%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL717^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:12:05 AM UTC 2026
% Result : Theorem 0.32s 0.34s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 62 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 631 ( 114 ~; 111 |; 11 &; 389 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 138 ( 68 ^; 70 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_48,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
epred1_0: $i > $i > $o ).
thf(decl_55,type,
esk1_4: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_56,type,
esk2_4: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_57,type,
esk3_0: $i ).
thf(decl_58,type,
esk4_0: $i ).
thf(decl_59,type,
esk5_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mor) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mand) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mor @ ( mbox @ X13 @ ( mimplies @ ( mand @ X18 @ ( mbox @ X13 @ X18 ) ) @ X19 ) ) @ ( mbox @ X13 @ ( mimplies @ ( mand @ X19 @ ( mbox @ X13 @ X19 ) ) @ X18 ) ) ) ) ) )
=> ( mweakly_connected @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',conj) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mbox) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mvalid) ).
thf(mweakly_connected,axiom,
( mweakly_connected
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X15 @ X17 ) )
=> ( ( X13 @ X16 @ X17 )
| ( X16 = X17 )
| ( X13 @ X17 @ X16 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p',mweakly_connected) ).
thf(c_0_9,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_11,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mor @ ( mbox @ X13 @ ( mimplies @ ( mand @ X18 @ ( mbox @ X13 @ X18 ) ) @ X19 ) ) @ ( mbox @ X13 @ ( mimplies @ ( mand @ X19 @ ( mbox @ X13 @ X19 ) ) @ X18 ) ) ) ) ) )
=> ( mweakly_connected @ X13 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_14,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_15,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_9,c_0_10]),c_0_11]) ).
thf(c_0_16,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_12,c_0_10]),c_0_11]) ).
thf(c_0_17,plain,
( mforall_prop
= ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_prop]) ).
thf(c_0_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,plain,
( mweakly_connected
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X15 @ X17 ) )
=> ( ( Z0 @ X16 @ X17 )
| ( X16 = X17 )
| ( Z0 @ X17 @ X16 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mweakly_connected]) ).
thf(c_0_20,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ! [X29: $i,X28: $i > $o,X27: $i > $o] :
( ! [X24: $i] :
( ~ ( X13 @ X29 @ X24 )
| ~ ~ ( ~ ( X28 @ X24 )
| ~ ! [X23: $i] :
( ~ ( X13 @ X24 @ X23 )
| ( X28 @ X23 ) ) )
| ( X27 @ X24 ) )
| ! [X26: $i] :
( ~ ( X13 @ X29 @ X26 )
| ~ ~ ( ~ ( X27 @ X26 )
| ~ ! [X25: $i] :
( ~ ( X13 @ X26 @ X25 )
| ( X27 @ X25 ) ) )
| ( X28 @ X26 ) ) )
=> ! [X30: $i,X31: $i,X32: $i] :
( ( ( X13 @ X30 @ X31 )
& ( X13 @ X30 @ X32 ) )
=> ( ( X13 @ X31 @ X32 )
| ( X31 = X32 )
| ( X13 @ X32 @ X31 ) ) ) ),
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_13]),c_0_14]),c_0_15]),c_0_16]),c_0_11]),c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X34: $i,X35: $i > $o,X36: $i > $o,X37: $i,X39: $i] :
( ( ( epred1_0 @ X39 @ ( esk2_4 @ X34 @ X35 @ X36 @ X39 ) )
| ~ ( X36 @ X39 )
| ( X35 @ X39 )
| ~ ( epred1_0 @ X34 @ X39 )
| ( epred1_0 @ X37 @ ( esk1_4 @ X34 @ X35 @ X36 @ X37 ) )
| ~ ( X35 @ X37 )
| ( X36 @ X37 )
| ~ ( epred1_0 @ X34 @ X37 ) )
& ( ~ ( X36 @ ( esk2_4 @ X34 @ X35 @ X36 @ X39 ) )
| ~ ( X36 @ X39 )
| ( X35 @ X39 )
| ~ ( epred1_0 @ X34 @ X39 )
| ( epred1_0 @ X37 @ ( esk1_4 @ X34 @ X35 @ X36 @ X37 ) )
| ~ ( X35 @ X37 )
| ( X36 @ X37 )
| ~ ( epred1_0 @ X34 @ X37 ) )
& ( ( epred1_0 @ X39 @ ( esk2_4 @ X34 @ X35 @ X36 @ X39 ) )
| ~ ( X36 @ X39 )
| ( X35 @ X39 )
| ~ ( epred1_0 @ X34 @ X39 )
| ~ ( X35 @ ( esk1_4 @ X34 @ X35 @ X36 @ X37 ) )
| ~ ( X35 @ X37 )
| ( X36 @ X37 )
| ~ ( epred1_0 @ X34 @ X37 ) )
& ( ~ ( X36 @ ( esk2_4 @ X34 @ X35 @ X36 @ X39 ) )
| ~ ( X36 @ X39 )
| ( X35 @ X39 )
| ~ ( epred1_0 @ X34 @ X39 )
| ~ ( X35 @ ( esk1_4 @ X34 @ X35 @ X36 @ X37 ) )
| ~ ( X35 @ X37 )
| ( X36 @ X37 )
| ~ ( epred1_0 @ X34 @ X37 ) )
& ( epred1_0 @ esk3_0 @ esk4_0 )
& ( epred1_0 @ esk3_0 @ esk5_0 )
& ~ ( epred1_0 @ esk4_0 @ esk5_0 )
& ( esk4_0 != esk5_0 )
& ~ ( epred1_0 @ esk5_0 @ 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_20])])])])])]) ).
thf(c_0_22,negated_conjecture,
! [X14: $i,X4: $i > $o,X5: $i > $o,X3: $i,X15: $i] :
( ( X5 @ X14 )
| ( X4 @ X15 )
| ~ ( X4 @ ( esk2_4 @ X3 @ X5 @ X4 @ X14 ) )
| ~ ( X4 @ X14 )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( X5 @ ( esk1_4 @ X3 @ X5 @ X4 @ X15 ) )
| ~ ( X5 @ X15 )
| ~ ( epred1_0 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X15: $i,X4: $i > $o,X3: $i,X14: $i] :
( ( ( esk1_4 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X4
@ X15 )
= X14 )
| ( X15 = X14 )
| ( X4 @ X15 )
| ~ ( X4
@ ( esk2_4 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X4
@ X14 ) )
| ~ ( epred1_0 @ X3 @ X15 )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( X4 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_22]) ).
thf(c_0_24,negated_conjecture,
! [X15: $i,X3: $i,X14: $i] :
( ( ( esk2_4 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 )
@ ^ [Z0: $i] : ( Z0 != X15 )
@ X14 )
= X15 )
| ( ( esk1_4 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 )
@ ^ [Z0: $i] : ( Z0 != X15 )
@ X15 )
= X14 )
| ( X15 = X14 )
| ~ ( epred1_0 @ X3 @ X15 )
| ~ ( epred1_0 @ X3 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_23]) ).
thf(c_0_25,negated_conjecture,
epred1_0 @ esk3_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i,X5: $i > $o,X4: $i > $o,X14: $i,X15: $i] :
( ( epred1_0 @ X3 @ ( esk2_4 @ X14 @ X4 @ X5 @ X3 ) )
| ( X4 @ X3 )
| ( X5 @ X15 )
| ~ ( X5 @ X3 )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( X4 @ ( esk1_4 @ X14 @ X4 @ X5 @ X15 ) )
| ~ ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
( ( ( esk1_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != X3 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ esk5_0 )
= X3 )
| ( ( esk2_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != X3 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ X3 )
= esk5_0 )
| ( esk5_0 = X3 )
| ~ ( epred1_0 @ esk3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
epred1_0 @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,negated_conjecture,
! [X14: $i,X4: $i > $o,X5: $i > $o,X3: $i,X15: $i] :
( ( X5 @ X14 )
| ( epred1_0 @ X15 @ ( esk1_4 @ X3 @ X5 @ X4 @ X15 ) )
| ( X4 @ X15 )
| ~ ( X4 @ ( esk2_4 @ X3 @ X5 @ X4 @ X14 ) )
| ~ ( X4 @ X14 )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( X5 @ X15 )
| ~ ( epred1_0 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,negated_conjecture,
! [X15: $i,X4: $i > $o,X3: $i,X14: $i] :
( ( X3 = X14 )
| ( epred1_0 @ X3
@ ( esk2_4 @ X15 @ X4
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X3 ) )
| ( X4 @ X3 )
| ~ ( X4
@ ( esk1_4 @ X15 @ X4
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X14 ) )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( X4 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_26]) ).
thf(c_0_32,negated_conjecture,
( ( ( esk2_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ esk4_0 )
= esk5_0 )
| ( ( esk1_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ esk5_0 )
= esk4_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_33,negated_conjecture,
~ ( epred1_0 @ esk4_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_34,negated_conjecture,
! [X5: $i > $o,X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( epred1_0 @ X3 @ ( esk2_4 @ X14 @ X4 @ X5 @ X3 ) )
| ( X4 @ X3 )
| ( epred1_0 @ X15 @ ( esk1_4 @ X14 @ X4 @ X5 @ X15 ) )
| ( X5 @ X15 )
| ~ ( X5 @ X3 )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_35,negated_conjecture,
! [X15: $i,X4: $i > $o,X3: $i,X14: $i] :
( ( X3 = X14 )
| ( epred1_0 @ X3
@ ( esk1_4 @ X15
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X4
@ X3 ) )
| ( X4 @ X3 )
| ~ ( X4
@ ( esk2_4 @ X15
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X4
@ X14 ) )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( X4 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_30]) ).
thf(c_0_36,negated_conjecture,
( ( esk1_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ esk5_0 )
= esk4_0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32])])]),c_0_25]),c_0_28])]),c_0_29]),c_0_33]) ).
thf(c_0_37,negated_conjecture,
~ ( epred1_0 @ esk5_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_38,negated_conjecture,
! [X15: $i,X4: $i > $o,X3: $i,X14: $i] :
( ( X3 = X14 )
| ( epred1_0 @ X3
@ ( esk2_4 @ X15 @ X4
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X3 ) )
| ( epred1_0 @ X14
@ ( esk1_4 @ X15 @ X4
@ ^ [Z0: $i] : ( Z0 != X14 )
@ X14 ) )
| ( X4 @ X3 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( X4 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_34]) ).
thf(c_0_39,negated_conjecture,
( ( esk2_4 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 )
@ ^ [Z0: $i] : ( Z0 != esk5_0 )
@ esk4_0 )
= esk5_0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36])])]),c_0_25]),c_0_28])]),c_0_29]),c_0_37]) ).
thf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39])])]),c_0_36]),c_0_25]),c_0_28])]),c_0_29]),c_0_33]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL717^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n013.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 09:53:06 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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/tmp/tmp.XYgcBUOxud/E---3.1_1885403.p
% 0.32/0.34 % Version: 3.5.1-ho
% 0.32/0.34 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.32/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.34 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.32/0.34 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.32/0.34 % Starting sh5l with 300s (1) cores
% 0.32/0.34 % Starting ho_unfolding_6 with 300s (1) cores
% 0.32/0.34 % lpo9_lambda_fix with pid 1885417 completed with status 0
% 0.32/0.34 % Result found by lpo9_lambda_fix
% 0.32/0.34 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.32/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.34 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.32/0.34 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.32/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.32/0.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.32/0.34 % Search class: HGUSF-FFSF33-SHHSMSBN
% 0.32/0.34 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 0.32/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.32/0.34 % SubtermCWHack with pid 1885420 completed with status 10
% 0.32/0.34 % Starting lpo9_lambda_fix with 31s (1) cores
% 0.32/0.34 % lpo9_lambda_fix with pid 1885428 completed with status 0
% 0.32/0.34 % Result found by lpo9_lambda_fix
% 0.32/0.34 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.32/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.34 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.32/0.34 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.32/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.32/0.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.32/0.34 % Search class: HGUSF-FFSF33-SHHSMSBN
% 0.32/0.34 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 0.32/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.32/0.34 % SubtermCWHack with pid 1885420 completed with status 10
% 0.32/0.34 % Starting lpo9_lambda_fix with 31s (1) cores
% 0.32/0.34 % Preprocessing time : 0.002 s
% 0.32/0.34 % Presaturation interreduction done
% 0.32/0.34
% 0.32/0.34 % Proof found!
% 0.32/0.34 % SZS status Theorem
% 0.32/0.34 % SZS output start CNFRefutation
% See solution above
% 0.32/0.35 % Parsed axioms : 64
% 0.32/0.35 % Removed by relevancy pruning/SinE : 50
% 0.32/0.35 % Initial clauses : 9
% 0.32/0.35 % Removed in clause preprocessing : 0
% 0.32/0.35 % Initial clauses in saturation : 9
% 0.32/0.35 % Processed clauses : 164
% 0.32/0.35 % ...of these trivial : 0
% 0.32/0.35 % ...subsumed : 29
% 0.32/0.35 % ...remaining for further processing : 135
% 0.32/0.35 % Other redundant clauses eliminated : 263
% 0.32/0.35 % Clauses deleted for lack of memory : 0
% 0.32/0.35 % Backward-subsumed : 2
% 0.32/0.35 % Backward-rewritten : 1
% 0.32/0.35 % Generated clauses : 653
% 0.32/0.35 % ...of the previous two non-redundant : 253
% 0.32/0.35 % ...aggressively subsumed : 0
% 0.32/0.35 % Contextual simplify-reflections : 0
% 0.32/0.35 % Paramodulations : 148
% 0.32/0.35 % Factorizations : 85
% 0.32/0.35 % NegExts : 9
% 0.32/0.35 % Equation resolutions : 263
% 0.32/0.35 % Disequality decompositions : 0
% 0.32/0.35 % Total rewrite steps : 172
% 0.32/0.35 % ...of those cached : 169
% 0.32/0.35 % Propositional unsat checks : 0
% 0.32/0.35 % Propositional check models : 0
% 0.32/0.35 % Propositional check unsatisfiable : 0
% 0.32/0.35 % Propositional clauses : 0
% 0.32/0.35 % Propositional clauses after purity: 0
% 0.32/0.35 % Propositional unsat core size : 0
% 0.32/0.35 % Propositional preprocessing time : 0.000
% 0.32/0.35 % Propositional encoding time : 0.000
% 0.32/0.35 % Propositional solver time : 0.000
% 0.32/0.35 % Success case prop preproc time : 0.000
% 0.32/0.35 % Success case prop encoding time : 0.000
% 0.32/0.35 % Success case prop solver time : 0.000
% 0.32/0.35 % Current number of processed clauses : 121
% 0.32/0.35 % Positive orientable unit clauses : 4
% 0.32/0.35 % Positive unorientable unit clauses: 0
% 0.32/0.35 % Negative unit clauses : 3
% 0.32/0.35 % Non-unit-clauses : 114
% 0.32/0.35 % Current number of unprocessed clauses: 105
% 0.32/0.35 % ...number of literals in the above : 990
% 0.32/0.35 % Current number of archived formulas : 0
% 0.32/0.35 % Current number of archived clauses : 14
% 0.32/0.35 % Clause-clause subsumption calls (NU) : 513
% 0.32/0.35 % Rec. Clause-clause subsumption calls : 48
% 0.32/0.35 % Non-unit clause-clause subsumptions : 31
% 0.32/0.35 % Unit Clause-clause subsumption calls : 2
% 0.32/0.35 % Rewrite failures with RHS unbound : 0
% 0.32/0.35 % BW rewrite match attempts : 10
% 0.32/0.35 % BW rewrite match successes : 1
% 0.32/0.35 % Condensation attempts : 0
% 0.32/0.35 % Condensation successes : 0
% 0.32/0.35 % Termbank termtop insertions : 42022
% 0.32/0.35 % Search garbage collected termcells : 1073
% 0.32/0.35
% 0.32/0.35 % -------------------------------------------------
% 0.32/0.35 % User time : 0.056 s
% 0.32/0.35 % System time : 0.006 s
% 0.32/0.35 % Total time : 0.062 s
% 0.32/0.35 % Maximum resident set size: 3952 pages
% 0.32/0.35
% 0.32/0.35 % -------------------------------------------------
% 0.32/0.35 % User time : 0.059 s
% 0.32/0.35 % System time : 0.010 s
% 0.32/0.35 % Total time : 0.069 s
% 0.32/0.35 % Maximum resident set size: 4864 pages
% 0.32/0.35 % E exiting
%------------------------------------------------------------------------------