%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEG009^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 07:49:21 AM UTC 2026
% Result : Theorem 0.33s 0.40s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 82 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 337 ( 30 equ; 0 cnn)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 941 ( 114 ~; 104 |; 60 &; 620 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 7 con; 0-3 aty)
% Number of variables : 232 ( 70 ^; 142 !; 20 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
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_63,type,
ntpp: reg > reg > $o ).
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_69,type,
fool: $i > $i > $o ).
thf(decl_70,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_72,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_79,type,
esk10_1: reg > reg ).
thf(decl_80,type,
esk11_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(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',p) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mor) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',ec) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mforall_prop) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',mvalid) ).
thf(eq,axiom,
( eq
= ( ^ [X26: reg,X27: reg] :
( ( p @ X26 @ X27 )
& ( p @ X27 @ X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',eq) ).
thf(t_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X40: $i > $o] : ( mimplies @ ( mbox @ fool @ X40 ) @ X40 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',t_axiom_for_fool) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',pp) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
? [X25: reg] :
( ~ ( o @ X25 @ paris )
& ~ ( eq @ X25 @ spain ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',con) ).
thf(ax2,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X42: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',ax2) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X38: reg,X39: reg] :
( ( pp @ X38 @ X39 )
& ~ ? [X25: reg] :
( ( ec @ X25 @ X38 )
& ( ec @ X25 @ X39 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',ntpp) ).
thf(c_reflexive,axiom,
! [X18: reg] : ( c @ X18 @ X18 ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',c_reflexive) ).
thf(c_symmetric,axiom,
! [X19: reg,X20: reg] :
( ( c @ X19 @ X20 )
=> ( c @ X20 @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',c_symmetric) ).
thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X43: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',ax3) ).
thf(i_axiom_for_fool_a,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ fool @ X6 ) @ ( mbox @ a @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p',i_axiom_for_fool_a) ).
thf(c_0_19,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_20,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X25: reg] :
( ( c @ X25 @ Z0 )
=> ( c @ X25 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_21,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_22,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_23,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_24,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_25,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_19,c_0_20]) ).
thf(c_0_26,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_27,plain,
( mforall_prop
= ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_prop]) ).
thf(c_0_28,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_29,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_30,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_31,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_24,c_0_25]) ).
thf(c_0_32,plain,
! [X83: $i,X82: $i > $o] :
( ~ ! [X81: $i] :
( ~ ( fool @ X83 @ X81 )
| ( X82 @ X81 ) )
| ( X82 @ X83 ) ),
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)],[t_axiom_for_fool]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]) ).
thf(c_0_33,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_34,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
? [X25: reg] :
( ~ ( o @ X25 @ paris )
& ~ ( eq @ X25 @ spain ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_35,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_30,c_0_20]) ).
thf(c_0_36,plain,
! [X108: $i,X107: $i] :
( ~ ( fool @ X108 @ X107 )
| ( ( c @ spain @ france )
& ~ ? [X104: reg] :
( ! [X105: reg] :
( ( c @ X105 @ X104 )
=> ( c @ X105 @ spain ) )
& ! [X106: reg] :
( ( c @ X106 @ X104 )
=> ( c @ X106 @ 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)],[ax2]),c_0_28]),c_0_29]),c_0_31])]) ).
thf(c_0_37,plain,
! [X130: $i,X131: $i > $o] :
( ( ( fool @ X130 @ ( esk1_2 @ X130 @ X131 ) )
| ( X131 @ X130 ) )
& ( ~ ( X131 @ ( esk1_2 @ X130 @ X131 ) )
| ( X131 @ X130 ) ) ),
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_32])])])])]) ).
thf(c_0_38,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_39,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_33,c_0_20]) ).
thf(c_0_40,negated_conjecture,
~ ! [X126: $i,X125: $i] :
( ~ ( a @ X126 @ X125 )
| ? [X25: reg] :
( ~ ? [X120: reg] :
( ! [X121: reg] :
( ( c @ X121 @ X120 )
=> ( c @ X121 @ X25 ) )
& ! [X122: reg] :
( ( c @ X122 @ X120 )
=> ( c @ X122 @ paris ) ) )
& ~ ( ! [X123: reg] :
( ( c @ X123 @ X25 )
=> ( c @ X123 @ spain ) )
& ! [X124: reg] :
( ( c @ X124 @ spain )
=> ( c @ X124 @ X25 ) ) ) ) ),
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_34]),c_0_28]),c_0_29]),c_0_35]),c_0_25])]) ).
thf(c_0_41,plain,
! [X153: $i,X154: $i,X155: reg] :
( ( ( c @ spain @ france )
| ~ ( fool @ X153 @ X154 ) )
& ( ( c @ ( esk11_1 @ X155 ) @ X155 )
| ( c @ ( esk10_1 @ X155 ) @ X155 )
| ~ ( fool @ X153 @ X154 ) )
& ( ~ ( c @ ( esk11_1 @ X155 ) @ france )
| ( c @ ( esk10_1 @ X155 ) @ X155 )
| ~ ( fool @ X153 @ X154 ) )
& ( ( c @ ( esk11_1 @ X155 ) @ X155 )
| ~ ( c @ ( esk10_1 @ X155 ) @ spain )
| ~ ( fool @ X153 @ X154 ) )
& ( ~ ( c @ ( esk11_1 @ X155 ) @ france )
| ~ ( c @ ( esk10_1 @ X155 ) @ spain )
| ~ ( fool @ X153 @ X154 ) ) ),
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_36])])])])])])]) ).
thf(c_0_42,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ X3 )
| ~ ( X4 @ ( esk1_2 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,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_38,c_0_31]),c_0_39]) ).
thf(c_0_45,negated_conjecture,
! [X171: reg,X173: reg,X174: reg,X175: reg,X176: reg] :
( ( a @ esk15_0 @ esk16_0 )
& ( ~ ( c @ X175 @ X171 )
| ( c @ X175 @ spain )
| ~ ( c @ X173 @ ( esk17_1 @ X171 ) )
| ( c @ X173 @ X171 ) )
& ( ~ ( c @ X176 @ spain )
| ( c @ X176 @ X171 )
| ~ ( c @ X173 @ ( esk17_1 @ X171 ) )
| ( c @ X173 @ X171 ) )
& ( ~ ( c @ X175 @ X171 )
| ( c @ X175 @ spain )
| ~ ( c @ X174 @ ( esk17_1 @ X171 ) )
| ( c @ X174 @ paris ) )
& ( ~ ( c @ X176 @ spain )
| ( c @ X176 @ X171 )
| ~ ( c @ X174 @ ( esk17_1 @ X171 ) )
| ( c @ X174 @ paris ) ) ),
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_40])])])])])]) ).
thf(c_0_46,plain,
! [X127: reg] : ( c @ X127 @ X127 ),
inference(variable_rename,[status(thm)],[c_reflexive]) ).
thf(c_0_47,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_48,plain,
! [X3: $i,X14: $i] :
( ( c @ spain @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_49,plain,
! [X3: $i] : ( fool @ X3 @ X3 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_50,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_28]),c_0_29]),c_0_44])]) ).
thf(c_0_51,negated_conjecture,
! [X18: reg,X20: reg,X19: reg] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ paris )
| ~ ( c @ X18 @ spain )
| ~ ( c @ X20 @ ( esk17_1 @ X19 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_52,plain,
! [X18: reg] : ( c @ X18 @ X18 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_53,plain,
! [X18: reg,X19: reg] :
( ( c @ X19 @ X18 )
| ~ ( c @ X18 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_54,plain,
c @ spain @ france,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_55,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_50])])])])])])]) ).
thf(c_0_56,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk17_1 @ X18 ) @ paris )
| ( c @ X19 @ X18 )
| ~ ( c @ X19 @ spain ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_57,plain,
c @ france @ spain,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_58,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_59,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk17_1 @ X18 ) @ paris )
| ( c @ france @ X18 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_60,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk17_1 @ X18 ) @ france )
| ( c @ france @ X18 )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_61,negated_conjecture,
a @ esk15_0 @ esk16_0,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_62,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk17_1 @ X18 ) @ france )
| ( c @ france @ X18 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_63,plain,
! [X92: $i,X91: $i > $o] :
( ~ ! [X89: $i] :
( ~ ( fool @ X92 @ X89 )
| ( X91 @ X89 ) )
| ! [X90: $i] :
( ~ ( a @ X92 @ X90 )
| ( X91 @ X90 ) ) ),
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)],[i_axiom_for_fool_a]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]) ).
thf(c_0_64,negated_conjecture,
! [X18: reg,X20: reg,X19: reg] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ X19 )
| ~ ( c @ X18 @ spain )
| ~ ( c @ X20 @ ( esk17_1 @ X19 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_65,negated_conjecture,
! [X18: reg] :
( ( c @ france @ ( esk17_1 @ X18 ) )
| ( c @ france @ X18 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_62]) ).
thf(c_0_66,plain,
! [X138: $i,X139: $i > $o,X141: $i] :
( ( ( fool @ X138 @ ( esk3_2 @ X138 @ X139 ) )
| ~ ( a @ X138 @ X141 )
| ( X139 @ X141 ) )
& ( ~ ( X139 @ ( esk3_2 @ X138 @ X139 ) )
| ~ ( a @ X138 @ X141 )
| ( X139 @ X141 ) ) ),
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_63])])])])])]) ).
thf(c_0_67,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ france @ X18 )
| ( c @ X19 @ X18 )
| ~ ( c @ X19 @ spain ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_68,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk3_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_69,negated_conjecture,
! [X18: reg] : ( c @ france @ X18 ),
inference(spm,[status(thm)],[c_0_67,c_0_57]) ).
thf(c_0_70,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk3_2 @ X3 @ X4 ) )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_71,negated_conjecture,
! [X4: $i > $o] :
( ( fool @ esk15_0 @ ( esk3_2 @ esk15_0 @ X4 ) )
| ( X4 @ esk16_0 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_61]) ).
thf(c_0_72,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk10_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk11_1 @ X18 ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_73,negated_conjecture,
! [X18: reg] : ( c @ X18 @ france ),
inference(spm,[status(thm)],[c_0_53,c_0_69]) ).
thf(c_0_74,negated_conjecture,
! [X3: $i] :
( ( fool @ esk15_0 @ esk16_0 )
| ( fool @ esk15_0 @ X3 )
| ~ ( a @ esk15_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,plain,
! [X18: reg,X3: $i,X14: $i] :
( ~ ( c @ ( esk11_1 @ X18 ) @ france )
| ~ ( c @ ( esk10_1 @ X18 ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_76,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk10_1 @ X18 ) @ X18 )
| ~ ( fool @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_77,negated_conjecture,
fool @ esk15_0 @ esk16_0,
inference(spm,[status(thm)],[c_0_74,c_0_61]) ).
thf(c_0_78,plain,
! [X18: reg,X3: $i,X14: $i] :
( ~ ( c @ ( esk10_1 @ X18 ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_73])]) ).
thf(c_0_79,negated_conjecture,
! [X18: reg] : ( c @ ( esk10_1 @ X18 ) @ X18 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_80,negated_conjecture,
! [X3: $i,X14: $i] :
~ ( fool @ X3 @ X14 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_81,plain,
$false,
inference(sr,[status(thm)],[c_0_49,c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG009^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 % Computer : n001.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue Sep 29 18:39:51 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.27 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.33 Running higher-order theorem proving
% 0.26/0.35 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.qw0tqCUNe3/E---3.1_1651997.p
% 0.33/0.40 % Version: 3.5.1-ho
% 0.33/0.40 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.33/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.40 % Starting post_as_ho3 with 300s (1) cores
% 0.33/0.40 % Starting new_ho_12 with 300s (1) cores
% 0.33/0.40 % Starting new_bool_2 with 300s (1) cores
% 0.33/0.40 % post_as_ho3 with pid 1652013 completed with status 0
% 0.33/0.40 % Result found by post_as_ho3
% 0.33/0.40 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.33/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.40 % Starting post_as_ho3 with 300s (1) cores
% 0.33/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.40 % No SInE strategy applied
% 0.33/0.40 % Search class: HGHNF-FFMF21-SHSSMSBN
% 0.33/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.40 % SubtermCWHack with pid 1652017 completed with status 0
% 0.33/0.40 % Result found by SubtermCWHack
% 0.33/0.40 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.33/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.40 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.33/0.40 % Starting post_as_ho3 with 300s (1) cores
% 0.33/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.40 % No SInE strategy applied
% 0.33/0.40 % Search class: HGHNF-FFMF21-SHSSMSBN
% 0.33/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.40 % Preprocessing time : 0.002 s
% 0.33/0.40
% 0.33/0.40 % Proof found!
% 0.33/0.40 % SZS status Theorem
% 0.33/0.40 % SZS output start CNFRefutation
% See solution above
% 0.33/0.40 % Parsed axioms : 98
% 0.33/0.40 % Removed by relevancy pruning/SinE : 0
% 0.33/0.40 % Initial clauses : 87
% 0.33/0.40 % Removed in clause preprocessing : 49
% 0.33/0.40 % Initial clauses in saturation : 38
% 0.33/0.40 % Processed clauses : 178
% 0.33/0.40 % ...of these trivial : 6
% 0.33/0.40 % ...subsumed : 19
% 0.33/0.40 % ...remaining for further processing : 153
% 0.33/0.40 % Other redundant clauses eliminated : 0
% 0.33/0.40 % Clauses deleted for lack of memory : 0
% 0.33/0.40 % Backward-subsumed : 18
% 0.33/0.40 % Backward-rewritten : 47
% 0.33/0.40 % Generated clauses : 424
% 0.33/0.40 % ...of the previous two non-redundant : 341
% 0.33/0.40 % ...aggressively subsumed : 0
% 0.33/0.40 % Contextual simplify-reflections : 0
% 0.33/0.40 % Paramodulations : 420
% 0.33/0.40 % Factorizations : 0
% 0.33/0.40 % NegExts : 0
% 0.33/0.40 % Equation resolutions : 0
% 0.33/0.40 % Disequality decompositions : 0
% 0.33/0.40 % Total rewrite steps : 138
% 0.33/0.40 % ...of those cached : 85
% 0.33/0.40 % Propositional unsat checks : 0
% 0.33/0.40 % Propositional check models : 0
% 0.33/0.40 % Propositional check unsatisfiable : 0
% 0.33/0.40 % Propositional clauses : 0
% 0.33/0.40 % Propositional clauses after purity: 0
% 0.33/0.40 % Propositional unsat core size : 0
% 0.33/0.40 % Propositional preprocessing time : 0.000
% 0.33/0.40 % Propositional encoding time : 0.000
% 0.33/0.40 % Propositional solver time : 0.000
% 0.33/0.40 % Success case prop preproc time : 0.000
% 0.33/0.40 % Success case prop encoding time : 0.000
% 0.33/0.40 % Success case prop solver time : 0.000
% 0.33/0.40 % Current number of processed clauses : 84
% 0.33/0.40 % Positive orientable unit clauses : 29
% 0.33/0.40 % Positive unorientable unit clauses: 0
% 0.33/0.40 % Negative unit clauses : 3
% 0.33/0.40 % Non-unit-clauses : 52
% 0.33/0.40 % Current number of unprocessed clauses: 177
% 0.33/0.40 % ...number of literals in the above : 617
% 0.33/0.40 % Current number of archived formulas : 0
% 0.33/0.40 % Current number of archived clauses : 69
% 0.33/0.40 % Clause-clause subsumption calls (NU) : 2337
% 0.33/0.40 % Rec. Clause-clause subsumption calls : 1950
% 0.33/0.40 % Non-unit clause-clause subsumptions : 29
% 0.33/0.40 % Unit Clause-clause subsumption calls : 118
% 0.33/0.40 % Rewrite failures with RHS unbound : 0
% 0.33/0.40 % BW rewrite match attempts : 38
% 0.33/0.40 % BW rewrite match successes : 35
% 0.33/0.40 % Condensation attempts : 0
% 0.33/0.40 % Condensation successes : 0
% 0.33/0.40 % Termbank termtop insertions : 11902
% 0.33/0.40 % Search garbage collected termcells : 1976
% 0.33/0.40
% 0.33/0.40 % -------------------------------------------------
% 0.33/0.40 % User time : 0.024 s
% 0.33/0.40 % System time : 0.004 s
% 0.33/0.40 % Total time : 0.028 s
% 0.33/0.40 % Maximum resident set size: 3992 pages
% 0.33/0.40
% 0.33/0.40 % -------------------------------------------------
% 0.33/0.40 % User time : 0.029 s
% 0.33/0.40 % System time : 0.010 s
% 0.33/0.40 % Total time : 0.039 s
% 0.33/0.40 % Maximum resident set size: 4864 pages
% 0.33/0.40 % E exiting
%------------------------------------------------------------------------------