TSTP Solution File: LCL460^7 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : LCL460^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 23:46:32 EDT 2024
% Result : Theorem 23.87s 3.95s
% Output : CNFRefutation 23.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 44
% Syntax : Number of formulae : 100 ( 29 unt; 30 typ; 0 def)
% Number of atoms : 337 ( 18 equ; 0 cnn)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 1145 ( 165 ~; 175 |; 16 &; 778 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 3 con; 0-3 aty)
% Number of variables : 194 ( 46 ^ 148 !; 0 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_36,type,
exists_in_world: mu > $i > $o ).
thf(decl_37,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s4: $i > $i > $o ).
thf(decl_55,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_74,type,
and_1: $i > $o ).
thf(decl_87,type,
kn2: $i > $o ).
thf(decl_88,type,
is_a_theorem: mu > $i > $o ).
thf(decl_91,type,
implies: mu > mu > mu ).
thf(decl_92,type,
and: mu > mu > mu ).
thf(decl_152,type,
esk59_2: $i > $i > $i ).
thf(decl_153,type,
esk60_2: $i > $i > $i ).
thf(decl_154,type,
esk61_2: $i > $i > mu ).
thf(decl_155,type,
esk62_2: $i > $i > $i ).
thf(decl_156,type,
esk63_2: $i > $i > mu ).
thf(decl_157,type,
esk64_2: $i > $i > $i ).
thf(decl_212,type,
esk119_2: $i > $i > $i ).
thf(decl_213,type,
esk120_2: $i > $i > $i ).
thf(decl_214,type,
esk121_2: $i > $i > mu ).
thf(decl_215,type,
esk122_2: $i > $i > $i ).
thf(decl_216,type,
esk123_2: $i > $i > mu ).
thf(decl_217,type,
esk124_2: $i > $i > $i ).
thf(decl_281,type,
esk188_0: $i ).
thf(decl_282,type,
esk189_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(rosser_kn2,conjecture,
mvalid @ ( mbox_s4 @ kn2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
thf(kn2,axiom,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ kn2 )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X93: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X94: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X93 @ X94 ) @ X93 ) ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X95: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X94: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X95 @ X94 ) @ X95 ) ) ) ) ) ) )
@ ( mbox_s4 @ kn2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
thf(and_1,axiom,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ and_1 )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X55: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X56: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X55 @ X56 ) @ X55 ) ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X57: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X58: mu] : ( mbox_s4 @ ( is_a_theorem @ ( implies @ ( and @ X57 @ X58 ) @ X57 ) ) ) ) ) ) )
@ ( mbox_s4 @ and_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
thf(hilbert_and_1,axiom,
mvalid @ ( mbox_s4 @ and_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(cumulative_ax,axiom,
! [X19: mu,X7: $i,X3: $i] :
( ( ( exists_in_world @ X19 @ X7 )
& ( rel_s4 @ X7 @ X3 ) )
=> ( exists_in_world @ X19 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).
thf(c_0_14,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_15,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_16,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_17,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,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_20,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_21,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_17,c_0_15]),c_0_16]) ).
thf(c_0_22,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_23,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_24,negated_conjecture,
~ ! [X774: $i,X773: $i] :
( ~ ( rel_s4 @ X774 @ X773 )
| ( kn2 @ X773 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[rosser_kn2]),c_0_18]),c_0_19])]) ).
thf(c_0_25,plain,
! [X547: $i] :
~ ( ~ ! [X539: $i] :
( ~ ( rel_s4 @ X547 @ X539 )
| ~ ! [X533: $i] :
( ~ ( rel_s4 @ X539 @ X533 )
| ( kn2 @ X533 ) )
| ! [X538: $i] :
( ~ ( rel_s4 @ X539 @ X538 )
| ! [X537: mu] :
( ( exists_in_world @ X537 @ X538 )
=> ! [X536: $i] :
( ~ ( rel_s4 @ X538 @ X536 )
| ! [X535: mu] :
( ( exists_in_world @ X535 @ X536 )
=> ! [X534: $i] :
( ~ ( rel_s4 @ X536 @ X534 )
| ( is_a_theorem @ ( implies @ ( and @ X537 @ X535 ) @ X537 ) @ X534 ) ) ) ) ) ) )
| ~ ! [X546: $i] :
( ~ ( rel_s4 @ X547 @ X546 )
| ~ ! [X544: $i] :
( ~ ( rel_s4 @ X546 @ X544 )
| ! [X543: mu] :
( ( exists_in_world @ X543 @ X544 )
=> ! [X542: $i] :
( ~ ( rel_s4 @ X544 @ X542 )
| ! [X541: mu] :
( ( exists_in_world @ X541 @ X542 )
=> ! [X540: $i] :
( ~ ( rel_s4 @ X542 @ X540 )
| ( is_a_theorem @ ( implies @ ( and @ X543 @ X541 ) @ X543 ) @ X540 ) ) ) ) ) )
| ! [X545: $i] :
( ~ ( rel_s4 @ X546 @ X545 )
| ( kn2 @ X545 ) ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[kn2]),c_0_20]),c_0_21]),c_0_22]),c_0_18]),c_0_19])]) ).
thf(c_0_26,plain,
! [X397: $i] :
~ ( ~ ! [X389: $i] :
( ~ ( rel_s4 @ X397 @ X389 )
| ~ ! [X383: $i] :
( ~ ( rel_s4 @ X389 @ X383 )
| ( and_1 @ X383 ) )
| ! [X388: $i] :
( ~ ( rel_s4 @ X389 @ X388 )
| ! [X387: mu] :
( ( exists_in_world @ X387 @ X388 )
=> ! [X386: $i] :
( ~ ( rel_s4 @ X388 @ X386 )
| ! [X385: mu] :
( ( exists_in_world @ X385 @ X386 )
=> ! [X384: $i] :
( ~ ( rel_s4 @ X386 @ X384 )
| ( is_a_theorem @ ( implies @ ( and @ X387 @ X385 ) @ X387 ) @ X384 ) ) ) ) ) ) )
| ~ ! [X396: $i] :
( ~ ( rel_s4 @ X397 @ X396 )
| ~ ! [X394: $i] :
( ~ ( rel_s4 @ X396 @ X394 )
| ! [X393: mu] :
( ( exists_in_world @ X393 @ X394 )
=> ! [X392: $i] :
( ~ ( rel_s4 @ X394 @ X392 )
| ! [X391: mu] :
( ( exists_in_world @ X391 @ X392 )
=> ! [X390: $i] :
( ~ ( rel_s4 @ X392 @ X390 )
| ( is_a_theorem @ ( implies @ ( and @ X393 @ X391 ) @ X393 ) @ X390 ) ) ) ) ) )
| ! [X395: $i] :
( ~ ( rel_s4 @ X396 @ X395 )
| ( and_1 @ X395 ) ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[and_1]),c_0_20]),c_0_21]),c_0_22]),c_0_18]),c_0_19])]) ).
thf(c_0_27,plain,
! [X748: $i,X747: $i] :
( ~ ( rel_s4 @ X748 @ X747 )
| ( and_1 @ X747 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hilbert_and_1,c_0_18]),c_0_19])]) ).
thf(c_0_28,plain,
! [X155: $i] : ( rel_s4 @ X155 @ X155 ),
inference(apply_def,[status(thm)],[a1,c_0_23]) ).
thf(c_0_29,negated_conjecture,
( ( rel_s4 @ esk188_0 @ esk189_0 )
& ~ ( kn2 @ esk189_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_30,plain,
! [X1188: $i,X1189: $i,X1191: $i,X1192: mu,X1193: $i,X1194: mu,X1195: $i,X1196: $i,X1197: $i,X1203: $i] :
( ( ( rel_s4 @ X1189 @ ( esk119_2 @ X1188 @ X1189 ) )
| ~ ( rel_s4 @ X1189 @ X1191 )
| ~ ( exists_in_world @ X1192 @ X1191 )
| ~ ( rel_s4 @ X1191 @ X1193 )
| ~ ( exists_in_world @ X1194 @ X1193 )
| ~ ( rel_s4 @ X1193 @ X1195 )
| ( is_a_theorem @ ( implies @ ( and @ X1192 @ X1194 ) @ X1192 ) @ X1195 )
| ~ ( rel_s4 @ X1188 @ X1189 ) )
& ( ~ ( kn2 @ ( esk119_2 @ X1188 @ X1189 ) )
| ~ ( rel_s4 @ X1189 @ X1191 )
| ~ ( exists_in_world @ X1192 @ X1191 )
| ~ ( rel_s4 @ X1191 @ X1193 )
| ~ ( exists_in_world @ X1194 @ X1193 )
| ~ ( rel_s4 @ X1193 @ X1195 )
| ( is_a_theorem @ ( implies @ ( and @ X1192 @ X1194 ) @ X1192 ) @ X1195 )
| ~ ( rel_s4 @ X1188 @ X1189 ) )
& ( ( rel_s4 @ X1197 @ ( esk120_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) )
& ( ( exists_in_world @ ( esk121_2 @ X1196 @ X1197 ) @ ( esk120_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) )
& ( ( rel_s4 @ ( esk120_2 @ X1196 @ X1197 ) @ ( esk122_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) )
& ( ( exists_in_world @ ( esk123_2 @ X1196 @ X1197 ) @ ( esk122_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) )
& ( ( rel_s4 @ ( esk122_2 @ X1196 @ X1197 ) @ ( esk124_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) )
& ( ~ ( is_a_theorem @ ( implies @ ( and @ ( esk121_2 @ X1196 @ X1197 ) @ ( esk123_2 @ X1196 @ X1197 ) ) @ ( esk121_2 @ X1196 @ X1197 ) ) @ ( esk124_2 @ X1196 @ X1197 ) )
| ~ ( rel_s4 @ X1197 @ X1203 )
| ( kn2 @ X1203 )
| ~ ( rel_s4 @ X1196 @ X1197 ) ) ),
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_25])])])])])])]) ).
thf(c_0_31,plain,
! [X1028: $i,X1029: $i,X1031: $i,X1032: mu,X1033: $i,X1034: mu,X1035: $i,X1036: $i,X1037: $i,X1043: $i] :
( ( ( rel_s4 @ X1029 @ ( esk59_2 @ X1028 @ X1029 ) )
| ~ ( rel_s4 @ X1029 @ X1031 )
| ~ ( exists_in_world @ X1032 @ X1031 )
| ~ ( rel_s4 @ X1031 @ X1033 )
| ~ ( exists_in_world @ X1034 @ X1033 )
| ~ ( rel_s4 @ X1033 @ X1035 )
| ( is_a_theorem @ ( implies @ ( and @ X1032 @ X1034 ) @ X1032 ) @ X1035 )
| ~ ( rel_s4 @ X1028 @ X1029 ) )
& ( ~ ( and_1 @ ( esk59_2 @ X1028 @ X1029 ) )
| ~ ( rel_s4 @ X1029 @ X1031 )
| ~ ( exists_in_world @ X1032 @ X1031 )
| ~ ( rel_s4 @ X1031 @ X1033 )
| ~ ( exists_in_world @ X1034 @ X1033 )
| ~ ( rel_s4 @ X1033 @ X1035 )
| ( is_a_theorem @ ( implies @ ( and @ X1032 @ X1034 ) @ X1032 ) @ X1035 )
| ~ ( rel_s4 @ X1028 @ X1029 ) )
& ( ( rel_s4 @ X1037 @ ( esk60_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) )
& ( ( exists_in_world @ ( esk61_2 @ X1036 @ X1037 ) @ ( esk60_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) )
& ( ( rel_s4 @ ( esk60_2 @ X1036 @ X1037 ) @ ( esk62_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) )
& ( ( exists_in_world @ ( esk63_2 @ X1036 @ X1037 ) @ ( esk62_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) )
& ( ( rel_s4 @ ( esk62_2 @ X1036 @ X1037 ) @ ( esk64_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) )
& ( ~ ( is_a_theorem @ ( implies @ ( and @ ( esk61_2 @ X1036 @ X1037 ) @ ( esk63_2 @ X1036 @ X1037 ) ) @ ( esk61_2 @ X1036 @ X1037 ) ) @ ( esk64_2 @ X1036 @ X1037 ) )
| ~ ( rel_s4 @ X1037 @ X1043 )
| ( and_1 @ X1043 )
| ~ ( rel_s4 @ X1036 @ X1037 ) ) ),
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_26])])])])])])]) ).
thf(c_0_32,plain,
! [X1412: $i,X1413: $i] :
( ~ ( rel_s4 @ X1412 @ X1413 )
| ( and_1 @ X1413 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
thf(c_0_33,plain,
! [X777: $i] : ( rel_s4 @ X777 @ X777 ),
inference(variable_rename,[status(thm)],[c_0_28]) ).
thf(c_0_34,negated_conjecture,
~ ( kn2 @ esk189_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( kn2 @ X16 )
| ~ ( is_a_theorem @ ( implies @ ( and @ ( esk121_2 @ X3 @ X7 ) @ ( esk123_2 @ X3 @ X7 ) ) @ ( esk121_2 @ X3 @ X7 ) ) @ ( esk124_2 @ X3 @ X7 ) )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
! [X16: $i,X3: $i,X10: mu,X18: $i,X17: $i,X12: mu,X7: $i] :
( ( is_a_theorem @ ( implies @ ( and @ X10 @ X12 ) @ X10 ) @ X18 )
| ~ ( and_1 @ ( esk59_2 @ X3 @ X7 ) )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( exists_in_world @ X10 @ X16 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( exists_in_world @ X12 @ X17 )
| ~ ( rel_s4 @ X17 @ X18 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
! [X3: $i,X7: $i] :
( ( and_1 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( rel_s4 @ ( esk122_2 @ X3 @ X7 ) @ ( esk124_2 @ X3 @ X7 ) )
| ( kn2 @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_40,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( exists_in_world @ ( esk123_2 @ X3 @ X7 ) @ ( esk122_2 @ X3 @ X7 ) )
| ( kn2 @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_41,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( rel_s4 @ ( esk120_2 @ X3 @ X7 ) @ ( esk122_2 @ X3 @ X7 ) )
| ( kn2 @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i,X7: $i] :
( ~ ( is_a_theorem @ ( implies @ ( and @ ( esk121_2 @ X3 @ X7 ) @ ( esk123_2 @ X3 @ X7 ) ) @ ( esk121_2 @ X3 @ X7 ) ) @ ( esk124_2 @ X3 @ X7 ) )
| ~ ( rel_s4 @ X7 @ esk189_0 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_43,plain,
! [X16: $i,X7: $i,X3: $i,X12: mu,X10: mu,X18: $i,X17: $i,X132: $i] :
( ( is_a_theorem @ ( implies @ ( and @ X10 @ X12 ) @ X10 ) @ X3 )
| ~ ( rel_s4 @ X7 @ ( esk59_2 @ X16 @ X17 ) )
| ~ ( rel_s4 @ X18 @ X3 )
| ~ ( rel_s4 @ X132 @ X18 )
| ~ ( rel_s4 @ X17 @ X132 )
| ~ ( rel_s4 @ X16 @ X17 )
| ~ ( exists_in_world @ X12 @ X18 )
| ~ ( exists_in_world @ X10 @ X132 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_44,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ ( esk122_2 @ X3 @ X7 ) @ ( esk124_2 @ X3 @ X7 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_45,plain,
! [X3: $i,X7: $i] :
( ( exists_in_world @ ( esk123_2 @ X3 @ X7 ) @ ( esk122_2 @ X3 @ X7 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
thf(c_0_46,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ ( esk120_2 @ X3 @ X7 ) @ ( esk122_2 @ X3 @ X7 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
thf(c_0_47,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( exists_in_world @ ( esk121_2 @ X3 @ X7 ) @ ( esk120_2 @ X3 @ X7 ) )
| ( kn2 @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i,X18: $i,X17: $i,X132: $i,X135: $i,X7: $i,X16: $i] :
( ~ ( rel_s4 @ X3 @ ( esk59_2 @ X7 @ X16 ) )
| ~ ( rel_s4 @ X17 @ ( esk124_2 @ X18 @ X132 ) )
| ~ ( exists_in_world @ ( esk123_2 @ X18 @ X132 ) @ X17 )
| ~ ( exists_in_world @ ( esk121_2 @ X18 @ X132 ) @ X135 )
| ~ ( rel_s4 @ X132 @ esk189_0 )
| ~ ( rel_s4 @ X18 @ X132 )
| ~ ( rel_s4 @ X135 @ X17 )
| ~ ( rel_s4 @ X16 @ X135 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_49,plain,
! [X3: $i] :
( ( rel_s4 @ ( esk122_2 @ X3 @ X3 ) @ ( esk124_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
thf(c_0_50,plain,
! [X3: $i] :
( ( exists_in_world @ ( esk123_2 @ X3 @ X3 ) @ ( esk122_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
thf(c_0_51,plain,
! [X781: mu,X782: $i,X783: $i] :
( ~ ( exists_in_world @ X781 @ X782 )
| ~ ( rel_s4 @ X782 @ X783 )
| ( exists_in_world @ X781 @ X783 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).
thf(c_0_52,plain,
! [X3: $i] :
( ( rel_s4 @ ( esk120_2 @ X3 @ X3 ) @ ( esk122_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
thf(c_0_53,plain,
! [X3: $i,X7: $i] :
( ( exists_in_world @ ( esk121_2 @ X3 @ X7 ) @ ( esk120_2 @ X3 @ X7 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
thf(c_0_54,plain,
! [X16: $i,X7: $i,X3: $i] :
( ( rel_s4 @ X3 @ ( esk120_2 @ X7 @ X3 ) )
| ( kn2 @ X16 )
| ~ ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X7 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_55,negated_conjecture,
! [X16: $i,X3: $i,X7: $i,X17: $i,X132: $i,X18: $i] :
( ~ ( rel_s4 @ X3 @ ( esk124_2 @ X7 @ X16 ) )
| ~ ( exists_in_world @ ( esk123_2 @ X7 @ X16 ) @ X3 )
| ~ ( exists_in_world @ ( esk121_2 @ X7 @ X16 ) @ X17 )
| ~ ( rel_s4 @ X16 @ esk189_0 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X17 @ X3 )
| ~ ( rel_s4 @ X18 @ X17 )
| ~ ( rel_s4 @ X132 @ X18 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_39]) ).
thf(c_0_56,negated_conjecture,
rel_s4 @ ( esk122_2 @ esk189_0 @ esk189_0 ) @ ( esk124_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_49]) ).
thf(c_0_57,negated_conjecture,
exists_in_world @ ( esk123_2 @ esk189_0 @ esk189_0 ) @ ( esk122_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
thf(c_0_58,plain,
! [X3: $i,X10: mu,X7: $i] :
( ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_59,negated_conjecture,
rel_s4 @ ( esk120_2 @ esk189_0 @ esk189_0 ) @ ( esk122_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
thf(c_0_60,plain,
! [X3: $i] :
( ( exists_in_world @ ( esk121_2 @ X3 @ X3 ) @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
thf(c_0_61,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_39]) ).
thf(c_0_62,negated_conjecture,
! [X16: $i,X3: $i,X7: $i] :
( ~ ( exists_in_world @ ( esk121_2 @ esk189_0 @ esk189_0 ) @ X3 )
| ~ ( rel_s4 @ X3 @ ( esk122_2 @ esk189_0 @ esk189_0 ) )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( rel_s4 @ X16 @ X7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_39])]) ).
thf(c_0_63,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ X10 @ ( esk122_2 @ esk189_0 @ esk189_0 ) )
| ~ ( exists_in_world @ X10 @ ( esk120_2 @ esk189_0 @ esk189_0 ) ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_64,negated_conjecture,
exists_in_world @ ( esk121_2 @ esk189_0 @ esk189_0 ) @ ( esk120_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_60]) ).
thf(c_0_65,plain,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_39]) ).
thf(c_0_66,negated_conjecture,
! [X7: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ ( esk122_2 @ esk189_0 @ esk189_0 ) )
| ~ ( rel_s4 @ X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_39]),c_0_64])]) ).
thf(c_0_67,negated_conjecture,
rel_s4 @ esk189_0 @ ( esk120_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_65]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i] :
~ ( rel_s4 @ X3 @ ( esk120_2 @ esk189_0 @ esk189_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_59]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_67,c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL460^7 : TPTP v8.2.0. Released v5.5.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 00:41:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 23.87/3.95 # Version: 3.1.0-ho
% 23.87/3.95 # Preprocessing class: HSLSSMSSMLLNHSN.
% 23.87/3.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.87/3.95 # Starting almost_fo_3 with 1500s (5) cores
% 23.87/3.95 # Starting sh10 with 300s (1) cores
% 23.87/3.95 # Starting new_ho_16 with 300s (1) cores
% 23.87/3.95 # Starting post_as_ho11 with 300s (1) cores
% 23.87/3.95 # new_ho_16 with pid 27892 completed with status 8
% 23.87/3.95 # post_as_ho11 with pid 27893 completed with status 0
% 23.87/3.95 # Result found by post_as_ho11
% 23.87/3.95 # Preprocessing class: HSLSSMSSMLLNHSN.
% 23.87/3.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.87/3.95 # Starting almost_fo_3 with 1500s (5) cores
% 23.87/3.95 # Starting sh10 with 300s (1) cores
% 23.87/3.95 # Starting new_ho_16 with 300s (1) cores
% 23.87/3.95 # Starting post_as_ho11 with 300s (1) cores
% 23.87/3.95 # No SInE strategy applied
% 23.87/3.95 # Search class: HGUNM-FSLF32-MHSSMFNN
% 23.87/3.95 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 23.87/3.95 # Starting almost_fo_3 with 60s (1) cores
% 23.87/3.95 # almost_fo_3 with pid 27914 completed with status 0
% 23.87/3.95 # Result found by almost_fo_3
% 23.87/3.95 # Preprocessing class: HSLSSMSSMLLNHSN.
% 23.87/3.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.87/3.95 # Starting almost_fo_3 with 1500s (5) cores
% 23.87/3.95 # Starting sh10 with 300s (1) cores
% 23.87/3.95 # Starting new_ho_16 with 300s (1) cores
% 23.87/3.95 # Starting post_as_ho11 with 300s (1) cores
% 23.87/3.95 # No SInE strategy applied
% 23.87/3.95 # Search class: HGUNM-FSLF32-MHSSMFNN
% 23.87/3.95 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 23.87/3.95 # Starting almost_fo_3 with 60s (1) cores
% 23.87/3.95 # Preprocessing time : 0.008 s
% 23.87/3.95 # Presaturation interreduction done
% 23.87/3.95
% 23.87/3.95 # Proof found!
% 23.87/3.95 # SZS status Theorem
% 23.87/3.95 # SZS output start CNFRefutation
% See solution above
% 23.87/3.95 # Parsed axioms : 180
% 23.87/3.95 # Removed by relevancy pruning/SinE : 0
% 23.87/3.95 # Initial clauses : 371
% 23.87/3.95 # Removed in clause preprocessing : 73
% 23.87/3.95 # Initial clauses in saturation : 298
% 23.87/3.95 # Processed clauses : 10058
% 23.87/3.95 # ...of these trivial : 0
% 23.87/3.95 # ...subsumed : 3414
% 23.87/3.95 # ...remaining for further processing : 6644
% 23.87/3.95 # Other redundant clauses eliminated : 0
% 23.87/3.95 # Clauses deleted for lack of memory : 0
% 23.87/3.95 # Backward-subsumed : 260
% 23.87/3.95 # Backward-rewritten : 18
% 23.87/3.95 # Generated clauses : 17563
% 23.87/3.95 # ...of the previous two non-redundant : 17490
% 23.87/3.95 # ...aggressively subsumed : 0
% 23.87/3.95 # Contextual simplify-reflections : 2
% 23.87/3.95 # Paramodulations : 17562
% 23.87/3.95 # Factorizations : 0
% 23.87/3.95 # NegExts : 0
% 23.87/3.95 # Equation resolutions : 0
% 23.87/3.95 # Disequality decompositions : 0
% 23.87/3.95 # Total rewrite steps : 1229
% 23.87/3.95 # ...of those cached : 1145
% 23.87/3.95 # Propositional unsat checks : 1
% 23.87/3.95 # Propositional check models : 1
% 23.87/3.95 # Propositional check unsatisfiable : 0
% 23.87/3.95 # Propositional clauses : 0
% 23.87/3.95 # Propositional clauses after purity: 0
% 23.87/3.95 # Propositional unsat core size : 0
% 23.87/3.95 # Propositional preprocessing time : 0.000
% 23.87/3.95 # Propositional encoding time : 0.011
% 23.87/3.95 # Propositional solver time : 0.001
% 23.87/3.95 # Success case prop preproc time : 0.000
% 23.87/3.95 # Success case prop encoding time : 0.000
% 23.87/3.95 # Success case prop solver time : 0.000
% 23.87/3.95 # Current number of processed clauses : 6169
% 23.87/3.95 # Positive orientable unit clauses : 19
% 23.87/3.95 # Positive unorientable unit clauses: 0
% 23.87/3.95 # Negative unit clauses : 2
% 23.87/3.95 # Non-unit-clauses : 6148
% 23.87/3.95 # Current number of unprocessed clauses: 7922
% 23.87/3.95 # ...number of literals in the above : 42543
% 23.87/3.95 # Current number of archived formulas : 0
% 23.87/3.95 # Current number of archived clauses : 475
% 23.87/3.95 # Clause-clause subsumption calls (NU) : 21552903
% 23.87/3.95 # Rec. Clause-clause subsumption calls : 7459737
% 23.87/3.95 # Non-unit clause-clause subsumptions : 3507
% 23.87/3.95 # Unit Clause-clause subsumption calls : 9994
% 23.87/3.95 # Rewrite failures with RHS unbound : 0
% 23.87/3.95 # BW rewrite match attempts : 12
% 23.87/3.95 # BW rewrite match successes : 10
% 23.87/3.95 # Condensation attempts : 0
% 23.87/3.95 # Condensation successes : 0
% 23.87/3.95 # Termbank termtop insertions : 618418
% 23.87/3.95 # Search garbage collected termcells : 31214
% 23.87/3.95
% 23.87/3.95 # -------------------------------------------------
% 23.87/3.95 # User time : 3.362 s
% 23.87/3.95 # System time : 0.026 s
% 23.87/3.95 # Total time : 3.388 s
% 23.87/3.95 # Maximum resident set size: 6832 pages
% 23.87/3.95
% 23.87/3.95 # -------------------------------------------------
% 23.87/3.95 # User time : 3.383 s
% 23.87/3.95 # System time : 0.053 s
% 23.87/3.95 # Total time : 3.436 s
% 23.87/3.95 # Maximum resident set size: 2048 pages
% 23.87/3.95 % E---3.1 exiting
% 23.87/3.95 % E exiting
%------------------------------------------------------------------------------