TSTP Solution File: SYN397^7 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 : Tue May 21 07:44:37 EDT 2024
% Result : Theorem 4.39s 0.98s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 40
% Syntax : Number of formulae : 181 ( 38 unt; 25 typ; 0 def)
% Number of atoms : 661 ( 23 equ; 0 cnn)
% Maximal formula atoms : 163 ( 4 avg)
% Number of connectives : 2408 ( 301 ~; 397 |; 45 &;1653 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 255 ( 50 ^ 204 !; 1 ?; 255 :)
% 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_38,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_43,type,
mtransitive: ( $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_57,type,
f: mu > $i > $o ).
thf(decl_58,type,
esk1_1: $i > mu ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(decl_61,type,
esk4_2: $i > mu > $i ).
thf(decl_62,type,
esk5_0: $i ).
thf(decl_63,type,
esk6_0: mu ).
thf(decl_64,type,
esk7_0: $i ).
thf(decl_65,type,
esk8_0: $i ).
thf(decl_66,type,
esk9_3: $i > mu > $i > $i ).
thf(decl_67,type,
esk10_0: $i ).
thf(decl_68,type,
esk11_0: mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X13: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
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/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
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/sandbox/benchmark/Axioms/LCL015^0.ax',mtransitive) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(kalish204,conjecture,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X20: mu] : ( mbox_s4 @ ( f @ X20 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X21 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X22: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X22 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X23: mu] : ( mbox_s4 @ ( f @ X23 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish204) ).
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/sandbox/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(nonempty_ax,axiom,
! [X7: $i] :
? [X10: mu] : ( exists_in_world @ X10 @ X7 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',nonempty_ax) ).
thf(c_0_15,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_19,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X30: mu] :
( ( exists_in_world @ X30 @ Z1 )
=> ~ ( Z0 @ X30 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_20,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_21,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_22,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_15,c_0_16]),c_0_17]) ).
thf(c_0_23,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_18,c_0_16]),c_0_17]) ).
thf(c_0_24,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X30: mu] :
( ( exists_in_world @ X30 @ Z1 )
=> ~ ( Z0 @ X30 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_16]),c_0_20]) ).
thf(c_0_25,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_26,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_27,plain,
! [X34: $i,X35: $i,X36: $i] :
( ( ( rel_s4 @ X34 @ X35 )
& ( rel_s4 @ X35 @ X36 ) )
=> ( rel_s4 @ X34 @ X36 ) ),
inference(apply_def,[status(thm)],[a2,c_0_21]) ).
thf(c_0_28,negated_conjecture,
~ ! [X53: $i] :
~ ( ~ ! [X44: $i] :
( ~ ( rel_s4 @ X53 @ X44 )
| ~ ! [X39: $i] :
( ~ ( rel_s4 @ X44 @ X39 )
| ~ ~ ! [X38: mu] :
( ( exists_in_world @ X38 @ X39 )
=> ~ ! [X37: $i] :
( ~ ( rel_s4 @ X39 @ X37 )
| ( f @ X38 @ X37 ) ) ) )
| ! [X43: $i] :
( ~ ( rel_s4 @ X44 @ X43 )
| ! [X42: mu] :
( ( exists_in_world @ X42 @ X43 )
=> ! [X41: $i] :
( ~ ( rel_s4 @ X43 @ X41 )
| ~ ! [X40: $i] :
( ~ ( rel_s4 @ X41 @ X40 )
| ( f @ X42 @ X40 ) ) ) ) ) )
| ~ ! [X52: $i] :
( ~ ( rel_s4 @ X53 @ X52 )
| ~ ! [X48: $i] :
( ~ ( rel_s4 @ X52 @ X48 )
| ! [X47: mu] :
( ( exists_in_world @ X47 @ X48 )
=> ! [X46: $i] :
( ~ ( rel_s4 @ X48 @ X46 )
| ~ ! [X45: $i] :
( ~ ( rel_s4 @ X46 @ X45 )
| ( f @ X47 @ X45 ) ) ) ) )
| ! [X51: $i] :
( ~ ( rel_s4 @ X52 @ X51 )
| ~ ~ ! [X50: mu] :
( ( exists_in_world @ X50 @ X51 )
=> ~ ! [X49: $i] :
( ~ ( rel_s4 @ X51 @ X49 )
| ( f @ X50 @ 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[kalish204])]),c_0_16]),c_0_22]),c_0_23]),c_0_20]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_29,plain,
! [X57: $i,X58: $i,X59: $i] :
( ~ ( rel_s4 @ X57 @ X58 )
| ~ ( rel_s4 @ X58 @ X59 )
| ( rel_s4 @ X57 @ X59 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
thf(c_0_30,negated_conjecture,
! [X65: $i,X66: mu,X71: $i,X73: $i,X74: mu,X75: $i,X79: $i] :
( ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).
thf(c_0_31,plain,
! [X7: $i,X3: $i,X16: $i] :
( ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_32,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_33,plain,
! [X60: mu,X61: $i,X62: $i] :
( ~ ( exists_in_world @ X60 @ X61 )
| ~ ( rel_s4 @ X61 @ X62 )
| ( exists_in_world @ X60 @ X62 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_35,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,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_33]) ).
thf(c_0_37,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
( ( rel_s4 @ esk3_0 @ esk7_0 )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
thf(c_0_40,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_41,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_42,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk7_0 )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_43,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,negated_conjecture,
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_45,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_46,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_47,negated_conjecture,
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,plain,
! [X33: $i] : ( rel_s4 @ X33 @ X33 ),
inference(apply_def,[status(thm)],[a1,c_0_45]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_50,negated_conjecture,
rel_s4 @ esk8_0 @ esk10_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_38]) ).
thf(c_0_51,plain,
! [X56: $i] : ( rel_s4 @ X56 @ X56 ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
thf(c_0_52,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_54,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_55,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_57,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_58,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_59,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_60,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_58]) ).
thf(c_0_62,negated_conjecture,
rel_s4 @ esk3_0 @ esk5_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_50]),c_0_53])]),c_0_55]) ).
thf(c_0_63,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_64,negated_conjecture,
! [X10: mu,X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_65,negated_conjecture,
( ( rel_s4 @ esk3_0 @ esk7_0 )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_66,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_58]) ).
thf(c_0_67,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk10_0 )
| ~ ( rel_s4 @ X3 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
thf(c_0_70,plain,
! [X54: $i] : ( exists_in_world @ ( esk1_1 @ X54 ) @ X54 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[nonempty_ax])]) ).
thf(c_0_71,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_72,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk7_0 )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_73,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_53])]) ).
thf(c_0_74,plain,
! [X3: $i] : ( exists_in_world @ ( esk1_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_75,negated_conjecture,
! [X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_76,negated_conjecture,
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_77,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_50]) ).
thf(c_0_78,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_79,negated_conjecture,
! [X10: mu,X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_80,negated_conjecture,
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
thf(c_0_81,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ X10 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
thf(c_0_82,negated_conjecture,
exists_in_world @ esk11_0 @ esk10_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_72]),c_0_65]) ).
thf(c_0_83,negated_conjecture,
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
thf(c_0_84,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_83]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_86,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_78]) ).
thf(c_0_87,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_88,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_89,negated_conjecture,
rel_s4 @ esk5_0 @ esk7_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_50]),c_0_82])]),c_0_78]) ).
thf(c_0_90,negated_conjecture,
! [X7: $i,X3: $i,X12: mu,X10: mu,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ X16 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_91,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_89]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i,X10: mu,X12: mu,X7: $i] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X12 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( exists_in_world @ X10 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X12 @ X7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_62])]) ).
thf(c_0_93,negated_conjecture,
! [X3: $i,X12: mu,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X12 ) )
| ~ ( exists_in_world @ X12 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_69]),c_0_53])]) ).
thf(c_0_94,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_89]) ).
thf(c_0_95,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_96,negated_conjecture,
! [X3: $i,X12: mu,X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X12 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X12 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
thf(c_0_97,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_50]) ).
thf(c_0_98,negated_conjecture,
! [X10: mu,X12: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X12 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 )
| ~ ( exists_in_world @ X12 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_53]) ).
thf(c_0_99,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_97,c_0_53]) ).
thf(c_0_100,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_98,c_0_82]) ).
thf(c_0_101,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_99,c_0_82]) ).
thf(c_0_102,negated_conjecture,
! [X10: mu,X7: $i,X3: $i,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( f @ esk6_0 @ X16 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ esk7_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_103,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
thf(c_0_104,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 ) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
thf(c_0_105,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_53]) ).
thf(c_0_106,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_69]),c_0_53])]) ).
thf(c_0_107,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_105,c_0_82]) ).
thf(c_0_108,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_53]) ).
thf(c_0_109,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_106,c_0_53]) ).
thf(c_0_110,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_107]) ).
thf(c_0_111,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_107]) ).
thf(c_0_112,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ X10 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_69]),c_0_53])]) ).
thf(c_0_113,negated_conjecture,
! [X7: $i,X10: mu,X12: mu,X3: $i,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( f @ X12 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_114,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_82]) ).
thf(c_0_115,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_110,c_0_101]) ).
thf(c_0_116,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_111,c_0_62]) ).
thf(c_0_117,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_112,c_0_74]) ).
thf(c_0_118,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_116]) ).
thf(c_0_119,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ X10 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_97,c_0_117]) ).
thf(c_0_120,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_69]),c_0_53])]) ).
thf(c_0_121,negated_conjecture,
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_119,c_0_82]) ).
thf(c_0_122,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ X7 @ ( esk4_2 @ X7 @ X10 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk3_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_123,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_120,c_0_53]) ).
thf(c_0_124,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_121]) ).
thf(c_0_125,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_91]),c_0_62])]) ).
thf(c_0_126,negated_conjecture,
rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ),
inference(spm,[status(thm)],[c_0_123,c_0_82]) ).
thf(c_0_127,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_128,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_124,c_0_117]) ).
thf(c_0_129,negated_conjecture,
! [X10: mu] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
thf(c_0_130,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_131,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
thf(c_0_132,negated_conjecture,
! [X10: mu] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_129,c_0_94]) ).
thf(c_0_133,negated_conjecture,
exists_in_world @ esk6_0 @ esk5_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_50]),c_0_82])]),c_0_117]) ).
thf(c_0_134,negated_conjecture,
! [X3: $i,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ( f @ esk6_0 @ X7 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_135,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
thf(c_0_136,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
thf(c_0_137,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ~ ( rel_s4 @ X3 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_126]) ).
thf(c_0_138,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( f @ X10 @ ( esk4_2 @ X7 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk3_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_139,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_53])]) ).
thf(c_0_140,negated_conjecture,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ esk5_0 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_91]) ).
thf(c_0_141,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
thf(c_0_142,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_140,c_0_62]) ).
thf(c_0_143,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_53])]) ).
thf(c_0_144,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_94]),c_0_133])]) ).
thf(c_0_145,negated_conjecture,
! [X10: mu,X7: $i,X3: $i,X16: $i] :
( ( f @ esk6_0 @ X16 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_146,negated_conjecture,
f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_137]),c_0_53])]) ).
thf(c_0_147,negated_conjecture,
! [X3: $i,X10: mu,X12: mu,X7: $i,X16: $i] :
( ( rel_s4 @ X16 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_148,negated_conjecture,
! [X7: $i,X10: mu,X12: mu,X3: $i,X16: $i] :
( ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( f @ X12 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_149,negated_conjecture,
! [X3: $i] :
( ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_50]),c_0_53]),c_0_82])]) ).
thf(c_0_150,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_146]),c_0_50]),c_0_53]),c_0_82])]) ).
thf(c_0_151,negated_conjecture,
! [X10: mu,X3: $i] :
( ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_146]),c_0_50]),c_0_53]),c_0_82])]) ).
thf(c_0_152,negated_conjecture,
! [X10: mu] :
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
thf(c_0_153,negated_conjecture,
( ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
thf(c_0_154,negated_conjecture,
~ ( rel_s4 @ esk3_0 @ esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_94]),c_0_133])]) ).
thf(c_0_155,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_142]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 15:00:08 EDT 2024
% 0.17/0.31 % CPUTime :
% 0.17/0.42 Running higher-order theorem proving
% 0.17/0.42 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/0.98 # Version: 3.1.0-ho
% 4.39/0.98 # Preprocessing class: HSMSSMSSMLMNHSN.
% 4.39/0.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/0.98 # Starting ho_unfolding_3 with 1500s (5) cores
% 4.39/0.98 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 4.39/0.98 # Starting almost_fo_3_lam with 300s (1) cores
% 4.39/0.98 # Starting post_as_ho1 with 300s (1) cores
% 4.39/0.98 # ho_unfolding_3 with pid 21533 completed with status 0
% 4.39/0.98 # Result found by ho_unfolding_3
% 4.39/0.98 # Preprocessing class: HSMSSMSSMLMNHSN.
% 4.39/0.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/0.98 # Starting ho_unfolding_3 with 1500s (5) cores
% 4.39/0.98 # No SInE strategy applied
% 4.39/0.98 # Search class: HGHNS-FFMM32-SHSSMFNN
% 4.39/0.98 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.39/0.98 # Starting new_ho_10 with 811s (1) cores
% 4.39/0.98 # Starting ho_unfolding_3 with 151s (1) cores
% 4.39/0.98 # Starting sh4l with 136s (1) cores
% 4.39/0.98 # Starting lpo8_s with 136s (1) cores
% 4.39/0.98 # Starting full_lambda_8 with 136s (1) cores
% 4.39/0.98 # ho_unfolding_3 with pid 21544 completed with status 0
% 4.39/0.98 # Result found by ho_unfolding_3
% 4.39/0.98 # Preprocessing class: HSMSSMSSMLMNHSN.
% 4.39/0.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/0.98 # Starting ho_unfolding_3 with 1500s (5) cores
% 4.39/0.98 # No SInE strategy applied
% 4.39/0.98 # Search class: HGHNS-FFMM32-SHSSMFNN
% 4.39/0.98 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.39/0.98 # Starting new_ho_10 with 811s (1) cores
% 4.39/0.98 # Starting ho_unfolding_3 with 151s (1) cores
% 4.39/0.98 # Preprocessing time : 0.001 s
% 4.39/0.98 # Presaturation interreduction done
% 4.39/0.98
% 4.39/0.98 # Proof found!
% 4.39/0.98 # SZS status Theorem
% 4.39/0.98 # SZS output start CNFRefutation
% See solution above
% 4.39/0.98 # Parsed axioms : 74
% 4.39/0.98 # Removed by relevancy pruning/SinE : 0
% 4.39/0.98 # Initial clauses : 83
% 4.39/0.98 # Removed in clause preprocessing : 37
% 4.39/0.98 # Initial clauses in saturation : 46
% 4.39/0.98 # Processed clauses : 5052
% 4.39/0.98 # ...of these trivial : 0
% 4.39/0.98 # ...subsumed : 2175
% 4.39/0.98 # ...remaining for further processing : 2877
% 4.39/0.98 # Other redundant clauses eliminated : 0
% 4.39/0.98 # Clauses deleted for lack of memory : 0
% 4.39/0.98 # Backward-subsumed : 266
% 4.39/0.98 # Backward-rewritten : 1114
% 4.39/0.98 # Generated clauses : 10082
% 4.39/0.98 # ...of the previous two non-redundant : 10010
% 4.39/0.98 # ...aggressively subsumed : 0
% 4.39/0.98 # Contextual simplify-reflections : 19
% 4.39/0.98 # Paramodulations : 10082
% 4.39/0.98 # Factorizations : 0
% 4.39/0.98 # NegExts : 0
% 4.39/0.98 # Equation resolutions : 0
% 4.39/0.98 # Disequality decompositions : 0
% 4.39/0.98 # Total rewrite steps : 1379
% 4.39/0.98 # ...of those cached : 1360
% 4.39/0.98 # Propositional unsat checks : 0
% 4.39/0.98 # Propositional check models : 0
% 4.39/0.98 # Propositional check unsatisfiable : 0
% 4.39/0.98 # Propositional clauses : 0
% 4.39/0.98 # Propositional clauses after purity: 0
% 4.39/0.98 # Propositional unsat core size : 0
% 4.39/0.98 # Propositional preprocessing time : 0.000
% 4.39/0.98 # Propositional encoding time : 0.000
% 4.39/0.98 # Propositional solver time : 0.000
% 4.39/0.98 # Success case prop preproc time : 0.000
% 4.39/0.98 # Success case prop encoding time : 0.000
% 4.39/0.98 # Success case prop solver time : 0.000
% 4.39/0.98 # Current number of processed clauses : 1451
% 4.39/0.98 # Positive orientable unit clauses : 21
% 4.39/0.98 # Positive unorientable unit clauses: 0
% 4.39/0.98 # Negative unit clauses : 1
% 4.39/0.98 # Non-unit-clauses : 1429
% 4.39/0.98 # Current number of unprocessed clauses: 3500
% 4.39/0.98 # ...number of literals in the above : 16279
% 4.39/0.98 # Current number of archived formulas : 0
% 4.39/0.98 # Current number of archived clauses : 1426
% 4.39/0.98 # Clause-clause subsumption calls (NU) : 128701
% 4.39/0.98 # Rec. Clause-clause subsumption calls : 56165
% 4.39/0.98 # Non-unit clause-clause subsumptions : 2451
% 4.39/0.98 # Unit Clause-clause subsumption calls : 1646
% 4.39/0.98 # Rewrite failures with RHS unbound : 0
% 4.39/0.98 # BW rewrite match attempts : 16
% 4.39/0.98 # BW rewrite match successes : 14
% 4.39/0.98 # Condensation attempts : 5052
% 4.39/0.98 # Condensation successes : 0
% 4.39/0.98 # Termbank termtop insertions : 251137
% 4.39/0.98 # Search garbage collected termcells : 1324
% 4.39/0.98
% 4.39/0.98 # -------------------------------------------------
% 4.39/0.98 # User time : 0.532 s
% 4.39/0.98 # System time : 0.010 s
% 4.39/0.98 # Total time : 0.542 s
% 4.39/0.98 # Maximum resident set size: 2160 pages
% 4.39/0.98
% 4.39/0.98 # -------------------------------------------------
% 4.39/0.98 # User time : 2.668 s
% 4.39/0.98 # System time : 0.035 s
% 4.39/0.98 # Total time : 2.703 s
% 4.39/0.98 # Maximum resident set size: 1804 pages
% 4.39/0.98 % E---3.1 exiting
% 4.39/0.98 % E exiting
%------------------------------------------------------------------------------