations : 562
% 0.23/0.32 % Factorizations : 0
% 0.23/0.32 % NegExts : 0
% 0.23/0.32 % Equation resolutions : 0
% 0.23/0.32 % Disequality decompositions : 0
% 0.23/0.32 % Total rewrite steps : 116
% 0.23/0.32 % ...of those cached : 61
% 0.23/0.32 % Propositional unsat checks : 0
% 0.23/0.32 % Propositional check models : 0
% 0.23/0.32 % Propositional check unsatisfiable : 0
% 0.23/0.32 % Propositional clauses : 0
% 0.23/0.32 % Propositional clauses after purity: 0
% 0.23/0.32 % Propositional unsat core size : 0
% 0.23/0.32 % Propositional preprocessing time : 0.000
% 0.23/0.32 % Propositional encoding time : 0.000
% 0.23/0.32 % Propositional solver time : 0.000
% 0.23/0.32 % Success case prop preproc time : 0.000
% 0.23/0.32 % Success case prop encoding time : 0.000
% 0.23/0.32 % Success case prop solver time : 0.000
% 0.23/0.32 % Current number of processed clauses : 186
% 0.23/0.32 % Positive orientable unit clauses : 71
% 0.23/0.32 % Positive unorientable unit clauses: 0
% 0.23/0.32 % Negative unit clauses : 4
% 0.23/0.32 % Non-unit-clauses : 111
% 0.23/0.32 % Current number of unprocessed clauses: 215
% 0.23/0.32 % ...number of literals in the above : 790
% 0.23/0.32 % Current number of archived formulas : 0
% 0.23/0.32 % Current number of archived clauses : 44
% 0.23/0.32 % Clause-clause subsumption calls (NU) : 6631
% 0.23/0.32 % Rec. Clause-clause subsumption calls : 5702
% 0.23/0.32 % Non-unit clause-clause subsumptions : 81
% 0.23/0.32 % Unit Clause-clause subsumption calls : 903
% 0.23/0.32 % Rewrite failures with RHS unbound : 0
% 0.23/0.32 % BW rewrite match attempts : 25
% 0.23/0.32 % BW rewrite match successes : 23
% 0.23/0.32 % Condensation attempts : 0
% 0.23/0.32 % Condensation successes : 0
% 0.23/0.32 % Termbank termtop insertions : 12679
% 0.23/0.32 % Search garbage collected termcells : 2027
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.020 s
% 0.23/0.32 % System time : 0.005 s
% 0.23/0.32 % Total time : 0.025 s
% 0.23/0.32 % Maximum resident set size: 3992 pages
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.073 s
% 0.23/0.32 % System time : 0.018 s
% 0.23/0.32 % Total time : 0.090 s
% 0.23/0.32 % Maximum resident set size: 4608 pages
% 0.23/0.32 % E exiting
%------------------------------------------------------------------------------