%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL956^18 : 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 : n020.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 0.23s 0.28s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 477 ( 10 equ; 0 cnn)
% Maximal formula atoms : 288 ( 9 avg)
% Number of connectives : 1487 ( 201 ~; 271 |; 77 &; 921 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 104 ( 30 ^; 68 !; 6 ?; 104 :)
% 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_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_35,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
p: mworld > $o ).
thf(decl_37,type,
big_q: $i > mworld > $o ).
thf(decl_39,type,
esk2_0: mworld ).
thf(decl_40,type,
esk3_0: $i ).
thf(decl_41,type,
esk4_0: mworld ).
thf(decl_42,type,
esk5_1: $i > mworld ).
thf(decl_43,type,
esk6_0: mworld ).
thf(decl_44,type,
esk7_0: $i ).
thf(decl_45,type,
esk8_1: $i > mworld ).
thf(decl_46,type,
esk9_1: $i > mworld ).
thf(x2109,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X6 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( big_q @ X6 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( big_q @ X6 ) ) ) )
@ ( mexists_di
@ ^ [X6: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Oi2DXruSYG/E---3.1_912707.p',x2109) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Oi2DXruSYG/E---3.1_912707.p',mlocal_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Oi2DXruSYG/E---3.1_912707.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.Oi2DXruSYG/E---3.1_912707.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.Oi2DXruSYG/E---3.1_912707.p',mbox_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.Oi2DXruSYG/E---3.1_912707.p',mexists_di_def) ).
thf(mrel_universal,axiom,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
file('/export/starexec/sandbox2/tmp/tmp.Oi2DXruSYG/E---3.1_912707.p',mrel_universal) ).
thf(eiw_di_cumul,axiom,
! [X3: mworld,X5: mworld,X6: $i] :
( ( ( eiw_di @ X6 @ X3 )
& ( mrel @ X3 @ X5 ) )
=> ( eiw_di @ X6 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Oi2DXruSYG/E---3.1_912707.p',eiw_di_cumul) ).
thf(c_0_8,negated_conjecture,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X6 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( big_q @ X6 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( big_q @ X6 ) ) ) )
@ ( mexists_di
@ ^ [X6: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X6 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2109]) ).
thf(c_0_9,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_10,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_12,plain,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_13,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_14,negated_conjecture,
~ ( ! [X22: mworld] :
( ( mrel @ mactual @ X22 )
=> ( ? [X18: $i] :
( ( eiw_di @ X18 @ X22 )
& ! [X16: mworld] :
( ( mrel @ X22 @ X16 )
=> ( p @ X16 ) )
& ! [X17: mworld] :
( ( mrel @ X22 @ X17 )
=> ( big_q @ X18 @ X17 ) ) )
=> ( ! [X19: mworld] :
( ( mrel @ X22 @ X19 )
=> ( p @ X19 ) )
& ? [X21: $i] :
( ( eiw_di @ X21 @ X22 )
& ! [X20: mworld] :
( ( mrel @ X22 @ X20 )
=> ( big_q @ X21 @ X20 ) ) ) ) ) )
& ! [X29: mworld] :
( ( mrel @ mactual @ X29 )
=> ( ( ! [X23: mworld] :
( ( mrel @ X29 @ X23 )
=> ( p @ X23 ) )
& ? [X25: $i] :
( ( eiw_di @ X25 @ X29 )
& ! [X24: mworld] :
( ( mrel @ X29 @ X24 )
=> ( big_q @ X25 @ X24 ) ) ) )
=> ? [X28: $i] :
( ( eiw_di @ X28 @ X29 )
& ! [X26: mworld] :
( ( mrel @ X29 @ X26 )
=> ( p @ X26 ) )
& ! [X27: mworld] :
( ( mrel @ X29 @ X27 )
=> ( big_q @ X28 @ X27 ) ) ) ) ) ),
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_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X39: mworld,X40: mworld,X42: $i,X45: mworld,X47: mworld,X48: $i] :
( ( ( mrel @ mactual @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ mactual @ esk2_0 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X39 )
| ( p @ X39 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( mrel @ esk2_0 @ X40 )
| ( big_q @ esk3_0 @ X40 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ( mrel @ esk2_0 @ esk4_0 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ( mrel @ esk2_0 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( mrel @ mactual @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X45 )
| ( p @ X45 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( mrel @ esk6_0 @ X47 )
| ( big_q @ esk7_0 @ X47 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ( mrel @ esk6_0 @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ( mrel @ esk6_0 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( big_q @ X48 @ ( esk9_1 @ X48 ) )
| ~ ( p @ ( esk8_1 @ X48 ) )
| ~ ( eiw_di @ X48 @ esk6_0 )
| ~ ( big_q @ X42 @ ( esk5_1 @ X42 ) )
| ~ ( eiw_di @ X42 @ esk2_0 )
| ~ ( p @ esk4_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_14])])])])])]) ).
thf(c_0_16,plain,
! [X30: mworld,X31: mworld] : ( mrel @ X30 @ X31 ),
inference(variable_rename,[status(thm)],[mrel_universal]) ).
thf(c_0_17,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( p @ X3 )
| ( p @ X5 )
| ~ ( mrel @ esk6_0 @ X3 )
| ~ ( mrel @ esk2_0 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X34: mworld,X35: mworld,X36: $i] :
( ~ ( eiw_di @ X36 @ X34 )
| ~ ( mrel @ X34 @ X35 )
| ( eiw_di @ X36 @ X35 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[eiw_di_cumul])])]) ).
thf(c_0_20,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( p @ X3 )
| ( p @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18])]) ).
thf(c_0_21,plain,
! [X3: mworld,X6: $i,X5: mworld] :
( ( eiw_di @ X6 @ X5 )
| ~ ( eiw_di @ X6 @ X3 )
| ~ ( mrel @ X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X6: $i] :
( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( big_q @ X6 @ ( esk5_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk2_0 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,negated_conjecture,
! [X3: mworld] : ( p @ X3 ),
inference(ef,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk7_0 @ esk6_0 )
| ( big_q @ esk3_0 @ X3 )
| ~ ( mrel @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_25,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_21,c_0_18])]) ).
thf(c_0_26,negated_conjecture,
( ( eiw_di @ esk7_0 @ esk6_0 )
| ( eiw_di @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_27,negated_conjecture,
! [X6: $i] :
( ( eiw_di @ esk7_0 @ esk6_0 )
| ~ ( big_q @ X6 @ ( esk5_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_28,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk7_0 @ esk6_0 )
| ( big_q @ esk3_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18])]) ).
thf(c_0_29,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk7_0 @ esk6_0 )
| ( eiw_di @ esk3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,negated_conjecture,
! [X6: $i] :
( ( eiw_di @ esk3_0 @ esk2_0 )
| ~ ( big_q @ X6 @ ( esk9_1 @ X6 ) )
| ~ ( p @ ( esk8_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_31,negated_conjecture,
! [X3: mworld] :
( ( big_q @ esk7_0 @ X3 )
| ( eiw_di @ esk3_0 @ esk2_0 )
| ~ ( mrel @ esk6_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_32,negated_conjecture,
eiw_di @ esk7_0 @ esk6_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X6: $i] :
( ( eiw_di @ esk3_0 @ esk2_0 )
| ~ ( big_q @ X6 @ ( esk9_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_23])]) ).
thf(c_0_34,negated_conjecture,
! [X3: mworld] :
( ( eiw_di @ esk3_0 @ esk2_0 )
| ( big_q @ esk7_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_18])]) ).
thf(c_0_35,negated_conjecture,
! [X3: mworld] : ( eiw_di @ esk7_0 @ X3 ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( big_q @ esk7_0 @ X3 )
| ~ ( mrel @ esk6_0 @ X3 )
| ~ ( big_q @ X6 @ ( esk5_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk2_0 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_37,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( big_q @ esk7_0 @ X3 )
| ( big_q @ esk3_0 @ X5 )
| ~ ( mrel @ esk6_0 @ X3 )
| ~ ( mrel @ esk2_0 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_38,negated_conjecture,
eiw_di @ esk3_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
thf(c_0_39,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( big_q @ esk7_0 @ X3 )
| ~ ( big_q @ X6 @ ( esk5_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_23]),c_0_18])]) ).
thf(c_0_40,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( big_q @ esk7_0 @ X3 )
| ( big_q @ esk3_0 @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_18]),c_0_18])]) ).
thf(c_0_41,negated_conjecture,
! [X3: mworld] : ( eiw_di @ esk3_0 @ X3 ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
thf(c_0_42,negated_conjecture,
! [X6: $i,X12: $i] :
( ~ ( big_q @ X6 @ ( esk9_1 @ X6 ) )
| ~ ( p @ ( esk8_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk6_0 )
| ~ ( big_q @ X12 @ ( esk5_1 @ X12 ) )
| ~ ( eiw_di @ X12 @ esk2_0 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_43,negated_conjecture,
! [X3: mworld,X5: mworld] :
( ( big_q @ esk7_0 @ X3 )
| ( big_q @ esk7_0 @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
thf(c_0_44,negated_conjecture,
! [X6: $i,X12: $i] :
( ~ ( big_q @ X6 @ ( esk5_1 @ X6 ) )
| ~ ( big_q @ X12 @ ( esk9_1 @ X12 ) )
| ~ ( eiw_di @ X6 @ esk2_0 )
| ~ ( eiw_di @ X12 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_23]),c_0_23])]) ).
thf(c_0_45,negated_conjecture,
! [X3: mworld] : ( big_q @ esk7_0 @ X3 ),
inference(ef,[status(thm)],[c_0_43]) ).
thf(c_0_46,negated_conjecture,
! [X6: $i] :
( ~ ( big_q @ X6 @ ( esk9_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_35])]) ).
thf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:58:19 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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.Oi2DXruSYG/E---3.1_912707.p
% 0.23/0.28 % Version: 3.5.1-ho
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.28 % post_as_ho1 with pid 912723 completed with status 0
% 0.23/0.28 % Result found by post_as_ho1
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.28 % No SInE strategy applied
% 0.23/0.28 % Search class: HGHNS-FFMS11-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNS-FFMF11-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.28 % SubtermCWHack with pid 912728 completed with status 0
% 0.23/0.28 % Result found by SubtermCWHack
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.28 % No SInE strategy applied
% 0.23/0.28 % Search class: HGHNS-FFMS11-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNS-FFMF11-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.28 % Preprocessing time : 0.001 s
% 0.23/0.28
% 0.23/0.28 % Proof found!
% 0.23/0.28 % SZS status Theorem
% 0.23/0.28 % SZS output start CNFRefutation
% See solution above
% 0.23/0.28 % Parsed axioms : 30
% 0.23/0.28 % Removed by relevancy pruning/SinE : 0
% 0.23/0.28 % Initial clauses : 83
% 0.23/0.28 % Removed in clause preprocessing : 16
% 0.23/0.28 % Initial clauses in saturation : 67
% 0.23/0.28 % Processed clauses : 69
% 0.23/0.28 % ...of these trivial : 41
% 0.23/0.28 % ...subsumed : 2
% 0.23/0.28 % ...remaining for further processing : 26
% 0.23/0.28 % Other redundant clauses eliminated : 0
% 0.23/0.28 % Clauses deleted for lack of memory : 0
% 0.23/0.28 % Backward-subsumed : 7
% 0.23/0.28 % Backward-rewritten : 10
% 0.23/0.28 % Generated clauses : 28
% 0.23/0.28 % ...of the previous two non-redundant : 23
% 0.23/0.28 % ...aggressively subsumed : 0
% 0.23/0.28 % Contextual simplify-reflections : 1
% 0.23/0.28 % Paramodulations : 24
% 0.23/0.28 % Factorizations : 4
% 0.23/0.28 % NegExts : 0
% 0.23/0.28 % Equation resolutions : 0
% 0.23/0.28 % Disequality decompositions : 0
% 0.23/0.28 % Total rewrite steps : 154
% 0.23/0.28 % ...of those cached : 127
% 0.23/0.28 % Propositional unsat checks : 0
% 0.23/0.28 % Propositional check models : 0
% 0.23/0.28 % Propositional check unsatisfiable : 0
% 0.23/0.28 % Propositional clauses : 0
% 0.23/0.28 % Propositional clauses after purity: 0
% 0.23/0.28 % Propositional unsat core size : 0
% 0.23/0.28 % Propositional preprocessing time : 0.000
% 0.23/0.28 % Propositional encoding time : 0.000
% 0.23/0.28 % Propositional solver time : 0.000
% 0.23/0.28 % Success case prop preproc time : 0.000
% 0.23/0.28 % Success case prop encoding time : 0.000
% 0.23/0.28 % Success case prop solver time : 0.000
% 0.23/0.28 % Current number of processed clauses : 9
% 0.23/0.28 % Positive orientable unit clauses : 7
% 0.23/0.28 % Positive unorientable unit clauses: 0
% 0.23/0.28 % Negative unit clauses : 0
% 0.23/0.28 % Non-unit-clauses : 2
% 0.23/0.28 % Current number of unprocessed clauses: 12
% 0.23/0.28 % ...number of literals in the above : 68
% 0.23/0.28 % Current number of archived formulas : 0
% 0.23/0.28 % Current number of archived clauses : 17
% 0.23/0.28 % Clause-clause subsumption calls (NU) : 16
% 0.23/0.28 % Rec. Clause-clause subsumption calls : 16
% 0.23/0.28 % Non-unit clause-clause subsumptions : 5
% 0.23/0.28 % Unit Clause-clause subsumption calls : 13
% 0.23/0.28 % Rewrite failures with RHS unbound : 0
% 0.23/0.28 % BW rewrite match attempts : 10
% 0.23/0.28 % BW rewrite match successes : 10
% 0.23/0.28 % Condensation attempts : 0
% 0.23/0.28 % Condensation successes : 0
% 0.23/0.28 % Termbank termtop insertions : 4711
% 0.23/0.28 % Search garbage collected termcells : 965
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.008 s
% 0.23/0.28 % System time : 0.000 s
% 0.23/0.28 % Total time : 0.008 s
% 0.23/0.28 % Maximum resident set size: 3656 pages
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.010 s
% 0.23/0.28 % System time : 0.005 s
% 0.23/0.28 % Total time : 0.014 s
% 0.23/0.28 % Maximum resident set size: 4864 pages
% 0.23/0.28 % E exiting
%------------------------------------------------------------------------------