%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:12:54 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 364 ( 14 equ; 0 cnn)
% Maximal formula atoms : 161 ( 6 avg)
% Number of connectives : 1137 ( 141 ~; 173 |; 49 &; 751 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 148 ( 38 ^; 106 !; 4 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mworld > mworld > $o ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_26,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_27,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
eiw_di: $i > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
f: $i > mworld > $o ).
thf(decl_38,type,
esk2_0: mworld ).
thf(decl_39,type,
esk3_1: mworld > mworld ).
thf(decl_40,type,
esk4_1: mworld > $i ).
thf(decl_41,type,
esk5_1: mworld > mworld ).
thf(decl_42,type,
esk6_1: $i > mworld ).
thf(decl_43,type,
esk7_0: mworld ).
thf(decl_44,type,
esk8_0: $i ).
thf(decl_45,type,
esk9_1: mworld > mworld ).
thf(decl_46,type,
esk10_0: mworld ).
thf(kalish203,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mbox @ ( f @ X6 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X9: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X9 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X9: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X9 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mbox @ ( f @ X6 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',kalish203) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mlocal_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mnot_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mand_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mbox_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X8: $i > mworld > $o,X3: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ X3 )
& ( X8 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mexists_di_def) ).
thf(eiw_di_decr,axiom,
! [X3: mworld,X5: mworld,X6: $i] :
( ( ( eiw_di @ X6 @ X3 )
& ( mrel @ X5 @ X3 ) )
=> ( eiw_di @ X6 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',eiw_di_decr) ).
thf(mrel_universal,axiom,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
file('/export/starexec/sandbox2/tmp/tmp.y7bGszyID4/E---3.1_1129227.p',mrel_universal) ).
thf(c_0_10,negated_conjecture,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mbox @ ( f @ X6 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X9: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X9 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X9: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X9 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mbox @ ( f @ X6 ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kalish203]) ).
thf(c_0_11,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_12,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_14,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_15,plain,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_16,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_17,plain,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
& ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_def]) ).
thf(c_0_18,negated_conjecture,
~ ( ! [X24: mworld] :
( ( mrel @ mactual @ X24 )
=> ( ! [X20: mworld] :
( ( mrel @ X24 @ X20 )
=> ~ ! [X19: mworld] :
( ( mrel @ X20 @ X19 )
=> ! [X18: $i] :
( ( eiw_di @ X18 @ X19 )
=> ! [X17: mworld] :
( ( mrel @ X19 @ X17 )
=> ( f @ X18 @ X17 ) ) ) ) )
=> ? [X23: $i] :
( ( eiw_di @ X23 @ X24 )
& ! [X22: mworld] :
( ( mrel @ X24 @ X22 )
=> ~ ! [X21: mworld] :
( ( mrel @ X22 @ X21 )
=> ( f @ X23 @ X21 ) ) ) ) ) )
& ! [X32: mworld] :
( ( mrel @ mactual @ X32 )
=> ( ? [X27: $i] :
( ( eiw_di @ X27 @ X32 )
& ! [X26: mworld] :
( ( mrel @ X32 @ X26 )
=> ~ ! [X25: mworld] :
( ( mrel @ X26 @ X25 )
=> ( f @ X27 @ X25 ) ) ) )
=> ! [X31: mworld] :
( ( mrel @ X32 @ X31 )
=> ~ ! [X30: mworld] :
( ( mrel @ X31 @ X30 )
=> ! [X29: $i] :
( ( eiw_di @ X29 @ X30 )
=> ! [X28: mworld] :
( ( mrel @ X30 @ X28 )
=> ( f @ X29 @ X28 ) ) ) ) ) ) ) ),
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)],[c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_19,plain,
! [X37: mworld,X38: mworld,X39: $i] :
( ~ ( eiw_di @ X39 @ X37 )
| ~ ( mrel @ X38 @ X37 )
| ( eiw_di @ X39 @ X38 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[eiw_di_decr])])]) ).
thf(c_0_20,plain,
! [X33: mworld,X34: mworld] : ( mrel @ X33 @ X34 ),
inference(variable_rename,[status(thm)],[mrel_universal]) ).
thf(c_0_21,negated_conjecture,
! [X41: mworld,X45: $i,X47: mworld,X50: mworld,X53: mworld,X54: $i,X55: mworld] :
( ( ( mrel @ mactual @ esk7_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ( mrel @ X41 @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ( eiw_di @ ( esk4_1 @ X41 ) @ ( esk3_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ( mrel @ ( esk3_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ~ ( f @ ( esk4_1 @ X41 ) @ ( esk5_1 @ X41 ) )
| ~ ( mrel @ esk2_0 @ X41 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ( mrel @ esk2_0 @ ( esk6_1 @ X45 ) )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( mrel @ mactual @ esk7_0 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( eiw_di @ esk8_0 @ esk7_0 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( mrel @ X50 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ~ ( f @ esk8_0 @ ( esk9_1 @ X50 ) )
| ~ ( mrel @ esk7_0 @ X50 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ( mrel @ esk7_0 @ esk10_0 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) )
& ( ~ ( mrel @ esk10_0 @ X53 )
| ~ ( eiw_di @ X54 @ X53 )
| ~ ( mrel @ X53 @ X55 )
| ( f @ X54 @ X55 )
| ~ ( mrel @ ( esk6_1 @ X45 ) @ X47 )
| ( f @ X45 @ X47 )
| ~ ( eiw_di @ X45 @ esk2_0 ) ) ),
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_18])])])])])]) ).
thf(c_0_22,plain,
! [X6: $i,X5: mworld,X3: mworld] :
( ( eiw_di @ X6 @ X5 )
| ~ ( eiw_di @ X6 @ X3 )
| ~ ( mrel @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ~ ( mrel @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ~ ( f @ ( esk4_1 @ X3 ) @ ( esk5_1 @ X3 ) )
| ~ ( mrel @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ( f @ X6 @ X3 )
| ~ ( mrel @ ( esk6_1 @ X6 ) @ X3 )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
! [X3: mworld,X6: $i,X5: mworld] :
( ( eiw_di @ X6 @ X3 )
| ~ ( eiw_di @ X6 @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_28,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ( eiw_di @ esk8_0 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23])]) ).
thf(c_0_29,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ~ ( f @ ( esk4_1 @ X3 ) @ ( esk5_1 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23])]) ).
thf(c_0_30,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ( f @ X6 @ X3 )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_23])]) ).
thf(c_0_31,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( eiw_di @ esk8_0 @ esk7_0 )
| ( eiw_di @ ( esk4_1 @ X3 ) @ X5 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i,X10: mworld] :
( ( f @ X6 @ X5 )
| ( eiw_di @ ( esk4_1 @ X10 ) @ ( esk3_1 @ X10 ) )
| ~ ( mrel @ esk10_0 @ X3 )
| ~ ( eiw_di @ X6 @ X3 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ esk2_0 @ X10 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_33,negated_conjecture,
eiw_di @ esk8_0 @ esk7_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_34,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i,X10: mworld,X9: $i] :
( ( f @ X6 @ X5 )
| ( f @ X9 @ X10 )
| ~ ( mrel @ esk10_0 @ X3 )
| ~ ( eiw_di @ X6 @ X3 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ ( esk6_1 @ X9 ) @ X10 )
| ~ ( eiw_di @ X9 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_35,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i,X10: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ( f @ X6 @ X5 )
| ~ ( eiw_di @ X6 @ X10 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_23]),c_0_23]),c_0_23])]) ).
thf(c_0_36,negated_conjecture,
! [X3: mworld] : ( eiw_di @ esk8_0 @ X3 ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
thf(c_0_37,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i,X9: $i,X10: mworld] :
( ( f @ X6 @ X3 )
| ( f @ X9 @ X5 )
| ~ ( eiw_di @ X9 @ esk2_0 )
| ~ ( eiw_di @ X6 @ X10 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_23]),c_0_23]),c_0_23])]) ).
thf(c_0_38,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( eiw_di @ ( esk4_1 @ X5 ) @ ( esk3_1 @ X5 ) )
| ~ ( f @ esk8_0 @ ( esk9_1 @ X3 ) )
| ~ ( mrel @ esk7_0 @ X3 )
| ~ ( mrel @ esk2_0 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_39,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ( f @ esk8_0 @ X5 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i] :
( ( f @ esk8_0 @ X3 )
| ( f @ X6 @ X5 )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ~ ( f @ esk8_0 @ ( esk9_1 @ X5 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_23]),c_0_23])]) ).
thf(c_0_42,negated_conjecture,
! [X3: mworld,X5: mworld,X10: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ X5 )
| ( f @ esk8_0 @ X10 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ~ ( f @ esk8_0 @ ( esk9_1 @ X3 ) )
| ~ ( mrel @ esk7_0 @ X3 )
| ~ ( f @ ( esk4_1 @ X5 ) @ ( esk5_1 @ X5 ) )
| ~ ( mrel @ esk2_0 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_44,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( f @ esk8_0 @ X3 )
| ( f @ esk8_0 @ X5 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
thf(c_0_45,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i] :
( ( f @ X6 @ X5 )
| ~ ( f @ esk8_0 @ ( esk9_1 @ X3 ) )
| ~ ( mrel @ esk7_0 @ X3 )
| ~ ( mrel @ ( esk6_1 @ X6 ) @ X5 )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_46,negated_conjecture,
! [X3: mworld,X5: mworld,X10: mworld] :
( ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) )
| ( eiw_di @ ( esk4_1 @ X5 ) @ X10 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_47,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ~ ( f @ ( esk4_1 @ X3 ) @ ( esk5_1 @ X3 ) )
| ~ ( f @ esk8_0 @ ( esk9_1 @ X5 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_23]),c_0_23])]) ).
thf(c_0_48,negated_conjecture,
! [X3: mworld] : ( f @ esk8_0 @ X3 ),
inference(ef,[status(thm)],[c_0_44]) ).
thf(c_0_49,negated_conjecture,
! [X3: mworld,X5: mworld,X6: $i] :
( ( f @ X6 @ X3 )
| ~ ( f @ esk8_0 @ ( esk9_1 @ X5 ) )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_23]),c_0_23])]) ).
thf(c_0_50,negated_conjecture,
! [X3: mworld] : ( eiw_di @ ( esk4_1 @ X3 ) @ ( esk3_1 @ X3 ) ),
inference(ef,[status(thm)],[c_0_46]) ).
thf(c_0_51,negated_conjecture,
! [X3: mworld] :
~ ( f @ ( esk4_1 @ X3 ) @ ( esk5_1 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_52,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( f @ X6 @ X3 )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48])]) ).
thf(c_0_53,negated_conjecture,
! [X3: mworld,X5: mworld] : ( eiw_di @ ( esk4_1 @ X3 ) @ X5 ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
thf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:59:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.y7bGszyID4/E---3.1_1129227.p
% 0.09/0.27 % Version: 3.5.1-ho
% 0.09/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.27 % almost_fo_3_lam with pid 1129242 completed with status 0
% 0.09/0.27 % Result found by almost_fo_3_lam
% 0.09/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.27 % No SInE strategy applied
% 0.09/0.27 % Search class: HGHNS-FFMS11-SHSSMFNN
% 0.09/0.27 % partial match(1): HGHNS-FFMF11-SHSSMFNN
% 0.09/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.27 % SubtermCWHack with pid 1129248 completed with status 0
% 0.09/0.27 % Result found by SubtermCWHack
% 0.09/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.27 % No SInE strategy applied
% 0.09/0.27 % Search class: HGHNS-FFMS11-SHSSMFNN
% 0.09/0.27 % partial match(1): HGHNS-FFMF11-SHSSMFNN
% 0.09/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.27 % Preprocessing time : 0.001 s
% 0.09/0.27
% 0.09/0.27 % Proof found!
% 0.09/0.27 % SZS status Theorem
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.27 % Parsed axioms : 29
% 0.09/0.27 % Removed by relevancy pruning/SinE : 0
% 0.09/0.27 % Initial clauses : 60
% 0.09/0.27 % Removed in clause preprocessing : 15
% 0.09/0.27 % Initial clauses in saturation : 45
% 0.09/0.27 % Processed clauses : 64
% 0.09/0.27 % ...of these trivial : 33
% 0.09/0.27 % ...subsumed : 3
% 0.09/0.27 % ...remaining for further processing : 28
% 0.09/0.27 % Other redundant clauses eliminated : 0
% 0.09/0.27 % Clauses deleted for lack of memory : 0
% 0.09/0.27 % Backward-subsumed : 9
% 0.09/0.27 % Backward-rewritten : 11
% 0.09/0.27 % Generated clauses : 40
% 0.09/0.27 % ...of the previous two non-redundant : 38
% 0.09/0.27 % ...aggressively subsumed : 0
% 0.09/0.27 % Contextual simplify-reflections : 1
% 0.09/0.27 % Paramodulations : 36
% 0.09/0.27 % Factorizations : 4
% 0.09/0.27 % NegExts : 0
% 0.09/0.27 % Equation resolutions : 0
% 0.09/0.27 % Disequality decompositions : 0
% 0.09/0.27 % Total rewrite steps : 119
% 0.09/0.27 % ...of those cached : 84
% 0.09/0.27 % Propositional unsat checks : 0
% 0.09/0.27 % Propositional check models : 0
% 0.09/0.27 % Propositional check unsatisfiable : 0
% 0.09/0.27 % Propositional clauses : 0
% 0.09/0.27 % Propositional clauses after purity: 0
% 0.09/0.27 % Propositional unsat core size : 0
% 0.09/0.27 % Propositional preprocessing time : 0.000
% 0.09/0.27 % Propositional encoding time : 0.000
% 0.09/0.27 % Propositional solver time : 0.000
% 0.09/0.27 % Success case prop preproc time : 0.000
% 0.09/0.27 % Success case prop encoding time : 0.000
% 0.09/0.27 % Success case prop solver time : 0.000
% 0.09/0.27 % Current number of processed clauses : 8
% 0.09/0.27 % Positive orientable unit clauses : 5
% 0.09/0.27 % Positive unorientable unit clauses: 0
% 0.09/0.27 % Negative unit clauses : 1
% 0.09/0.27 % Non-unit-clauses : 2
% 0.09/0.27 % Current number of unprocessed clauses: 6
% 0.09/0.27 % ...number of literals in the above : 16
% 0.09/0.27 % Current number of archived formulas : 0
% 0.09/0.27 % Current number of archived clauses : 20
% 0.09/0.27 % Clause-clause subsumption calls (NU) : 32
% 0.09/0.27 % Rec. Clause-clause subsumption calls : 24
% 0.09/0.27 % Non-unit clause-clause subsumptions : 8
% 0.09/0.27 % Unit Clause-clause subsumption calls : 6
% 0.09/0.27 % Rewrite failures with RHS unbound : 0
% 0.09/0.27 % BW rewrite match attempts : 10
% 0.09/0.27 % BW rewrite match successes : 10
% 0.09/0.27 % Condensation attempts : 0
% 0.09/0.27 % Condensation successes : 0
% 0.09/0.27 % Termbank termtop insertions : 4107
% 0.09/0.27 % Search garbage collected termcells : 1004
% 0.09/0.27
% 0.09/0.27 % -------------------------------------------------
% 0.09/0.27 % User time : 0.006 s
% 0.09/0.27 % System time : 0.002 s
% 0.09/0.27 % Total time : 0.008 s
% 0.09/0.27 % Maximum resident set size: 3656 pages
% 0.09/0.27
% 0.09/0.27 % -------------------------------------------------
% 0.09/0.27 % User time : 0.007 s
% 0.09/0.27 % System time : 0.007 s
% 0.09/0.27 % Total time : 0.014 s
% 0.09/0.27 % Maximum resident set size: 4864 pages
% 0.09/0.27 % E exiting
%------------------------------------------------------------------------------