%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:41:04 AM UTC 2026
% Result : ContradictoryAxioms 1.07s 0.40s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of formulae : 119 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 635 ( 17 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1587 ( 346 ~; 359 |; 4 &; 875 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 344 ( 27 ^; 317 !; 0 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_29,type,
mtrue: $i > $o ).
thf(decl_41,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_44,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
v1: $i > $o ).
thf(decl_59,type,
v3: $i > $o ).
thf(decl_60,type,
v2: $i > $o ).
thf(decl_61,type,
v4: $i > $o ).
thf(decl_63,type,
esk2_1: $i > $i ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mor) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mbox_s4) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mreflexive) ).
thf(persat25,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat25) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',a1) ).
thf(persat3,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat3) ).
thf(mdia_s4,axiom,
( mdia_s4
= ( ^ [X4: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mdia_s4) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i,X17: $i,X18: $i] :
( ( ( X6 @ X16 @ X17 )
& ( X6 @ X17 @ X18 ) )
=> ( X6 @ X16 @ X18 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mtransitive) ).
thf(mtrue,axiom,
( mtrue
= ( ^ [X3: $i] : $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',mtrue) ).
thf(persat10,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat10) ).
thf(persat4,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat4) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',a2) ).
thf(deontic1,axiom,
mvalid @ ( mdia_s4 @ mtrue ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',deontic1) ).
thf(persat15,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat15) ).
thf(persat18,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat18) ).
thf(persat14,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat14) ).
thf(persat16,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat16) ).
thf(persat21,axiom,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat21) ).
thf(persat5,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p',persat5) ).
thf(c_0_21,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_22,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_23,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_24,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_25,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_26,plain,
! [X155: $i] :
( ~ ( v1 @ X155 )
| ! [X151: $i] :
( ~ ( rel_s4 @ X155 @ X151 )
| ~ ( v1 @ X151 ) )
| ! [X152: $i] :
( ~ ( rel_s4 @ X155 @ X152 )
| ~ ( v3 @ X152 ) )
| ! [X154: $i] :
( ~ ( rel_s4 @ X155 @ X154 )
| ! [X153: $i] :
( ~ ( rel_s4 @ X154 @ X153 )
| ~ ( v1 @ X153 ) ) ) ),
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)],[persat25,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_27,plain,
! [X29: $i] : ( rel_s4 @ X29 @ X29 ),
inference(apply_def,[status(thm)],[a1,c_0_25]) ).
thf(c_0_28,plain,
! [X318: $i,X319: $i,X320: $i,X321: $i,X322: $i] :
( ~ ( v1 @ X318 )
| ~ ( rel_s4 @ X318 @ X319 )
| ~ ( v1 @ X319 )
| ~ ( rel_s4 @ X318 @ X320 )
| ~ ( v3 @ X320 )
| ~ ( rel_s4 @ X318 @ X321 )
| ~ ( rel_s4 @ X321 @ X322 )
| ~ ( v1 @ X322 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])])]) ).
thf(c_0_29,plain,
! [X193: $i] : ( rel_s4 @ X193 @ X193 ),
inference(variable_rename,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ~ ( v1 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v1 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( v3 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( v1 @ X18 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_31,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_32,plain,
! [X7: $i,X3: $i,X17: $i,X16: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 )
| ~ ( v1 @ X7 )
| ~ ( v1 @ X17 )
| ~ ( v1 @ X3 )
| ~ ( v3 @ X16 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_33,plain,
! [X46: $i] :
( ( v1 @ X46 )
| ~ ( v3 @ X46 )
| ! [X43: $i] :
( ~ ( rel_s4 @ X46 @ X43 )
| ~ ( v4 @ X43 ) )
| ! [X45: $i] :
( ~ ( rel_s4 @ X46 @ X45 )
| ! [X44: $i] :
( ~ ( rel_s4 @ X45 @ X44 )
| ( v1 @ X44 ) ) ) ),
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)],[persat3,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_34,plain,
! [X3: $i,X16: $i,X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( v1 @ X3 )
| ~ ( v1 @ X16 )
| ~ ( v3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_35,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X28: $i] :
( ~ ( rel_s4 @ Z1 @ X28 )
| ~ ( Z0 @ X28 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_s4]) ).
thf(c_0_36,plain,
! [X210: $i,X211: $i,X212: $i,X213: $i] :
( ( v1 @ X210 )
| ~ ( v3 @ X210 )
| ~ ( rel_s4 @ X210 @ X211 )
| ~ ( v4 @ X211 )
| ~ ( rel_s4 @ X210 @ X212 )
| ~ ( rel_s4 @ X212 @ X213 )
| ( v1 @ X213 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])])]) ).
thf(c_0_37,plain,
! [X7: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v1 @ X3 )
| ~ ( v1 @ X7 )
| ~ ( v3 @ X3 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
thf(c_0_38,plain,
( mtransitive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i,X17: $i,X18: $i] :
( ( ( Z0 @ X16 @ X17 )
& ( Z0 @ X17 @ X18 ) )
=> ( Z0 @ X16 @ X18 ) ) ) ),
inference(fof_simplification,[status(thm)],[mtransitive]) ).
thf(c_0_39,plain,
( mtrue
= ( ^ [Z0: $i] : $true ) ),
inference(fof_simplification,[status(thm)],[mtrue]) ).
thf(c_0_40,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X28: $i] :
( ~ ( rel_s4 @ Z1 @ X28 )
| ~ ( Z0 @ X28 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_21]),c_0_24]) ).
thf(c_0_41,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v1 @ X3 )
| ( v1 @ X17 )
| ~ ( v3 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v4 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_42,plain,
! [X3: $i] :
( ~ ( v1 @ X3 )
| ~ ( v3 @ X3 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
thf(c_0_43,plain,
! [X81: $i] :
( ( v2 @ X81 )
| ~ ( v4 @ X81 )
| ! [X78: $i] :
( ~ ( rel_s4 @ X81 @ X78 )
| ~ ( v4 @ X78 ) )
| ! [X80: $i] :
( ~ ( rel_s4 @ X81 @ X80 )
| ! [X79: $i] :
( ~ ( rel_s4 @ X80 @ X79 )
| ~ ( v4 @ X79 ) ) ) ),
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)],[persat10,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_44,plain,
! [X51: $i] :
( ( v1 @ X51 )
| ~ ( v3 @ X51 )
| ! [X48: $i] :
( ~ ( rel_s4 @ X51 @ X48 )
| ! [X47: $i] :
( ~ ( rel_s4 @ X48 @ X47 )
| ( v2 @ X47 ) ) )
| ! [X50: $i] :
( ~ ( rel_s4 @ X51 @ X50 )
| ! [X49: $i] :
( ~ ( rel_s4 @ X50 @ X49 )
| ~ ( v3 @ X49 ) ) ) ),
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)],[persat4,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_45,plain,
! [X30: $i,X31: $i,X32: $i] :
( ( ( rel_s4 @ X30 @ X31 )
& ( rel_s4 @ X31 @ X32 ) )
=> ( rel_s4 @ X30 @ X32 ) ),
inference(apply_def,[status(thm)],[a2,c_0_38]) ).
thf(c_0_46,plain,
! [X189: $i] :
~ ! [X188: $i] :
( ~ ( rel_s4 @ X189 @ X188 )
| ~ $true ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[deontic1,c_0_39]),c_0_23]),c_0_40])]) ).
thf(c_0_47,plain,
! [X102: $i] :
( ( v3 @ X102 )
| ~ ( v2 @ X102 )
| ! [X99: $i] :
( ~ ( rel_s4 @ X102 @ X99 )
| ! [X98: $i] :
( ~ ( rel_s4 @ X99 @ X98 )
| ~ ( v2 @ X98 ) ) )
| ! [X101: $i] :
( ~ ( rel_s4 @ X102 @ X101 )
| ! [X100: $i] :
( ~ ( rel_s4 @ X101 @ X100 )
| ~ ( v4 @ X100 ) ) ) ),
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)],[persat15,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_48,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v1 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X16 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( v3 @ X16 )
| ~ ( v4 @ X17 ) ),
inference(csr,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_49,plain,
! [X245: $i,X246: $i,X247: $i,X248: $i] :
( ( v2 @ X245 )
| ~ ( v4 @ X245 )
| ~ ( rel_s4 @ X245 @ X246 )
| ~ ( v4 @ X246 )
| ~ ( rel_s4 @ X245 @ X247 )
| ~ ( rel_s4 @ X247 @ X248 )
| ~ ( v4 @ X248 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_43])])]) ).
thf(c_0_50,plain,
! [X214: $i,X215: $i,X216: $i,X217: $i,X218: $i] :
( ( v1 @ X214 )
| ~ ( v3 @ X214 )
| ~ ( rel_s4 @ X214 @ X215 )
| ~ ( rel_s4 @ X215 @ X216 )
| ( v2 @ X216 )
| ~ ( rel_s4 @ X214 @ X217 )
| ~ ( rel_s4 @ X217 @ X218 )
| ~ ( v3 @ X218 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])])]) ).
thf(c_0_51,plain,
! [X194: $i,X195: $i,X196: $i] :
( ~ ( rel_s4 @ X194 @ X195 )
| ~ ( rel_s4 @ X195 @ X196 )
| ( rel_s4 @ X194 @ X196 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
thf(c_0_52,plain,
! [X355: $i] :
( ( rel_s4 @ X355 @ ( esk2_1 @ X355 ) )
& $true ),
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_46])])])])])]) ).
thf(c_0_53,plain,
! [X265: $i,X266: $i,X267: $i,X268: $i,X269: $i] :
( ( v3 @ X265 )
| ~ ( v2 @ X265 )
| ~ ( rel_s4 @ X265 @ X266 )
| ~ ( rel_s4 @ X266 @ X267 )
| ~ ( v2 @ X267 )
| ~ ( rel_s4 @ X265 @ X268 )
| ~ ( rel_s4 @ X268 @ X269 )
| ~ ( v4 @ X269 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_47])])]) ).
thf(c_0_54,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( v1 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( v3 @ X7 )
| ~ ( v4 @ X16 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
thf(c_0_55,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v2 @ X3 )
| ~ ( v4 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v4 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( v4 @ X17 ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_56,plain,
! [X119: $i] :
( ( v3 @ X119 )
| ! [X114: $i] :
( ~ ( rel_s4 @ X119 @ X114 )
| ~ ( v3 @ X114 ) )
| ! [X116: $i] :
( ~ ( rel_s4 @ X119 @ X116 )
| ! [X115: $i] :
( ~ ( rel_s4 @ X116 @ X115 )
| ( v2 @ X115 ) ) )
| ! [X118: $i] :
( ~ ( rel_s4 @ X119 @ X118 )
| ! [X117: $i] :
( ~ ( rel_s4 @ X118 @ X117 )
| ( v3 @ X117 ) ) ) ),
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)],[persat18,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_57,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v1 @ X3 )
| ( v2 @ X16 )
| ~ ( v3 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( v3 @ X18 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_58,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_59,plain,
! [X3: $i] : ( rel_s4 @ X3 @ ( esk2_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_60,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v3 @ X3 )
| ~ ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( v2 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( v4 @ X18 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_61,plain,
! [X3: $i,X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v3 @ X3 )
| ~ ( v4 @ X7 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_31]),c_0_42]) ).
thf(c_0_62,plain,
! [X16: $i,X7: $i,X3: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( v4 @ X7 )
| ~ ( v4 @ X16 )
| ~ ( v4 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
thf(c_0_63,plain,
! [X281: $i,X282: $i,X283: $i,X284: $i,X285: $i,X286: $i] :
( ( v3 @ X281 )
| ~ ( rel_s4 @ X281 @ X282 )
| ~ ( v3 @ X282 )
| ~ ( rel_s4 @ X281 @ X283 )
| ~ ( rel_s4 @ X283 @ X284 )
| ( v2 @ X284 )
| ~ ( rel_s4 @ X281 @ X285 )
| ~ ( rel_s4 @ X285 @ X286 )
| ( v3 @ X286 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_56])])]) ).
thf(c_0_64,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X17 @ X3 )
| ~ ( rel_s4 @ X18 @ X7 )
| ~ ( rel_s4 @ X18 @ X17 )
| ~ ( v3 @ X16 )
| ~ ( v3 @ X18 ) ),
inference(csr,[status(thm)],[c_0_57,c_0_42]) ).
thf(c_0_65,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk2_1 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_66,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( v2 @ X7 )
| ~ ( v2 @ X16 )
| ~ ( v4 @ X17 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_61]) ).
thf(c_0_67,plain,
! [X3: $i,X7: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v4 @ X3 )
| ~ ( v4 @ X7 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_31]) ).
thf(c_0_68,plain,
! [X7: $i,X3: $i,X17: $i,X16: $i,X18: $i,X20: $i] :
( ( v3 @ X3 )
| ( v2 @ X17 )
| ( v3 @ X20 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X3 @ X18 )
| ~ ( rel_s4 @ X18 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_69,plain,
! [X3: $i,X7: $i,X17: $i,X16: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X16 @ X7 )
| ~ ( v3 @ X17 )
| ~ ( v3 @ X16 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_31]) ).
thf(c_0_70,plain,
! [X97: $i] :
( ( v3 @ X97 )
| ~ ( v1 @ X97 )
| ! [X94: $i] :
( ~ ( rel_s4 @ X97 @ X94 )
| ~ ( v3 @ X94 ) )
| ! [X96: $i] :
( ~ ( rel_s4 @ X97 @ X96 )
| ! [X95: $i] :
( ~ ( rel_s4 @ X96 @ X95 )
| ( v4 @ X95 ) ) ) ),
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)],[persat14,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_71,plain,
! [X3: $i,X16: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk2_1 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X7 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_65]) ).
thf(c_0_72,plain,
! [X108: $i] :
( ( v3 @ X108 )
| ! [X103: $i] :
( ~ ( rel_s4 @ X108 @ X103 )
| ( v4 @ X103 ) )
| ! [X105: $i] :
( ~ ( rel_s4 @ X108 @ X105 )
| ! [X104: $i] :
( ~ ( rel_s4 @ X105 @ X104 )
| ( v2 @ X104 ) ) )
| ! [X107: $i] :
( ~ ( rel_s4 @ X108 @ X107 )
| ! [X106: $i] :
( ~ ( rel_s4 @ X107 @ X106 )
| ( v3 @ X106 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[persat16,c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_73,plain,
! [X3: $i,X16: $i,X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( v2 @ X16 )
| ~ ( v2 @ X3 )
| ~ ( v4 @ X7 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
thf(c_0_74,plain,
! [X3: $i] :
( ( v2 @ X3 )
| ~ ( v4 @ X3 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_31]) ).
thf(c_0_75,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i,X20: $i] :
( ( v3 @ X3 )
| ( v2 @ X7 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X17 @ X7 )
| ~ ( rel_s4 @ X18 @ X16 )
| ~ ( rel_s4 @ X18 @ X17 )
| ~ ( rel_s4 @ X18 @ X20 )
| ~ ( v3 @ X20 ) ),
inference(csr,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_76,plain,
! [X135: $i] :
( ( v4 @ X135 )
| ~ ( v2 @ X135 )
| ! [X132: $i] :
( ~ ( rel_s4 @ X135 @ X132 )
| ! [X131: $i] :
( ~ ( rel_s4 @ X132 @ X131 )
| ( v3 @ X131 ) ) )
| ! [X134: $i] :
( ~ ( rel_s4 @ X135 @ X134 )
| ! [X133: $i] :
( ~ ( rel_s4 @ X134 @ X133 )
| ~ ( v1 @ X133 ) ) ) ),
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)],[persat21,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_77,plain,
! [X261: $i,X262: $i,X263: $i,X264: $i] :
( ( v3 @ X261 )
| ~ ( v1 @ X261 )
| ~ ( rel_s4 @ X261 @ X262 )
| ~ ( v3 @ X262 )
| ~ ( rel_s4 @ X261 @ X263 )
| ~ ( rel_s4 @ X263 @ X264 )
| ( v4 @ X264 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_70])])]) ).
thf(c_0_78,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk2_1 @ X7 ) )
| ~ ( rel_s4 @ ( esk2_1 @ X3 ) @ X7 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_59]) ).
thf(c_0_79,plain,
! [X270: $i,X271: $i,X272: $i,X273: $i,X274: $i,X275: $i] :
( ( v3 @ X270 )
| ~ ( rel_s4 @ X270 @ X271 )
| ( v4 @ X271 )
| ~ ( rel_s4 @ X270 @ X272 )
| ~ ( rel_s4 @ X272 @ X273 )
| ( v2 @ X273 )
| ~ ( rel_s4 @ X270 @ X274 )
| ~ ( rel_s4 @ X274 @ X275 )
| ( v3 @ X275 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_72])])]) ).
thf(c_0_80,plain,
! [X7: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v2 @ X7 )
| ~ ( v4 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_31]),c_0_74]) ).
thf(c_0_81,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v2 @ X3 )
| ( v3 @ X7 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X17 @ X7 )
| ~ ( rel_s4 @ X17 @ X16 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( v3 @ X18 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_31]) ).
thf(c_0_82,plain,
! [X3: $i,X16: $i,X7: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( v3 @ X16 )
| ~ ( v3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_31]) ).
thf(c_0_83,plain,
! [X298: $i,X299: $i,X300: $i,X301: $i,X302: $i] :
( ( v4 @ X298 )
| ~ ( v2 @ X298 )
| ~ ( rel_s4 @ X298 @ X299 )
| ~ ( rel_s4 @ X299 @ X300 )
| ( v3 @ X300 )
| ~ ( rel_s4 @ X298 @ X301 )
| ~ ( rel_s4 @ X301 @ X302 )
| ~ ( v1 @ X302 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_76])])]) ).
thf(c_0_84,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v3 @ X3 )
| ( v4 @ X17 )
| ~ ( v1 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_85,plain,
! [X3: $i] : ( rel_s4 @ X3 @ ( esk2_1 @ ( esk2_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_31]) ).
thf(c_0_86,plain,
! [X7: $i,X3: $i,X17: $i,X16: $i,X18: $i,X20: $i] :
( ( v3 @ X3 )
| ( v4 @ X7 )
| ( v2 @ X17 )
| ( v3 @ X20 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X3 @ X18 )
| ~ ( rel_s4 @ X18 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_87,plain,
! [X3: $i] :
~ ( v4 @ X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_31]),c_0_74]) ).
thf(c_0_88,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v3 @ X3 )
| ( v2 @ X7 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X16 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( v3 @ X17 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_31]) ).
thf(c_0_89,plain,
! [X3: $i,X7: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( v3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_82,c_0_31]) ).
thf(c_0_90,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v4 @ X3 )
| ( v3 @ X16 )
| ~ ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( v1 @ X18 ) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_91,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v4 @ ( esk2_1 @ X3 ) )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X7 @ X17 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( v1 @ X7 )
| ~ ( v3 @ X17 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_65]),c_0_42]) ).
thf(c_0_92,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk2_1 @ ( esk2_1 @ X7 ) ) )
| ~ ( rel_s4 @ ( esk2_1 @ X3 ) @ X7 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_65]) ).
thf(c_0_93,plain,
! [X3: $i] : ( rel_s4 @ X3 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ X3 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_85]) ).
thf(c_0_94,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ( v3 @ ( esk2_1 @ X3 ) )
| ( v2 @ X7 )
| ( v3 @ X16 )
| ~ ( rel_s4 @ X17 @ X7 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X16 @ X18 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_59]),c_0_87]) ).
thf(c_0_95,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( v3 @ X16 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_31]),c_0_89]) ).
thf(c_0_96,plain,
! [X3: $i,X7: $i,X17: $i,X16: $i] :
( ( v3 @ X3 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X16 @ X7 )
| ~ ( v1 @ X17 )
| ~ ( v2 @ X16 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_31]),c_0_87]) ).
thf(c_0_97,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( v4 @ ( esk2_1 @ X3 ) )
| ~ ( rel_s4 @ ( esk2_1 @ ( esk2_1 @ X7 ) ) @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( v1 @ X7 )
| ~ ( v3 @ X16 ) ),
inference(spm,[status(thm)],[c_0_91,c_0_85]) ).
thf(c_0_98,plain,
! [X3: $i] : ( rel_s4 @ X3 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ ( esk2_1 @ X3 ) ) ) ) ) ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
thf(c_0_99,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ( v3 @ ( esk2_1 @ X3 ) )
| ( v2 @ X7 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X16 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_31]),c_0_89]) ).
thf(c_0_100,plain,
! [X3: $i,X7: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_31]) ).
thf(c_0_101,plain,
! [X3: $i,X16: $i,X7: $i] :
( ( v3 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( v1 @ X16 )
| ~ ( v2 @ X7 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_31]) ).
thf(c_0_102,plain,
! [X3: $i,X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v1 @ X3 )
| ~ ( v3 @ X7 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_87]) ).
thf(c_0_103,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( v3 @ ( esk2_1 @ X3 ) )
| ( v2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 ) ),
inference(spm,[status(thm)],[c_0_99,c_0_31]) ).
thf(c_0_104,plain,
! [X3: $i] :
( ( v2 @ X3 )
| ~ ( v3 @ ( esk2_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_59]) ).
thf(c_0_105,plain,
! [X57: $i] :
( ( v1 @ X57 )
| ! [X52: $i] :
( ~ ( rel_s4 @ X57 @ X52 )
| ( v1 @ X52 ) )
| ! [X54: $i] :
( ~ ( rel_s4 @ X57 @ X54 )
| ! [X53: $i] :
( ~ ( rel_s4 @ X54 @ X53 )
| ( v4 @ X53 ) ) )
| ! [X56: $i] :
( ~ ( rel_s4 @ X57 @ X56 )
| ! [X55: $i] :
( ~ ( rel_s4 @ X56 @ X55 )
| ~ ( v2 @ X55 ) ) ) ),
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)],[persat5,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
thf(c_0_106,plain,
! [X7: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( v1 @ X3 )
| ~ ( v2 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_31]),c_0_102]) ).
thf(c_0_107,plain,
! [X3: $i,X7: $i] :
( ( v2 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_31]),c_0_104]) ).
thf(c_0_108,plain,
! [X219: $i,X220: $i,X221: $i,X222: $i,X223: $i,X224: $i] :
( ( v1 @ X219 )
| ~ ( rel_s4 @ X219 @ X220 )
| ( v1 @ X220 )
| ~ ( rel_s4 @ X219 @ X221 )
| ~ ( rel_s4 @ X221 @ X222 )
| ( v4 @ X222 )
| ~ ( rel_s4 @ X219 @ X223 )
| ~ ( rel_s4 @ X223 @ X224 )
| ~ ( v2 @ X224 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_105])])]) ).
thf(c_0_109,plain,
! [X3: $i] :
( ~ ( v1 @ X3 )
| ~ ( v2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_106,c_0_98]) ).
thf(c_0_110,plain,
! [X3: $i] : ( v2 @ X3 ),
inference(spm,[status(thm)],[c_0_107,c_0_98]) ).
thf(c_0_111,plain,
! [X7: $i,X3: $i,X16: $i,X17: $i,X18: $i,X20: $i] :
( ( v1 @ X3 )
| ( v1 @ X7 )
| ( v4 @ X17 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X3 @ X18 )
| ~ ( rel_s4 @ X18 @ X20 )
| ~ ( v2 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
thf(c_0_112,plain,
! [X3: $i] :
~ ( v1 @ X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
thf(c_0_113,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i,X20: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X18 @ X3 )
| ~ ( rel_s4 @ X18 @ X16 )
| ~ ( rel_s4 @ X18 @ X20 ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_110])]),c_0_87]),c_0_112]),c_0_112]) ).
thf(c_0_114,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i,X18: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( rel_s4 @ X16 @ X3 )
| ~ ( rel_s4 @ X16 @ X18 ) ),
inference(spm,[status(thm)],[c_0_113,c_0_98]) ).
thf(c_0_115,plain,
! [X3: $i,X7: $i,X16: $i,X17: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X17 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_98]) ).
thf(c_0_116,plain,
! [X3: $i,X7: $i,X16: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X3 @ X16 ) ),
inference(spm,[status(thm)],[c_0_115,c_0_98]) ).
thf(c_0_117,plain,
! [X3: $i,X7: $i] :
~ ( rel_s4 @ X3 @ X7 ),
inference(spm,[status(thm)],[c_0_116,c_0_98]) ).
thf(c_0_118,plain,
$false,
inference(sr,[status(thm)],[c_0_31,c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.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 16:19:30 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.CaVBJfm2Z5/E---3.1_4786.p
% 1.07/0.40 % Version: 3.5.1-ho
% 1.07/0.40 % Preprocessing class: HSMSSMSSMLMNHSN.
% 1.07/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.07/0.40 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 1.07/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 1.07/0.40 % Starting post_as_ho1 with 300s (1) cores
% 1.07/0.40 % ho_unfolding_3 with pid 4799 completed with status 0
% 1.07/0.40 % Result found by ho_unfolding_3
% 1.07/0.40 % Preprocessing class: HSMSSMSSMLMNHSN.
% 1.07/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.07/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.40 % No SInE strategy applied
% 1.07/0.40 % Search class: HGHNS-FFMF11-SHSSMFNN
% 1.07/0.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.40 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.40 % Starting ho_unfolding_3 with 151s (1) cores
% 1.07/0.40 % Starting ehoh_best_nonlift_rwall with 136s (1) cores
% 1.07/0.40 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 1.07/0.40 % Starting lpo1_lambda_fix with 136s (1) cores
% 1.07/0.40 % lpo1_lambda_fix with pid 4807 completed with status 0
% 1.07/0.40 % Result found by lpo1_lambda_fix
% 1.07/0.40 % Preprocessing class: HSMSSMSSMLMNHSN.
% 1.07/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.07/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.40 % No SInE strategy applied
% 1.07/0.40 % Search class: HGHNS-FFMF11-SHSSMFNN
% 1.07/0.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.40 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.40 % Starting ho_unfolding_3 with 151s (1) cores
% 1.07/0.40 % Starting ehoh_best_nonlift_rwall with 136s (1) cores
% 1.07/0.40 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 1.07/0.40 % Starting lpo1_lambda_fix with 136s (1) cores
% 1.07/0.40 % Preprocessing time : 0.002 s
% 1.07/0.40 % Presaturation interreduction done
% 1.07/0.40
% 1.07/0.40 % Proof found!
% 1.07/0.40 % SZS status ContradictoryAxioms
% 1.07/0.40 % SZS output start CNFRefutation
% See solution above
% 1.07/0.40 % Parsed axioms : 108
% 1.07/0.40 % Removed by relevancy pruning/SinE : 0
% 1.07/0.40 % Initial clauses : 77
% 1.07/0.40 % Removed in clause preprocessing : 42
% 1.07/0.40 % Initial clauses in saturation : 35
% 1.07/0.40 % Processed clauses : 1441
% 1.07/0.40 % ...of these trivial : 51
% 1.07/0.40 % ...subsumed : 684
% 1.07/0.40 % ...remaining for further processing : 706
% 1.07/0.40 % Other redundant clauses eliminated : 0
% 1.07/0.40 % Clauses deleted for lack of memory : 0
% 1.07/0.40 % Backward-subsumed : 380
% 1.07/0.40 % Backward-rewritten : 269
% 1.07/0.40 % Generated clauses : 4334
% 1.07/0.40 % ...of the previous two non-redundant : 4339
% 1.07/0.40 % ...aggressively subsumed : 0
% 1.07/0.40 % Contextual simplify-reflections : 47
% 1.07/0.40 % Paramodulations : 4324
% 1.07/0.40 % Factorizations : 0
% 1.07/0.40 % NegExts : 0
% 1.07/0.40 % Equation resolutions : 0
% 1.07/0.40 % Disequality decompositions : 0
% 1.07/0.40 % Total rewrite steps : 399
% 1.07/0.40 % ...of those cached : 372
% 1.07/0.40 % Propositional unsat checks : 0
% 1.07/0.40 % Propositional check models : 0
% 1.07/0.40 % Propositional check unsatisfiable : 0
% 1.07/0.40 % Propositional clauses : 0
% 1.07/0.40 % Propositional clauses after purity: 0
% 1.07/0.40 % Propositional unsat core size : 0
% 1.07/0.40 % Propositional preprocessing time : 0.000
% 1.07/0.40 % Propositional encoding time : 0.000
% 1.07/0.40 % Propositional solver time : 0.000
% 1.07/0.40 % Success case prop preproc time : 0.000
% 1.07/0.40 % Success case prop encoding time : 0.000
% 1.07/0.40 % Success case prop solver time : 0.000
% 1.07/0.40 % Current number of processed clauses : 12
% 1.07/0.40 % Positive orientable unit clauses : 2
% 1.07/0.40 % Positive unorientable unit clauses: 0
% 1.07/0.40 % Negative unit clauses : 3
% 1.07/0.40 % Non-unit-clauses : 7
% 1.07/0.40 % Current number of unprocessed clauses: 1853
% 1.07/0.40 % ...number of literals in the above : 8071
% 1.07/0.40 % Current number of archived formulas : 0
% 1.07/0.40 % Current number of archived clauses : 694
% 1.07/0.40 % Clause-clause subsumption calls (NU) : 52202
% 1.07/0.40 % Rec. Clause-clause subsumption calls : 28355
% 1.07/0.40 % Non-unit clause-clause subsumptions : 806
% 1.07/0.40 % Unit Clause-clause subsumption calls : 231
% 1.07/0.40 % Rewrite failures with RHS unbound : 0
% 1.07/0.40 % BW rewrite match attempts : 67
% 1.07/0.40 % BW rewrite match successes : 20
% 1.07/0.40 % Condensation attempts : 0
% 1.07/0.40 % Condensation successes : 0
% 1.07/0.40 % Termbank termtop insertions : 98937
% 1.07/0.40 % Search garbage collected termcells : 6242
% 1.07/0.40
% 1.07/0.40 % -------------------------------------------------
% 1.07/0.40 % User time : 0.124 s
% 1.07/0.40 % System time : 0.007 s
% 1.07/0.40 % Total time : 0.131 s
% 1.07/0.40 % Maximum resident set size: 4756 pages
% 1.07/0.40
% 1.07/0.40 % -------------------------------------------------
% 1.07/0.40 % User time : 0.571 s
% 1.07/0.40 % System time : 0.039 s
% 1.07/0.40 % Total time : 0.609 s
% 1.07/0.40 % Maximum resident set size: 4864 pages
% 1.07/0.40 % E exiting
%------------------------------------------------------------------------------