%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEG003^1 : 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 : 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 07:49:20 AM UTC 2026
% Result : Theorem 7.83s 1.43s
% Output : CNFRefutation 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 19
% Syntax : Number of formulae : 136 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 34 equ; 0 cnn)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 2012 ( 211 ~; 255 |; 86 &;1407 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 10 con; 0-3 aty)
% Number of variables : 346 ( 75 ^; 245 !; 26 ?; 346 :)
% 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_55,type,
dc: reg > reg > $o ).
thf(decl_56,type,
p: 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_69,type,
fool: $i > $i > $o ).
thf(decl_70,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_71,type,
esk2_0: reg ).
thf(decl_72,type,
esk3_0: reg ).
thf(decl_73,type,
esk4_1: reg > reg ).
thf(decl_74,type,
esk5_1: reg > 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_79,type,
esk10_0: reg ).
thf(decl_80,type,
esk11_1: reg > reg ).
thf(decl_81,type,
esk12_1: reg > reg ).
thf(decl_82,type,
esk13_0: $i ).
thf(decl_83,type,
esk14_0: $i ).
thf(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',p) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',ec) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',pp) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',mor) ).
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.CRzXDP7x4L/E---3.1_1671773.p',ntpp) ).
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.CRzXDP7x4L/E---3.1_1671773.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.CRzXDP7x4L/E---3.1_1671773.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',mvalid) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X43: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',con) ).
thf(dc,axiom,
( dc
= ( ^ [X21: reg,X22: reg] :
~ ( c @ X21 @ X22 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',dc) ).
thf(tpp,axiom,
( tpp
= ( ^ [X36: reg,X37: reg] :
( ( pp @ X36 @ X37 )
& ? [X25: reg] :
( ( ec @ X25 @ X36 )
& ( ec @ X25 @ X37 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',tpp) ).
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.CRzXDP7x4L/E---3.1_1671773.p',i_axiom_for_fool_a) ).
thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X42: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',ax3) ).
thf(ax2,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X41: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',ax2) ).
thf(ax1,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X40: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',ax1) ).
thf(c_symmetric,axiom,
! [X19: reg,X20: reg] :
( ( c @ X19 @ X20 )
=> ( c @ X20 @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.CRzXDP7x4L/E---3.1_1671773.p',c_symmetric) ).
thf(c_0_19,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X52: reg] :
( ( c @ X52 @ X25 )
=> ( c @ X52 @ Z0 ) )
& ! [X53: reg] :
( ( c @ X53 @ X25 )
=> ( c @ X53 @ 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,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X59: reg] :
( ! [X60: reg] :
( ( c @ X60 @ X59 )
=> ( c @ X60 @ Z0 ) )
& ! [X61: reg] :
( ( c @ X61 @ X59 )
=> ( c @ X61 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_22,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X52: reg] :
( ( c @ X52 @ X25 )
=> ( c @ X52 @ Z0 ) )
& ! [X53: reg] :
( ( c @ X53 @ X25 )
=> ( c @ X53 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X62: reg] :
( ( c @ X62 @ Z0 )
=> ( c @ X62 @ Z1 ) )
& ~ ! [X63: reg] :
( ( c @ X63 @ Z1 )
=> ( c @ X63 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_24,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_25,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_26,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_27,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X72: reg] :
( ( c @ X72 @ Z0 )
=> ( c @ X72 @ Z1 ) )
& ~ ! [X73: reg] :
( ( c @ X73 @ Z1 )
=> ( c @ X73 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X74: reg] :
( ! [X75: reg] :
( ( c @ X75 @ X74 )
=> ( c @ X75 @ X25 ) )
& ! [X76: reg] :
( ( c @ X76 @ X74 )
=> ( c @ X76 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X77: reg] :
( ! [X78: reg] :
( ( c @ X78 @ X77 )
=> ( c @ X78 @ X25 ) )
& ! [X79: reg] :
( ( c @ X79 @ X77 )
=> ( c @ X79 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ntpp]) ).
thf(c_0_28,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X59: reg] :
( ! [X60: reg] :
( ( c @ X60 @ X59 )
=> ( c @ X60 @ Z0 ) )
& ! [X61: reg] :
( ( c @ X61 @ X59 )
=> ( c @ X61 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_29,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X62: reg] :
( ( c @ X62 @ Z0 )
=> ( c @ X62 @ Z1 ) )
& ~ ! [X63: reg] :
( ( c @ X63 @ Z1 )
=> ( c @ X63 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_20]) ).
thf(c_0_30,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_24,c_0_25]),c_0_26]) ).
thf(c_0_31,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_32,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_33,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_34,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X43: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_35,plain,
( dc
= ( ^ [Z0: reg,Z1: reg] :
~ ( c @ Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[dc]) ).
thf(c_0_36,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X64: reg] :
( ( c @ X64 @ Z0 )
=> ( c @ X64 @ Z1 ) )
& ~ ! [X65: reg] :
( ( c @ X65 @ Z1 )
=> ( c @ X65 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X66: reg] :
( ! [X67: reg] :
( ( c @ X67 @ X66 )
=> ( c @ X67 @ X25 ) )
& ! [X68: reg] :
( ( c @ X68 @ X66 )
=> ( c @ X68 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X69: reg] :
( ! [X70: reg] :
( ( c @ X70 @ X69 )
=> ( c @ X70 @ X25 ) )
& ! [X71: reg] :
( ( c @ X71 @ X69 )
=> ( c @ X71 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[tpp]) ).
thf(c_0_37,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X72: reg] :
( ( c @ X72 @ Z0 )
=> ( c @ X72 @ Z1 ) )
& ~ ! [X73: reg] :
( ( c @ X73 @ Z1 )
=> ( c @ X73 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X74: reg] :
( ! [X75: reg] :
( ( c @ X75 @ X74 )
=> ( c @ X75 @ X25 ) )
& ! [X76: reg] :
( ( c @ X76 @ X74 )
=> ( c @ X76 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X77: reg] :
( ! [X78: reg] :
( ( c @ X78 @ X77 )
=> ( c @ X78 @ X25 ) )
& ! [X79: reg] :
( ( c @ X79 @ X77 )
=> ( c @ X79 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_38,plain,
! [X83: $i,X82: $i > $o] :
( ~ ! [X80: $i] :
( ~ ( fool @ X83 @ X80 )
| ( X82 @ X80 ) )
| ! [X81: $i] :
( ~ ( a @ X83 @ X81 )
| ( X82 @ X81 ) ) ),
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_30]),c_0_31]),c_0_32]),c_0_33])]) ).
thf(c_0_39,negated_conjecture,
~ ! [X112: $i,X111: $i] :
( ~ ( a @ X112 @ X111 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ),
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)],[c_0_34]),c_0_32]),c_0_33]),c_0_35])]) ).
thf(c_0_40,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X64: reg] :
( ( c @ X64 @ Z0 )
=> ( c @ X64 @ Z1 ) )
& ~ ! [X65: reg] :
( ( c @ X65 @ Z1 )
=> ( c @ X65 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X66: reg] :
( ! [X67: reg] :
( ( c @ X67 @ X66 )
=> ( c @ X67 @ X25 ) )
& ! [X68: reg] :
( ( c @ X68 @ X66 )
=> ( c @ X68 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X69: reg] :
( ! [X70: reg] :
( ( c @ X70 @ X69 )
=> ( c @ X70 @ X25 ) )
& ! [X71: reg] :
( ( c @ X71 @ X69 )
=> ( c @ X71 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,c_0_28]),c_0_29]) ).
thf(c_0_41,plain,
! [X110: $i,X109: $i] :
( ~ ( a @ X110 @ X109 )
| ( ! [X100: reg] :
( ( c @ X100 @ paris )
=> ( c @ X100 @ france ) )
& ~ ! [X101: reg] :
( ( c @ X101 @ france )
=> ( c @ X101 @ paris ) )
& ~ ? [X102: reg] :
( ( c @ X102 @ paris )
& ~ ? [X103: reg] :
( ! [X104: reg] :
( ( c @ X104 @ X103 )
=> ( c @ X104 @ X102 ) )
& ! [X105: reg] :
( ( c @ X105 @ X103 )
=> ( c @ X105 @ paris ) ) )
& ( c @ X102 @ france )
& ~ ? [X106: reg] :
( ! [X107: reg] :
( ( c @ X107 @ X106 )
=> ( c @ X107 @ X102 ) )
& ! [X108: reg] :
( ( c @ X108 @ X106 )
=> ( c @ X108 @ 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_32]),c_0_33]),c_0_37])]) ).
thf(c_0_42,plain,
! [X99: $i,X98: $i] :
( ~ ( fool @ X99 @ X98 )
| ( ( c @ spain @ france )
& ~ ? [X95: reg] :
( ! [X96: reg] :
( ( c @ X96 @ X95 )
=> ( c @ X96 @ spain ) )
& ! [X97: reg] :
( ( c @ X97 @ X95 )
=> ( c @ X97 @ 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_32]),c_0_33]),c_0_28])]) ).
thf(c_0_43,plain,
! [X116: $i,X117: $i > $o,X119: $i] :
( ( ( fool @ X116 @ ( esk1_2 @ X116 @ X117 ) )
| ~ ( a @ X116 @ X119 )
| ( X117 @ X119 ) )
& ( ~ ( X117 @ ( esk1_2 @ X116 @ X117 ) )
| ~ ( a @ X116 @ X119 )
| ( X117 @ X119 ) ) ),
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_38])])])])])]) ).
thf(c_0_44,negated_conjecture,
( ( a @ esk13_0 @ esk14_0 )
& ( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
thf(c_0_45,plain,
! [X94: $i,X93: $i] :
( ~ ( a @ X94 @ X93 )
| ( ! [X84: reg] :
( ( c @ X84 @ catalunya )
=> ( c @ X84 @ spain ) )
& ~ ! [X85: reg] :
( ( c @ X85 @ spain )
=> ( c @ X85 @ catalunya ) )
& ? [X86: reg] :
( ( c @ X86 @ catalunya )
& ~ ? [X87: reg] :
( ! [X88: reg] :
( ( c @ X88 @ X87 )
=> ( c @ X88 @ X86 ) )
& ! [X89: reg] :
( ( c @ X89 @ X87 )
=> ( c @ X89 @ catalunya ) ) )
& ( c @ X86 @ spain )
& ~ ? [X90: reg] :
( ! [X91: reg] :
( ( c @ X91 @ X90 )
=> ( c @ X91 @ X86 ) )
& ! [X92: reg] :
( ( c @ X92 @ X90 )
=> ( c @ X92 @ 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_32]),c_0_33]),c_0_40])]) ).
thf(c_0_46,plain,
! [X114: reg,X115: reg] :
( ~ ( c @ X114 @ X115 )
| ( c @ X115 @ X114 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])])]) ).
thf(c_0_47,plain,
! [X136: $i,X137: $i,X138: reg,X140: reg,X142: reg,X143: reg,X145: reg,X146: reg] :
( ( ~ ( c @ X138 @ paris )
| ( c @ X138 @ france )
| ~ ( a @ X136 @ X137 ) )
& ( ( c @ esk10_0 @ france )
| ~ ( a @ X136 @ X137 ) )
& ( ~ ( c @ esk10_0 @ paris )
| ~ ( a @ X136 @ X137 ) )
& ( ~ ( c @ X145 @ ( esk12_1 @ X140 ) )
| ( c @ X145 @ X140 )
| ~ ( c @ X140 @ france )
| ~ ( c @ X142 @ ( esk11_1 @ X140 ) )
| ( c @ X142 @ X140 )
| ~ ( c @ X140 @ paris )
| ~ ( a @ X136 @ X137 ) )
& ( ~ ( c @ X146 @ ( esk12_1 @ X140 ) )
| ( c @ X146 @ france )
| ~ ( c @ X140 @ france )
| ~ ( c @ X142 @ ( esk11_1 @ X140 ) )
| ( c @ X142 @ X140 )
| ~ ( c @ X140 @ paris )
| ~ ( a @ X136 @ X137 ) )
& ( ~ ( c @ X145 @ ( esk12_1 @ X140 ) )
| ( c @ X145 @ X140 )
| ~ ( c @ X140 @ france )
| ~ ( c @ X143 @ ( esk11_1 @ X140 ) )
| ( c @ X143 @ paris )
| ~ ( c @ X140 @ paris )
| ~ ( a @ X136 @ X137 ) )
& ( ~ ( c @ X146 @ ( esk12_1 @ X140 ) )
| ( c @ X146 @ france )
| ~ ( c @ X140 @ france )
| ~ ( c @ X143 @ ( esk11_1 @ X140 ) )
| ( c @ X143 @ paris )
| ~ ( c @ X140 @ paris )
| ~ ( a @ X136 @ X137 ) ) ),
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_41])])])])])])]) ).
thf(c_0_48,plain,
! [X131: $i,X132: $i,X133: reg] :
( ( ( c @ spain @ france )
| ~ ( fool @ X131 @ X132 ) )
& ( ( c @ ( esk9_1 @ X133 ) @ X133 )
| ( c @ ( esk8_1 @ X133 ) @ X133 )
| ~ ( fool @ X131 @ X132 ) )
& ( ~ ( c @ ( esk9_1 @ X133 ) @ france )
| ( c @ ( esk8_1 @ X133 ) @ X133 )
| ~ ( fool @ X131 @ X132 ) )
& ( ( c @ ( esk9_1 @ X133 ) @ X133 )
| ~ ( c @ ( esk8_1 @ X133 ) @ spain )
| ~ ( fool @ X131 @ X132 ) )
& ( ~ ( c @ ( esk9_1 @ X133 ) @ france )
| ~ ( c @ ( esk8_1 @ X133 ) @ spain )
| ~ ( fool @ X131 @ X132 ) ) ),
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_42])])])])])])]) ).
thf(c_0_49,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
a @ esk13_0 @ esk14_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_51,plain,
! [X120: $i,X121: $i,X122: reg,X125: reg,X128: reg] :
( ( ~ ( c @ X122 @ catalunya )
| ( c @ X122 @ spain )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ esk2_0 @ spain )
| ~ ( a @ X120 @ X121 ) )
& ( ~ ( c @ esk2_0 @ catalunya )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ esk3_0 @ catalunya )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ ( esk5_1 @ X125 ) @ X125 )
| ( c @ ( esk4_1 @ X125 ) @ X125 )
| ~ ( a @ X120 @ X121 ) )
& ( ~ ( c @ ( esk5_1 @ X125 ) @ catalunya )
| ( c @ ( esk4_1 @ X125 ) @ X125 )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ ( esk5_1 @ X125 ) @ X125 )
| ~ ( c @ ( esk4_1 @ X125 ) @ esk3_0 )
| ~ ( a @ X120 @ X121 ) )
& ( ~ ( c @ ( esk5_1 @ X125 ) @ catalunya )
| ~ ( c @ ( esk4_1 @ X125 ) @ esk3_0 )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ esk3_0 @ spain )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ ( esk7_1 @ X128 ) @ X128 )
| ( c @ ( esk6_1 @ X128 ) @ X128 )
| ~ ( a @ X120 @ X121 ) )
& ( ~ ( c @ ( esk7_1 @ X128 ) @ spain )
| ( c @ ( esk6_1 @ X128 ) @ X128 )
| ~ ( a @ X120 @ X121 ) )
& ( ( c @ ( esk7_1 @ X128 ) @ X128 )
| ~ ( c @ ( esk6_1 @ X128 ) @ esk3_0 )
| ~ ( a @ X120 @ X121 ) )
& ( ~ ( c @ ( esk7_1 @ X128 ) @ spain )
| ~ ( c @ ( esk6_1 @ X128 ) @ esk3_0 )
| ~ ( a @ X120 @ X121 ) ) ),
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_45])])])])])])]) ).
thf(c_0_52,plain,
! [X18: reg,X19: reg] :
( ( c @ X19 @ X18 )
| ~ ( c @ X18 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_53,negated_conjecture,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_54,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ( c @ X20 @ paris )
| ~ ( c @ X18 @ ( esk12_1 @ X19 ) )
| ~ ( c @ X19 @ france )
| ~ ( c @ X20 @ ( esk11_1 @ X19 ) )
| ~ ( c @ X19 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_55,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_56,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ X18 ) @ X18 )
| ( c @ ( esk8_1 @ X18 ) @ X18 )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_57,negated_conjecture,
! [X4: $i > $o] :
( ( fool @ esk13_0 @ ( esk1_2 @ esk13_0 @ X4 ) )
| ( X4 @ esk14_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_58,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ spain )
| ~ ( c @ X18 @ catalunya )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_59,negated_conjecture,
( ( c @ spain @ paris )
| ( c @ paris @ catalunya ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_60,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ( c @ X19 @ paris )
| ~ ( c @ X19 @ ( esk11_1 @ X20 ) )
| ~ ( c @ X18 @ ( esk12_1 @ X20 ) )
| ~ ( c @ X20 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_61,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk9_1 @ X18 ) @ X18 )
| ( c @ ( esk8_1 @ X18 ) @ X18 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_56]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ paris @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52]) ).
thf(c_0_63,negated_conjecture,
! [X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ X18 ) ) @ ( esk11_1 @ X18 ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ X18 ) ) @ paris )
| ( c @ X19 @ france )
| ~ ( c @ X19 @ ( esk12_1 @ X18 ) )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,negated_conjecture,
c @ paris @ spain,
inference(spm,[status(thm)],[c_0_62,c_0_50]) ).
thf(c_0_65,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ X18 ) ) @ ( esk12_1 @ X18 ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ X18 ) ) @ ( esk11_1 @ X18 ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ X18 ) ) @ france )
| ( c @ ( esk9_1 @ ( esk11_1 @ X18 ) ) @ paris )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_61]) ).
thf(c_0_66,negated_conjecture,
c @ spain @ paris,
inference(spm,[status(thm)],[c_0_52,c_0_64]) ).
thf(c_0_67,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_68,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk1_2 @ X3 @ X4 ) )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_69,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ paris )
| ~ ( c @ X18 @ ( esk12_1 @ X19 ) )
| ~ ( c @ X19 @ france )
| ~ ( c @ X20 @ ( esk11_1 @ X19 ) )
| ~ ( c @ X19 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_70,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk9_1 @ X18 ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_71,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_67,c_0_50]) ).
thf(c_0_72,plain,
! [X3: $i,X14: $i] :
( ( ( esk1_2 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 ) )
= X14 )
| ~ ( a @ X3 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_68]) ).
thf(c_0_73,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ paris )
| ( c @ X19 @ X20 )
| ~ ( c @ X18 @ ( esk11_1 @ X20 ) )
| ~ ( c @ X19 @ ( esk12_1 @ X20 ) )
| ~ ( c @ X20 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[c_0_69,c_0_55]) ).
thf(c_0_74,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,negated_conjecture,
fool @ esk13_0 @ esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_72])])]),c_0_50])]) ).
thf(c_0_76,negated_conjecture,
! [X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ X18 ) ) @ ( esk11_1 @ X18 ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ X18 ) ) @ paris )
| ( c @ X19 @ X18 )
| ~ ( c @ X19 @ ( esk12_1 @ X18 ) )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_61]) ).
thf(c_0_77,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
thf(c_0_78,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_66])]) ).
thf(c_0_79,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk8_1 @ X18 ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_80,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain ) ),
inference(spm,[status(thm)],[c_0_78,c_0_50]) ).
thf(c_0_81,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_82,negated_conjecture,
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_81,c_0_75]) ).
thf(c_0_83,plain,
! [X18: reg,X3: $i,X14: $i] :
( ~ ( c @ ( esk9_1 @ X18 ) @ france )
| ~ ( c @ ( esk8_1 @ X18 ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_84,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_82]),c_0_66])]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_80]) ).
thf(c_0_86,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_84,c_0_50]) ).
thf(c_0_87,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_88,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_87,c_0_75]) ).
thf(c_0_89,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_88]) ).
thf(c_0_90,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_89,c_0_50]) ).
thf(c_0_91,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ( c @ X20 @ X19 )
| ~ ( c @ X18 @ ( esk12_1 @ X19 ) )
| ~ ( c @ X19 @ france )
| ~ ( c @ X20 @ ( esk11_1 @ X19 ) )
| ~ ( c @ X19 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_90]) ).
thf(c_0_93,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ( c @ X19 @ X20 )
| ~ ( c @ X19 @ ( esk11_1 @ X20 ) )
| ~ ( c @ X18 @ ( esk12_1 @ X20 ) )
| ~ ( c @ X20 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[c_0_91,c_0_55]) ).
thf(c_0_94,negated_conjecture,
c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ),
inference(spm,[status(thm)],[c_0_92,c_0_75]) ).
thf(c_0_95,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ X18 @ france )
| ~ ( c @ X18 @ ( esk12_1 @ spain ) )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_66])]) ).
thf(c_0_96,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_61]) ).
thf(c_0_97,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ X19 )
| ~ ( c @ X18 @ ( esk12_1 @ X19 ) )
| ~ ( c @ X19 @ france )
| ~ ( c @ X20 @ ( esk11_1 @ X19 ) )
| ~ ( c @ X19 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_98,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_96,c_0_50]) ).
thf(c_0_99,plain,
! [X20: reg,X19: reg,X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ X19 )
| ~ ( c @ X20 @ ( esk11_1 @ X19 ) )
| ~ ( c @ X18 @ ( esk12_1 @ X19 ) )
| ~ ( c @ X19 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[c_0_97,c_0_55]) ).
thf(c_0_100,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_98]) ).
thf(c_0_101,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ X18 @ spain )
| ~ ( c @ X18 @ ( esk12_1 @ spain ) )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_94]),c_0_66])]) ).
thf(c_0_102,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
inference(spm,[status(thm)],[c_0_100,c_0_75]) ).
thf(c_0_103,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
thf(c_0_104,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain ) ),
inference(spm,[status(thm)],[c_0_103,c_0_50]) ).
thf(c_0_105,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_104]) ).
thf(c_0_106,negated_conjecture,
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
inference(spm,[status(thm)],[c_0_105,c_0_75]) ).
thf(c_0_107,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_106]) ).
thf(c_0_108,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_104]) ).
thf(c_0_109,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_107,c_0_50]) ).
thf(c_0_110,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
thf(c_0_111,negated_conjecture,
c @ ( esk8_1 @ ( esk11_1 @ spain ) ) @ spain,
inference(spm,[status(thm)],[c_0_110,c_0_75]) ).
thf(c_0_112,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_111]) ).
thf(c_0_113,negated_conjecture,
c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ),
inference(spm,[status(thm)],[c_0_112,c_0_75]) ).
thf(c_0_114,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ X18 @ france )
| ~ ( c @ X18 @ ( esk12_1 @ spain ) )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_113]),c_0_66])]) ).
thf(c_0_115,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_61]) ).
thf(c_0_116,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_115,c_0_50]) ).
thf(c_0_117,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_116]) ).
thf(c_0_118,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ X18 @ spain )
| ~ ( c @ X18 @ ( esk12_1 @ spain ) )
| ~ ( a @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_113]),c_0_66])]) ).
thf(c_0_119,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_117,c_0_75]) ).
thf(c_0_120,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
thf(c_0_121,negated_conjecture,
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk8_1 @ ( esk12_1 @ spain ) ) @ spain ) ),
inference(spm,[status(thm)],[c_0_120,c_0_50]) ).
thf(c_0_122,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_121]) ).
thf(c_0_123,negated_conjecture,
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ ( esk12_1 @ spain ) )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_122,c_0_75]) ).
thf(c_0_124,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_123]) ).
thf(c_0_125,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_121]) ).
thf(c_0_126,negated_conjecture,
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ( c @ ( esk9_1 @ ( esk12_1 @ spain ) ) @ france ) ),
inference(spm,[status(thm)],[c_0_124,c_0_50]) ).
thf(c_0_127,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
thf(c_0_128,negated_conjecture,
c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ paris,
inference(spm,[status(thm)],[c_0_127,c_0_75]) ).
thf(c_0_129,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_128]) ).
thf(c_0_130,negated_conjecture,
! [X3: $i,X4: $i > $o] :
( ( fool @ esk13_0 @ ( esk1_2 @ esk13_0 @ ( a @ X3 ) ) )
| ( fool @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ esk14_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_57]) ).
thf(c_0_131,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_111]) ).
thf(c_0_132,negated_conjecture,
c @ ( esk9_1 @ ( esk11_1 @ spain ) ) @ france,
inference(spm,[status(thm)],[c_0_129,c_0_50]) ).
thf(c_0_133,negated_conjecture,
! [X3: $i] :
( ( fool @ esk13_0 @ ( esk1_2 @ esk13_0 @ ( a @ X3 ) ) )
| ( fool @ X3 @ esk14_0 ) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_72])])]),c_0_57]) ).
thf(c_0_134,negated_conjecture,
! [X3: $i,X14: $i] :
~ ( fool @ X3 @ X14 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132])]) ).
thf(c_0_135,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_133,c_0_134]),c_0_134]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG003^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 18:34:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.CRzXDP7x4L/E---3.1_1671773.p
% 7.83/1.43 % Version: 3.5.1-ho
% 7.83/1.43 % Preprocessing class: HSMSSMSSMLMNHSN.
% 7.83/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.83/1.43 % Starting ho_unfolding_3 with 1500s (5) cores
% 7.83/1.43 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 7.83/1.43 % Starting almost_fo_3_lam with 300s (1) cores
% 7.83/1.43 % Starting post_as_ho1 with 300s (1) cores
% 7.83/1.43 % ho_unfolding_3 with pid 1671807 completed with status 0
% 7.83/1.43 % Result found by ho_unfolding_3
% 7.83/1.43 % Preprocessing class: HSMSSMSSMLMNHSN.
% 7.83/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.83/1.43 % Starting ho_unfolding_3 with 1500s (5) cores
% 7.83/1.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.83/1.43 % No SInE strategy applied
% 7.83/1.43 % Search class: HGHNF-FFMF21-SHSSMFBN
% 7.83/1.43 % partial match(1): HGHNF-FFMF21-SHSSMSBN
% 7.83/1.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.83/1.43 % Starting SubtermCWHack with 136s (1) cores
% 7.83/1.43 % Starting ho_unfolding_3 with 151s (1) cores
% 7.83/1.43 % Starting post_as_ho11 with 136s (1) cores
% 7.83/1.43 % Starting pre_casc_8 with 136s (1) cores
% 7.83/1.43 % Starting post_as_ho2 with 136s (1) cores
% 7.83/1.43 % ho_unfolding_3 with pid 1671815 completed with status 0
% 7.83/1.43 % Result found by ho_unfolding_3
% 7.83/1.43 % Preprocessing class: HSMSSMSSMLMNHSN.
% 7.83/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.83/1.43 % Starting ho_unfolding_3 with 1500s (5) cores
% 7.83/1.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.83/1.43 % No SInE strategy applied
% 7.83/1.43 % Search class: HGHNF-FFMF21-SHSSMFBN
% 7.83/1.43 % partial match(1): HGHNF-FFMF21-SHSSMSBN
% 7.83/1.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.83/1.43 % Starting SubtermCWHack with 136s (1) cores
% 7.83/1.43 % Starting ho_unfolding_3 with 151s (1) cores
% 7.83/1.43 % Preprocessing time : 0.002 s
% 7.83/1.43 % Presaturation interreduction done
% 7.83/1.43
% 7.83/1.43 % Proof found!
% 7.83/1.43 % SZS status Theorem
% 7.83/1.43 % SZS output start CNFRefutation
% See solution above
% 7.83/1.43 % Parsed axioms : 96
% 7.83/1.43 % Removed by relevancy pruning/SinE : 0
% 7.83/1.43 % Initial clauses : 80
% 7.83/1.43 % Removed in clause preprocessing : 49
% 7.83/1.43 % Initial clauses in saturation : 31
% 7.83/1.43 % Processed clauses : 3663
% 7.83/1.43 % ...of these trivial : 14
% 7.83/1.43 % ...subsumed : 1061
% 7.83/1.43 % ...remaining for further processing : 2588
% 7.83/1.43 % Other redundant clauses eliminated : 5
% 7.83/1.43 % Clauses deleted for lack of memory : 0
% 7.83/1.43 % Backward-subsumed : 1129
% 7.83/1.43 % Backward-rewritten : 543
% 7.83/1.43 % Generated clauses : 25977
% 7.83/1.43 % ...of the previous two non-redundant : 19066
% 7.83/1.43 % ...aggressively subsumed : 0
% 7.83/1.43 % Contextual simplify-reflections : 57
% 7.83/1.43 % Paramodulations : 25931
% 7.83/1.43 % Factorizations : 18
% 7.83/1.43 % NegExts : 5
% 7.83/1.43 % Equation resolutions : 6
% 7.83/1.43 % Disequality decompositions : 0
% 7.83/1.43 % Total rewrite steps : 12904
% 7.83/1.43 % ...of those cached : 12839
% 7.83/1.43 % Propositional unsat checks : 0
% 7.83/1.43 % Propositional check models : 0
% 7.83/1.43 % Propositional check unsatisfiable : 0
% 7.83/1.43 % Propositional clauses : 0
% 7.83/1.43 % Propositional clauses after purity: 0
% 7.83/1.43 % Propositional unsat core size : 0
% 7.83/1.43 % Propositional preprocessing time : 0.000
% 7.83/1.43 % Propositional encoding time : 0.000
% 7.83/1.43 % Propositional solver time : 0.000
% 7.83/1.43 % Success case prop preproc time : 0.000
% 7.83/1.43 % Success case prop encoding time : 0.000
% 7.83/1.43 % Success case prop solver time : 0.000
% 7.83/1.43 % Current number of processed clauses : 874
% 7.83/1.43 % Positive orientable unit clauses : 71
% 7.83/1.43 % Positive unorientable unit clauses: 0
% 7.83/1.43 % Negative unit clauses : 1
% 7.83/1.43 % Non-unit-clauses : 802
% 7.83/1.43 % Current number of unprocessed clauses: 13412
% 7.83/1.43 % ...number of literals in the above : 86431
% 7.83/1.43 % Current number of archived formulas : 0
% 7.83/1.43 % Current number of archived clauses : 1714
% 7.83/1.43 % Clause-clause subsumption calls (NU) : 742671
% 7.83/1.43 % Rec. Clause-clause subsumption calls : 83739
% 7.83/1.43 % Non-unit clause-clause subsumptions : 2234
% 7.83/1.43 % Unit Clause-clause subsumption calls : 7601
% 7.83/1.43 % Rewrite failures with RHS unbound : 0
% 7.83/1.43 % BW rewrite match attempts : 56
% 7.83/1.43 % BW rewrite match successes : 39
% 7.83/1.43 % Condensation attempts : 3663
% 7.83/1.43 % Condensation successes : 0
% 7.83/1.43 % Termbank termtop insertions : 816805
% 7.83/1.43 % Search garbage collected termcells : 1500
% 7.83/1.43
% 7.83/1.43 % -------------------------------------------------
% 7.83/1.43 % User time : 1.052 s
% 7.83/1.43 % System time : 0.025 s
% 7.83/1.43 % Total time : 1.077 s
% 7.83/1.43 % Maximum resident set size: 3988 pages
% 7.83/1.43
% 7.83/1.43 % -------------------------------------------------
% 7.83/1.43 % User time : 5.299 s
% 7.83/1.43 % System time : 0.110 s
% 7.83/1.43 % Total time : 5.410 s
% 7.83/1.43 % Maximum resident set size: 4864 pages
% 7.83/1.43 % E exiting
%------------------------------------------------------------------------------