TSTP Solution File: GEG009^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : GEG009^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:56:53 EDT 2024
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 58
% Syntax : Number of formulae : 131 ( 51 unt; 34 typ; 0 def)
% Number of atoms : 359 ( 30 equ; 0 cnn)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 964 ( 134 ~; 109 |; 58 &; 614 @)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 13 con; 0-3 aty)
% Number of variables : 229 ( 68 ^ 142 !; 19 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_37,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_49,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
c: reg > reg > $o ).
thf(decl_55,type,
p: reg > reg > $o ).
thf(decl_56,type,
eq: reg > reg > $o ).
thf(decl_57,type,
o: reg > reg > $o ).
thf(decl_59,type,
ec: reg > reg > $o ).
thf(decl_60,type,
pp: reg > reg > $o ).
thf(decl_62,type,
ntpp: reg > reg > $o ).
thf(decl_64,type,
france: reg ).
thf(decl_65,type,
spain: reg ).
thf(decl_66,type,
paris: reg ).
thf(decl_67,type,
a: $i > $i > $o ).
thf(decl_68,type,
fool: $i > $i > $o ).
thf(decl_69,type,
esk1_0: $i ).
thf(decl_70,type,
esk2_0: $i ).
thf(decl_71,type,
esk3_1: reg > reg ).
thf(decl_72,type,
esk4_1: reg > reg ).
thf(decl_73,type,
esk5_1: reg > reg ).
thf(decl_74,type,
esk6_0: reg ).
thf(decl_75,type,
esk7_1: reg > reg ).
thf(decl_76,type,
esk8_1: reg > reg ).
thf(decl_78,type,
esk10_2: $i > ( $i > $o ) > $i ).
thf(decl_80,type,
epred1_0: $o ).
thf(decl_81,type,
epred2_0: $o ).
thf(decl_82,type,
epred3_0: $o ).
thf(decl_83,type,
epred4_0: $o ).
thf(decl_88,type,
epred9_0: $o ).
thf(decl_89,type,
epred10_0: $o ).
thf(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X38: reg,X39: reg] :
( ( pp @ X38 @ X39 )
& ~ ? [X25: reg] :
( ( ec @ X25 @ X38 )
& ( ec @ X25 @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(eq,axiom,
( eq
= ( ^ [X26: reg,X27: reg] :
( ( p @ X26 @ X27 )
& ( p @ X27 @ X26 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X43: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
? [X25: reg] :
( ~ ( o @ X25 @ paris )
& ~ ( eq @ X25 @ spain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(t_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X40: $i > $o] : ( mimplies @ ( mbox @ fool @ X40 ) @ X40 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(ax2,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X42: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(c_symmetric,axiom,
! [X19: reg,X20: reg] :
( ( c @ X19 @ X20 )
=> ( c @ X20 @ X19 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
thf(c_reflexive,axiom,
! [X18: reg] : ( c @ X18 @ X18 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_reflexive) ).
thf(c_0_18,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X50: reg] :
( ( c @ X50 @ X25 )
=> ( c @ X50 @ Z0 ) )
& ! [X51: reg] :
( ( c @ X51 @ X25 )
=> ( c @ X51 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[o]) ).
thf(c_0_19,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X25: reg] :
( ( c @ X25 @ Z0 )
=> ( c @ X25 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_20,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X55: reg] :
( ( c @ X55 @ Z0 )
=> ( c @ X55 @ Z1 ) )
& ~ ! [X56: reg] :
( ( c @ X56 @ Z1 )
=> ( c @ X56 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_21,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X52: reg] :
( ! [X53: reg] :
( ( c @ X53 @ X52 )
=> ( c @ X53 @ Z0 ) )
& ! [X54: reg] :
( ( c @ X54 @ X52 )
=> ( c @ X54 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_22,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X50: reg] :
( ( c @ X50 @ X25 )
=> ( c @ X50 @ Z0 ) )
& ! [X51: reg] :
( ( c @ X51 @ X25 )
=> ( c @ X51 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,plain,
( ntpp
= ( ^ [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)],[ntpp]) ).
thf(c_0_24,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X55: reg] :
( ( c @ X55 @ Z0 )
=> ( c @ X55 @ Z1 ) )
& ~ ! [X56: reg] :
( ( c @ X56 @ Z1 )
=> ( c @ X56 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_19]) ).
thf(c_0_25,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X52: reg] :
( ! [X53: reg] :
( ( c @ X53 @ X52 )
=> ( c @ X53 @ Z0 ) )
& ! [X54: reg] :
( ( c @ X54 @ X52 )
=> ( c @ X54 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,plain,
( eq
= ( ^ [Z0: reg,Z1: reg] :
( ! [X48: reg] :
( ( c @ X48 @ Z0 )
=> ( c @ X48 @ Z1 ) )
& ! [X49: reg] :
( ( c @ X49 @ Z1 )
=> ( c @ X49 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[eq]) ).
thf(c_0_27,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_28,plain,
( ntpp
= ( ^ [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_23,c_0_24]),c_0_25]) ).
thf(c_0_29,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_30,plain,
( eq
= ( ^ [Z0: reg,Z1: reg] :
( ! [X48: reg] :
( ( c @ X48 @ Z0 )
=> ( c @ X48 @ Z1 ) )
& ! [X49: reg] :
( ( c @ X49 @ Z1 )
=> ( c @ X49 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_26,c_0_19]) ).
thf(c_0_31,plain,
! [X95: $i,X94: $i] :
( ~ ( a @ X95 @ X94 )
| ( ! [X85: reg] :
( ( c @ X85 @ paris )
=> ( c @ X85 @ france ) )
& ~ ! [X86: reg] :
( ( c @ X86 @ france )
=> ( c @ X86 @ paris ) )
& ~ ? [X87: reg] :
( ( c @ X87 @ paris )
& ~ ? [X88: reg] :
( ! [X89: reg] :
( ( c @ X89 @ X88 )
=> ( c @ X89 @ X87 ) )
& ! [X90: reg] :
( ( c @ X90 @ X88 )
=> ( c @ X90 @ paris ) ) )
& ( c @ X87 @ france )
& ~ ? [X91: reg] :
( ! [X92: reg] :
( ( c @ X92 @ X91 )
=> ( c @ X92 @ X87 ) )
& ! [X93: reg] :
( ( c @ X93 @ X91 )
=> ( c @ X93 @ 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_27]),c_0_28]),c_0_29])]) ).
thf(c_0_32,negated_conjecture,
~ ! [X79: $i,X78: $i] :
( ~ ( a @ X79 @ X78 )
| ? [X25: reg] :
( ~ ? [X73: reg] :
( ! [X74: reg] :
( ( c @ X74 @ X73 )
=> ( c @ X74 @ X25 ) )
& ! [X75: reg] :
( ( c @ X75 @ X73 )
=> ( c @ X75 @ paris ) ) )
& ~ ( ! [X76: reg] :
( ( c @ X76 @ X25 )
=> ( c @ X76 @ spain ) )
& ! [X77: reg] :
( ( c @ X77 @ spain )
=> ( c @ X77 @ 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)],[inference(assume_negation,[status(cth)],[con])]),c_0_27]),c_0_22]),c_0_30]),c_0_29])]) ).
thf(c_0_33,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_34,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_35,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_36,plain,
! [X121: $i,X122: $i,X123: reg,X125: reg,X127: reg,X128: reg,X130: reg,X131: reg] :
( ( ~ ( c @ X123 @ paris )
| ( c @ X123 @ france )
| ~ ( a @ X121 @ X122 ) )
& ( ( c @ esk6_0 @ france )
| ~ ( a @ X121 @ X122 ) )
& ( ~ ( c @ esk6_0 @ paris )
| ~ ( a @ X121 @ X122 ) )
& ( ~ ( c @ X130 @ ( esk8_1 @ X125 ) )
| ( c @ X130 @ X125 )
| ~ ( c @ X125 @ france )
| ~ ( c @ X127 @ ( esk7_1 @ X125 ) )
| ( c @ X127 @ X125 )
| ~ ( c @ X125 @ paris )
| ~ ( a @ X121 @ X122 ) )
& ( ~ ( c @ X131 @ ( esk8_1 @ X125 ) )
| ( c @ X131 @ france )
| ~ ( c @ X125 @ france )
| ~ ( c @ X127 @ ( esk7_1 @ X125 ) )
| ( c @ X127 @ X125 )
| ~ ( c @ X125 @ paris )
| ~ ( a @ X121 @ X122 ) )
& ( ~ ( c @ X130 @ ( esk8_1 @ X125 ) )
| ( c @ X130 @ X125 )
| ~ ( c @ X125 @ france )
| ~ ( c @ X128 @ ( esk7_1 @ X125 ) )
| ( c @ X128 @ paris )
| ~ ( c @ X125 @ paris )
| ~ ( a @ X121 @ X122 ) )
& ( ~ ( c @ X131 @ ( esk8_1 @ X125 ) )
| ( c @ X131 @ france )
| ~ ( c @ X125 @ france )
| ~ ( c @ X128 @ ( esk7_1 @ X125 ) )
| ( c @ X128 @ paris )
| ~ ( c @ X125 @ paris )
| ~ ( a @ X121 @ X122 ) ) ),
inference(distribute,[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_31])])])])])]) ).
thf(c_0_37,plain,
( ~ epred4_0
<=> ! [X3: $i,X14: $i] :
~ ( a @ X3 @ X14 ) ),
introduced(definition) ).
thf(c_0_38,negated_conjecture,
! [X110: reg,X112: reg,X113: reg,X114: reg,X115: reg] :
( ( a @ esk1_0 @ esk2_0 )
& ( ~ ( c @ X114 @ X110 )
| ( c @ X114 @ spain )
| ~ ( c @ X112 @ ( esk3_1 @ X110 ) )
| ( c @ X112 @ X110 ) )
& ( ~ ( c @ X115 @ spain )
| ( c @ X115 @ X110 )
| ~ ( c @ X112 @ ( esk3_1 @ X110 ) )
| ( c @ X112 @ X110 ) )
& ( ~ ( c @ X114 @ X110 )
| ( c @ X114 @ spain )
| ~ ( c @ X113 @ ( esk3_1 @ X110 ) )
| ( c @ X113 @ paris ) )
& ( ~ ( c @ X115 @ spain )
| ( c @ X115 @ X110 )
| ~ ( c @ X113 @ ( esk3_1 @ X110 ) )
| ( c @ X113 @ paris ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])]) ).
thf(c_0_39,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_33,c_0_34]),c_0_35]) ).
thf(c_0_40,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_41,plain,
( ~ epred3_0
<=> ! [X18: reg] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris ) ) ),
introduced(definition) ).
thf(c_0_42,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_43,plain,
! [X3: $i,X14: $i] :
( epred4_0
| ~ ( a @ X3 @ X14 ) ),
inference(split_equiv,[status(thm)],[c_0_37]) ).
thf(c_0_44,negated_conjecture,
a @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_45,plain,
! [X102: $i,X101: $i > $o] :
( ~ ! [X100: $i] :
( ~ ( fool @ X102 @ X100 )
| ( X101 @ X100 ) )
| ( X101 @ X102 ) ),
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_27]),c_0_39]),c_0_40]),c_0_29])]) ).
thf(c_0_46,plain,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_42,c_0_41]),c_0_37]) ).
thf(c_0_47,negated_conjecture,
epred4_0,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,plain,
! [X84: $i,X83: $i] :
( ~ ( fool @ X84 @ X83 )
| ( ( c @ spain @ france )
& ~ ? [X80: reg] :
( ! [X81: reg] :
( ( c @ X81 @ X80 )
=> ( c @ X81 @ spain ) )
& ! [X82: reg] :
( ( c @ X82 @ X80 )
=> ( c @ X82 @ 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_27]),c_0_25]),c_0_29])]) ).
thf(c_0_49,plain,
! [X136: $i,X137: $i > $o] :
( ( ( fool @ X136 @ ( esk10_2 @ X136 @ X137 ) )
| ( X137 @ X136 ) )
& ( ~ ( X137 @ ( esk10_2 @ X136 @ X137 ) )
| ( X137 @ X136 ) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
thf(c_0_50,plain,
( ~ epred10_0
<=> ! [X3: $i,X14: $i] :
~ ( fool @ X3 @ X14 ) ),
introduced(definition) ).
thf(c_0_51,plain,
! [X18: reg] :
( ( c @ X18 @ france )
| epred3_0
| ~ ( c @ X18 @ paris ) ),
inference(split_equiv,[status(thm)],[c_0_41]) ).
thf(c_0_52,plain,
~ epred3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_53,plain,
! [X145: reg,X146: reg] :
( ~ ( c @ X145 @ X146 )
| ( c @ X146 @ X145 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])]) ).
thf(c_0_54,plain,
! [X116: $i,X117: $i,X118: reg] :
( ( ( c @ spain @ france )
| ~ ( fool @ X116 @ X117 ) )
& ( ( c @ ( esk5_1 @ X118 ) @ X118 )
| ( c @ ( esk4_1 @ X118 ) @ X118 )
| ~ ( fool @ X116 @ X117 ) )
& ( ~ ( c @ ( esk5_1 @ X118 ) @ france )
| ( c @ ( esk4_1 @ X118 ) @ X118 )
| ~ ( fool @ X116 @ X117 ) )
& ( ( c @ ( esk5_1 @ X118 ) @ X118 )
| ~ ( c @ ( esk4_1 @ X118 ) @ spain )
| ~ ( fool @ X116 @ X117 ) )
& ( ~ ( c @ ( esk5_1 @ X118 ) @ france )
| ~ ( c @ ( esk4_1 @ X118 ) @ spain )
| ~ ( fool @ X116 @ X117 ) ) ),
inference(distribute,[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_48])])])])])]) ).
thf(c_0_55,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ X3 )
| ~ ( X4 @ ( esk10_2 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_56,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk10_2 @ X3 @ X4 ) )
| ( X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_57,plain,
( ~ epred2_0
<=> ! [X3: $i,X14: $i] :
~ ( fool @ X3 @ X14 ) ),
introduced(definition) ).
thf(c_0_58,plain,
! [X3: $i,X14: $i] :
( epred10_0
| ~ ( fool @ X3 @ X14 ) ),
inference(split_equiv,[status(thm)],[c_0_50]) ).
thf(c_0_59,plain,
! [X18: reg] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris ) ),
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_60,plain,
! [X18: reg,X19: reg] :
( ( c @ X19 @ X18 )
| ~ ( c @ X18 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_61,plain,
! [X144: reg] : ( c @ X144 @ X144 ),
inference(variable_rename,[status(thm)],[c_reflexive]) ).
thf(c_0_62,plain,
! [X3: $i,X14: $i] :
( ( c @ spain @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_63,plain,
! [X3: $i] : ( fool @ X3 @ X3 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_64,plain,
! [X3: $i,X14: $i] :
( epred2_0
| ~ ( fool @ X3 @ X14 ) ),
inference(split_equiv,[status(thm)],[c_0_57]) ).
thf(c_0_65,plain,
( ~ epred9_0
<=> ! [X18: reg] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ) ),
introduced(definition) ).
thf(c_0_66,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_67,plain,
! [X4: $i > $o,X3: $i] :
( ( X4 @ X3 )
| epred10_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
thf(c_0_68,plain,
! [X18: reg] :
( ( c @ X18 @ france )
| ~ ( c @ paris @ X18 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_69,negated_conjecture,
! [X18: reg,X20: reg,X19: reg] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ paris )
| ~ ( c @ X18 @ spain )
| ~ ( c @ X20 @ ( esk3_1 @ X19 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_70,plain,
! [X18: reg] : ( c @ X18 @ X18 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_71,plain,
c @ spain @ france,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_72,plain,
( ~ epred1_0
<=> ! [X18: reg] :
( ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X18 ) @ spain ) ) ),
introduced(definition) ).
thf(c_0_73,plain,
! [X18: reg,X3: $i,X14: $i] :
( ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X18 ) @ spain )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_74,plain,
! [X4: $i > $o,X3: $i] :
( ( X4 @ X3 )
| epred2_0 ),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
thf(c_0_75,plain,
( ~ epred10_0
| ~ epred9_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_66,c_0_65]),c_0_50]) ).
thf(c_0_76,plain,
epred10_0,
inference(spm,[status(thm)],[c_0_58,c_0_67]) ).
thf(c_0_77,plain,
! [X18: reg] :
( ( c @ france @ X18 )
| ~ ( c @ paris @ X18 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_68]) ).
thf(c_0_78,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk3_1 @ X18 ) @ paris )
| ( c @ X19 @ X18 )
| ~ ( c @ X19 @ spain ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_79,plain,
c @ france @ spain,
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
thf(c_0_80,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_73,c_0_72]),c_0_57]) ).
thf(c_0_81,plain,
epred2_0,
inference(spm,[status(thm)],[c_0_64,c_0_74]) ).
thf(c_0_82,plain,
! [X18: reg] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| epred9_0
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(split_equiv,[status(thm)],[c_0_65]) ).
thf(c_0_83,plain,
~ epred9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
thf(c_0_84,plain,
! [X18: reg] :
( ( c @ france @ X18 )
| ~ ( c @ X18 @ paris ) ),
inference(spm,[status(thm)],[c_0_77,c_0_60]) ).
thf(c_0_85,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ X18 ) @ paris )
| ( c @ france @ X18 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_86,plain,
! [X18: reg] :
( epred1_0
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X18 ) @ spain ) ),
inference(split_equiv,[status(thm)],[c_0_72]) ).
thf(c_0_87,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
thf(c_0_88,plain,
! [X18: reg] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(sr,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_89,negated_conjecture,
! [X18: reg,X20: reg,X19: reg] :
( ( c @ X18 @ X19 )
| ( c @ X20 @ X19 )
| ~ ( c @ X18 @ spain )
| ~ ( c @ X20 @ ( esk3_1 @ X19 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_90,negated_conjecture,
! [X18: reg] :
( ( c @ france @ ( esk3_1 @ X18 ) )
| ( c @ france @ X18 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_91,plain,
! [X18: reg] :
( ~ ( c @ ( esk4_1 @ X18 ) @ spain )
| ~ ( c @ france @ ( esk5_1 @ X18 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_60]),c_0_87]) ).
thf(c_0_92,plain,
! [X18: reg] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ france @ ( esk5_1 @ X18 ) ) ),
inference(spm,[status(thm)],[c_0_88,c_0_60]) ).
thf(c_0_93,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ france @ X18 )
| ( c @ X19 @ X18 )
| ~ ( c @ X19 @ spain ) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_94,plain,
~ ( c @ france @ ( esk5_1 @ spain ) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
thf(c_0_95,negated_conjecture,
! [X18: reg] : ( c @ france @ X18 ),
inference(spm,[status(thm)],[c_0_93,c_0_79]) ).
thf(c_0_96,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEG009^1 : TPTP v8.2.0. Released v4.1.0.
% 0.13/0.15 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n008.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat May 18 21:55:38 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 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/benchmark/theBenchmark.p
% 0.20/0.52 # Version: 3.1.0-ho
% 0.20/0.52 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_12 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # new_bool_2 with pid 21674 completed with status 0
% 0.20/0.52 # Result found by new_bool_2
% 0.20/0.52 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_12 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 # Search class: HGHNF-FFMF21-SHSSMSBN
% 0.20/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_9 with 163s (1) cores
% 0.20/0.52 # new_ho_9 with pid 21675 completed with status 0
% 0.20/0.52 # Result found by new_ho_9
% 0.20/0.52 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_12 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 # Search class: HGHNF-FFMF21-SHSSMSBN
% 0.20/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_9 with 163s (1) cores
% 0.20/0.52 # Preprocessing time : 0.003 s
% 0.20/0.52 # Presaturation interreduction done
% 0.20/0.52
% 0.20/0.52 # Proof found!
% 0.20/0.52 # SZS status Theorem
% 0.20/0.52 # SZS output start CNFRefutation
% See solution above
% 0.20/0.52 # Parsed axioms : 98
% 0.20/0.52 # Removed by relevancy pruning/SinE : 77
% 0.20/0.52 # Initial clauses : 25
% 0.20/0.52 # Removed in clause preprocessing : 0
% 0.20/0.52 # Initial clauses in saturation : 25
% 0.20/0.52 # Processed clauses : 185
% 0.20/0.52 # ...of these trivial : 4
% 0.20/0.52 # ...subsumed : 12
% 0.20/0.52 # ...remaining for further processing : 169
% 0.20/0.52 # Other redundant clauses eliminated : 0
% 0.20/0.52 # Clauses deleted for lack of memory : 0
% 0.20/0.52 # Backward-subsumed : 3
% 0.20/0.52 # Backward-rewritten : 41
% 0.20/0.52 # Generated clauses : 300
% 0.20/0.52 # ...of the previous two non-redundant : 268
% 0.20/0.52 # ...aggressively subsumed : 0
% 0.20/0.52 # Contextual simplify-reflections : 6
% 0.20/0.52 # Paramodulations : 273
% 0.20/0.52 # Factorizations : 0
% 0.20/0.52 # NegExts : 0
% 0.20/0.52 # Equation resolutions : 0
% 0.20/0.52 # Disequality decompositions : 0
% 0.20/0.52 # Total rewrite steps : 76
% 0.20/0.52 # ...of those cached : 41
% 0.20/0.52 # Propositional unsat checks : 0
% 0.20/0.52 # Propositional check models : 0
% 0.20/0.52 # Propositional check unsatisfiable : 0
% 0.20/0.52 # Propositional clauses : 0
% 0.20/0.52 # Propositional clauses after purity: 0
% 0.20/0.52 # Propositional unsat core size : 0
% 0.20/0.52 # Propositional preprocessing time : 0.000
% 0.20/0.52 # Propositional encoding time : 0.000
% 0.20/0.52 # Propositional solver time : 0.000
% 0.20/0.52 # Success case prop preproc time : 0.000
% 0.20/0.52 # Success case prop encoding time : 0.000
% 0.20/0.52 # Success case prop solver time : 0.000
% 0.20/0.52 # Current number of processed clauses : 73
% 0.20/0.52 # Positive orientable unit clauses : 21
% 0.20/0.52 # Positive unorientable unit clauses: 0
% 0.20/0.52 # Negative unit clauses : 14
% 0.20/0.52 # Non-unit-clauses : 38
% 0.20/0.52 # Current number of unprocessed clauses: 122
% 0.20/0.52 # ...number of literals in the above : 468
% 0.20/0.52 # Current number of archived formulas : 0
% 0.20/0.52 # Current number of archived clauses : 87
% 0.20/0.52 # Clause-clause subsumption calls (NU) : 1852
% 0.20/0.52 # Rec. Clause-clause subsumption calls : 882
% 0.20/0.52 # Non-unit clause-clause subsumptions : 15
% 0.20/0.52 # Unit Clause-clause subsumption calls : 207
% 0.20/0.52 # Rewrite failures with RHS unbound : 0
% 0.20/0.52 # BW rewrite match attempts : 32
% 0.20/0.52 # BW rewrite match successes : 23
% 0.20/0.52 # Condensation attempts : 193
% 0.20/0.52 # Condensation successes : 0
% 0.20/0.52 # Termbank termtop insertions : 8387
% 0.20/0.52 # Search garbage collected termcells : 1453
% 0.20/0.52
% 0.20/0.52 # -------------------------------------------------
% 0.20/0.52 # User time : 0.022 s
% 0.20/0.52 # System time : 0.003 s
% 0.20/0.52 # Total time : 0.025 s
% 0.20/0.52 # Maximum resident set size: 2132 pages
% 0.20/0.52
% 0.20/0.52 # -------------------------------------------------
% 0.20/0.52 # User time : 0.026 s
% 0.20/0.52 # System time : 0.004 s
% 0.20/0.52 # Total time : 0.031 s
% 0.20/0.52 # Maximum resident set size: 1832 pages
% 0.20/0.52 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------