%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL460^7 : 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 : n010.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 08:11:56 AM UTC 2026
% Result : Theorem 55.69s 9.74s
% Output : CNFRefutation 55.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 340 ( 18 equ; 0 cnn)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 1148 ( 166 ~; 175 |; 16 &; 780 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 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_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
exists_in_world: mu > $i > $o ).
thf(decl_38,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_41,type,
mreflexive: ( $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_75,type,
and_1: $i > $o ).
thf(decl_88,type,
kn2: $i > $o ).
thf(decl_89,type,
is_a_theorem: mu > $i > $o ).
thf(decl_92,type,
implies: mu > mu > mu ).
thf(decl_93,type,
and: mu > mu > mu ).
thf(decl_153,type,
esk59_2: $i > $i > $i ).
thf(decl_154,type,
esk60_2: $i > $i > $i ).
thf(decl_155,type,
esk61_2: $i > $i > mu ).
thf(decl_156,type,
esk62_2: $i > $i > $i ).
thf(decl_157,type,
esk63_2: $i > $i > mu ).
thf(decl_158,type,
esk64_2: $i > $i > $i ).
thf(decl_213,type,
esk119_2: $i > $i > $i ).
thf(decl_214,type,
esk120_2: $i > $i > $i ).
thf(decl_215,type,
esk121_2: $i > $i > mu ).
thf(decl_216,type,
esk122_2: $i > $i > $i ).
thf(decl_217,type,
esk123_2: $i > $i > mu ).
thf(decl_218,type,
esk124_2: $i > $i > $i ).
thf(decl_282,type,
esk188_0: $i ).
thf(decl_283,type,
esk189_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mimplies) ).
thf(rosser_kn2,conjecture,
mvalid @ ( mbox_s4 @ kn2 ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',rosser_kn2) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.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.WVwWDB1kwk/E---3.1_2577075.p',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/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mforall_ind) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',mreflexive) ).
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/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.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/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',and_1) ).
thf(hilbert_and_1,axiom,
mvalid @ ( mbox_s4 @ and_1 ),
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',hilbert_and_1) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',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/tmp/tmp.WVwWDB1kwk/E---3.1_2577075.p',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,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ kn2 ) ),
inference(assume_negation,[status(cth)],[rosser_kn2]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,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_21,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_22,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_23,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_24,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_25,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)],[c_0_18,c_0_19]),c_0_20])]) ).
thf(c_0_26,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_21]),c_0_22]),c_0_23]),c_0_19]),c_0_20])]) ).
thf(c_0_27,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_21]),c_0_22]),c_0_23]),c_0_19]),c_0_20])]) ).
thf(c_0_28,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_19]),c_0_20])]) ).
thf(c_0_29,plain,
! [X155: $i] : ( rel_s4 @ X155 @ X155 ),
inference(apply_def,[status(thm)],[a1,c_0_24]) ).
thf(c_0_30,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_25])])])]) ).
thf(c_0_31,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_26])])])])])])]) ).
thf(c_0_32,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_27])])])])])])]) ).
thf(c_0_33,plain,
! [X1412: $i,X1413: $i] :
( ~ ( rel_s4 @ X1412 @ X1413 )
| ( and_1 @ X1413 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
thf(c_0_34,plain,
! [X777: $i] : ( rel_s4 @ X777 @ X777 ),
inference(variable_rename,[status(thm)],[c_0_29]) ).
thf(c_0_35,negated_conjecture,
~ ( kn2 @ esk189_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
! [X3: $i,X16: $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_31]) ).
thf(c_0_37,plain,
! [X3: $i,X10: mu,X16: $i,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_32]) ).
thf(c_0_38,plain,
! [X3: $i,X7: $i] :
( ( and_1 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_39,plain,
! [X3: $i,X16: $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_31]) ).
thf(c_0_40,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_41,plain,
! [X3: $i,X16: $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_31]) ).
thf(c_0_42,plain,
! [X3: $i,X16: $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_31]) ).
thf(c_0_43,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_35,c_0_36]) ).
thf(c_0_44,plain,
! [X3: $i,X7: $i,X12: mu,X10: mu,X17: $i,X18: $i,X16: $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_37,c_0_38]) ).
thf(c_0_45,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_39,c_0_40]) ).
thf(c_0_46,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_41,c_0_40]) ).
thf(c_0_47,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_42,c_0_40]) ).
thf(c_0_48,plain,
! [X3: $i,X16: $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_31]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i,X7: $i,X18: $i,X132: $i,X135: $i,X17: $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_43,c_0_44]) ).
thf(c_0_50,plain,
! [X3: $i] :
( ( rel_s4 @ ( esk122_2 @ X3 @ X3 ) @ ( esk124_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
thf(c_0_51,plain,
! [X3: $i] :
( ( exists_in_world @ ( esk123_2 @ X3 @ X3 ) @ ( esk122_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
thf(c_0_52,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_53,plain,
! [X3: $i] :
( ( rel_s4 @ ( esk120_2 @ X3 @ X3 ) @ ( esk122_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
thf(c_0_54,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_48,c_0_40]) ).
thf(c_0_55,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_31]) ).
thf(c_0_56,negated_conjecture,
! [X7: $i,X3: $i,X16: $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_49,c_0_40]) ).
thf(c_0_57,negated_conjecture,
rel_s4 @ ( esk122_2 @ esk189_0 @ esk189_0 ) @ ( esk124_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
thf(c_0_58,negated_conjecture,
exists_in_world @ ( esk123_2 @ esk189_0 @ esk189_0 ) @ ( esk122_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
thf(c_0_59,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_52]) ).
thf(c_0_60,negated_conjecture,
rel_s4 @ ( esk120_2 @ esk189_0 @ esk189_0 ) @ ( esk122_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
thf(c_0_61,plain,
! [X3: $i] :
( ( exists_in_world @ ( esk121_2 @ X3 @ X3 ) @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_40]) ).
thf(c_0_62,plain,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_40]) ).
thf(c_0_63,negated_conjecture,
! [X3: $i,X16: $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_56,c_0_57]),c_0_58]),c_0_40])]) ).
thf(c_0_64,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_59,c_0_60]) ).
thf(c_0_65,negated_conjecture,
exists_in_world @ ( esk121_2 @ esk189_0 @ esk189_0 ) @ ( esk120_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_61]) ).
thf(c_0_66,plain,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk120_2 @ X3 @ X3 ) )
| ( kn2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_40]) ).
thf(c_0_67,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_63,c_0_64]),c_0_40]),c_0_65])]) ).
thf(c_0_68,negated_conjecture,
rel_s4 @ esk189_0 @ ( esk120_2 @ esk189_0 @ esk189_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_66]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
~ ( rel_s4 @ X3 @ ( esk120_2 @ esk189_0 @ esk189_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_60]) ).
thf(c_0_70,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_68,c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL460^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 % Computer : n010.cluster.edu
% 0.06/0.21 % Model : x86_64 x86_64
% 0.06/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.21 % Memory : 8046.5625MB
% 0.06/0.21 % OS : Linux 6.8.0-71-generic
% 0.06/0.21 % CPULimit : 300
% 0.06/0.21 % WCLimit : 300
% 0.06/0.21 % DateTime : Tue Sep 29 08:50:33 UTC 2026
% 0.06/0.21 % CPUTime :
% 0.06/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.26 Running higher-order theorem proving
% 0.24/0.31 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.WVwWDB1kwk/E---3.1_2577075.p
% 55.69/9.74 % Version: 3.5.1-ho
% 55.69/9.74 % Preprocessing class: HSLSSMSSMLLNHSN.
% 55.69/9.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.69/9.74 % Starting almost_fo_3 with 1500s (5) cores
% 55.69/9.74 % Starting sh10 with 300s (1) cores
% 55.69/9.74 % Starting new_ho_16 with 300s (1) cores
% 55.69/9.74 % Starting post_as_ho11 with 300s (1) cores
% 55.69/9.74 % new_ho_16 with pid 2577090 completed with status 9
% 55.69/9.74 % almost_fo_3 with pid 2577088 completed with status 0
% 55.69/9.74 % Result found by almost_fo_3
% 55.69/9.74 % Preprocessing class: HSLSSMSSMLLNHSN.
% 55.69/9.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.69/9.74 % Starting almost_fo_3 with 1500s (5) cores
% 55.69/9.74 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 55.69/9.74 % No SInE strategy applied
% 55.69/9.74 % Search class: HGUNM-FSLF32-MHSSMFNN
% 55.69/9.74 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 55.69/9.74 % Starting SubtermCWHack with 151s (1) cores
% 55.69/9.74 % Starting almost_fo_3 with 329s (1) cores
% 55.69/9.74 % Starting ho_unfolding_7 with 329s (1) cores
% 55.69/9.74 % Starting new_bool_3 with 329s (1) cores
% 55.69/9.74 % Starting new_bool_1 with 329s (1) cores
% 55.69/9.74 % almost_fo_3 with pid 2577107 completed with status 0
% 55.69/9.74 % Result found by almost_fo_3
% 55.69/9.74 % Preprocessing class: HSLSSMSSMLLNHSN.
% 55.69/9.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.69/9.74 % Starting almost_fo_3 with 1500s (5) cores
% 55.69/9.74 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 55.69/9.74 % No SInE strategy applied
% 55.69/9.74 % Search class: HGUNM-FSLF32-MHSSMFNN
% 55.69/9.74 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 55.69/9.74 % Starting SubtermCWHack with 151s (1) cores
% 55.69/9.74 % Starting almost_fo_3 with 329s (1) cores
% 55.69/9.74 % Preprocessing time : 0.014 s
% 55.69/9.74 % Presaturation interreduction done
% 55.69/9.74
% 55.69/9.74 % Proof found!
% 55.69/9.74 % SZS status Theorem
% 55.69/9.74 % SZS output start CNFRefutation
% See solution above
% 55.69/9.74 % Parsed axioms : 180
% 55.69/9.74 % Removed by relevancy pruning/SinE : 0
% 55.69/9.74 % Initial clauses : 371
% 55.69/9.74 % Removed in clause preprocessing : 73
% 55.69/9.74 % Initial clauses in saturation : 298
% 55.69/9.74 % Processed clauses : 10069
% 55.69/9.74 % ...of these trivial : 0
% 55.69/9.74 % ...subsumed : 3417
% 55.69/9.74 % ...remaining for further processing : 6652
% 55.69/9.74 % Other redundant clauses eliminated : 0
% 55.69/9.74 % Clauses deleted for lack of memory : 0
% 55.69/9.74 % Backward-subsumed : 260
% 55.69/9.74 % Backward-rewritten : 18
% 55.69/9.74 % Generated clauses : 17596
% 55.69/9.74 % ...of the previous two non-redundant : 17523
% 55.69/9.74 % ...aggressively subsumed : 0
% 55.69/9.74 % Contextual simplify-reflections : 2
% 55.69/9.74 % Paramodulations : 17595
% 55.69/9.74 % Factorizations : 0
% 55.69/9.74 % NegExts : 0
% 55.69/9.74 % Equation resolutions : 0
% 55.69/9.74 % Disequality decompositions : 0
% 55.69/9.74 % Total rewrite steps : 1231
% 55.69/9.74 % ...of those cached : 1147
% 55.69/9.74 % Propositional unsat checks : 1
% 55.69/9.74 % Propositional check models : 1
% 55.69/9.74 % Propositional check unsatisfiable : 0
% 55.69/9.74 % Propositional clauses : 0
% 55.69/9.74 % Propositional clauses after purity: 0
% 55.69/9.74 % Propositional unsat core size : 0
% 55.69/9.74 % Propositional preprocessing time : 0.000
% 55.69/9.74 % Propositional encoding time : 0.035
% 55.69/9.74 % Propositional solver time : 0.003
% 55.69/9.74 % Success case prop preproc time : 0.000
% 55.69/9.74 % Success case prop encoding time : 0.000
% 55.69/9.74 % Success case prop solver time : 0.000
% 55.69/9.74 % Current number of processed clauses : 6177
% 55.69/9.74 % Positive orientable unit clauses : 19
% 55.69/9.74 % Positive unorientable unit clauses: 0
% 55.69/9.74 % Negative unit clauses : 2
% 55.69/9.74 % Non-unit-clauses : 6156
% 55.69/9.74 % Current number of unprocessed clauses: 7944
% 55.69/9.74 % ...number of literals in the above : 42718
% 55.69/9.74 % Current number of archived formulas : 0
% 55.69/9.74 % Current number of archived clauses : 475
% 55.69/9.74 % Clause-clause subsumption calls (NU) : 21171425
% 55.69/9.74 % Rec. Clause-clause subsumption calls : 7233144
% 55.69/9.74 % Non-unit clause-clause subsumptions : 3510
% 55.69/9.74 % Unit Clause-clause subsumption calls : 10001
% 55.69/9.74 % Rewrite failures with RHS unbound : 0
% 55.69/9.74 % BW rewrite match attempts : 12
% 55.69/9.74 % BW rewrite match successes : 10
% 55.69/9.74 % Condensation attempts : 0
% 55.69/9.74 % Condensation successes : 0
% 55.69/9.74 % Termbank termtop insertions : 622394
% 55.69/9.74 % Search garbage collected termcells : 31213
% 55.69/9.74
% 55.69/9.74 % -------------------------------------------------
% 55.69/9.74 % User time : 9.137 s
% 55.69/9.74 % System time : 0.061 s
% 55.69/9.74 % Total time : 9.198 s
% 55.69/9.74 % Maximum resident set size: 8564 pages
% 55.69/9.74
% 55.69/9.74 % -------------------------------------------------
% 55.69/9.74 % User time : 44.951 s
% 55.69/9.74 % System time : 1.030 s
% 55.69/9.74 % Total time : 45.981 s
% 55.69/9.74 % Maximum resident set size: 5120 pages
% 55.69/9.74 % E exiting
%------------------------------------------------------------------------------