%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PHI007^5 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:20:11 AM UTC 2026
% Result : ContradictoryAxioms 0.23s 0.32s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 9 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 550 ( 70 ~; 54 |; 12 &; 392 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 4 con; 0-5 aty)
% Number of variables : 179 ( 53 ^; 124 !; 2 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
qML_mu: $tType ).
thf(decl_sort2,type,
qML_i: $tType ).
thf(decl_23,type,
inconsistency_G: qML_mu > qML_i > $o ).
thf(decl_24,type,
incons1905966852QML_mu: qML_mu > qML_i > $o ).
thf(decl_25,type,
inconsistency_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(decl_26,type,
incons1389517216QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(decl_27,type,
qML_r: qML_i > qML_i > $o ).
thf(decl_28,type,
esk1_3: qML_i > ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf(decl_29,type,
esk2_3: qML_i > ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(decl_30,type,
epred1_2: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_31,type,
esk3_4: qML_mu > qML_i > ( qML_mu > qML_i > $o ) > qML_i > qML_mu ).
thf(decl_32,type,
epred2_2: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_33,type,
esk4_2: qML_mu > qML_i > qML_i ).
thf(decl_34,type,
epred3_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_35,type,
esk5_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_i ).
thf(decl_36,type,
esk6_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu ).
thf(decl_104,type,
esk71_1: ( qML_mu > qML_i > $o ) > qML_mu ).
thf(decl_105,type,
esk72_1: ( qML_mu > qML_i > $o ) > qML_i ).
thf(decl_151,type,
esk118_0: qML_mu ).
thf(decl_152,type,
esk119_0: qML_i ).
thf(fact_0_A1a,axiom,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ( inconsistency_P
@ ^ [X3: qML_mu,X4: qML_i] :
~ ( X2 @ X3 @ X4 )
@ X1 )
=> ~ ( inconsistency_P @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_0_A1a) ).
thf(fact_2_A2,axiom,
! [X1: qML_i,X2: qML_mu > qML_i > $o,X5: qML_mu > qML_i > $o] :
( ( ( inconsistency_P @ X2 @ X1 )
& ! [X6: qML_i] :
( ( qML_r @ X1 @ X6 )
=> ! [X7: qML_mu] :
( ( X2 @ X7 @ X6 )
=> ( X5 @ X7 @ X6 ) ) ) )
=> ( inconsistency_P @ X5 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_2_A2) ).
thf(fact_1_A1b,axiom,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( inconsistency_P @ X2 @ X1 )
=> ( inconsistency_P
@ ^ [X3: qML_mu,X4: qML_i] :
~ ( X2 @ X3 @ X4 )
@ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_1_A1b) ).
thf(fact_5_A5,axiom,
! [X8: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ X8 ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_5_A5) ).
thf(fact_8_ess__def,axiom,
( incons1389517216QML_mu
= ( ^ [X16: qML_mu > qML_i > $o,X10: qML_mu,X11: qML_i] :
! [X17: qML_mu > qML_i > $o] :
( ( X17 @ X10 @ X11 )
=> ! [X14: qML_i] :
( ( qML_r @ X11 @ X14 )
=> ! [X18: qML_mu] :
( ( X16 @ X18 @ X14 )
=> ( X17 @ X18 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_8_ess__def) ).
thf(fact_3_A3,axiom,
! [X8: qML_i] : ( inconsistency_P @ inconsistency_G @ X8 ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_3_A3) ).
thf(fact_6_G__def,axiom,
( inconsistency_G
= ( ^ [X10: qML_mu,X11: qML_i] :
! [X12: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X12 @ X11 )
=> ( X12 @ X10 @ X11 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_6_G__def) ).
thf(fact_7_NE__def,axiom,
( incons1905966852QML_mu
= ( ^ [X10: qML_mu,X11: qML_i] :
! [X13: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ X13 @ X10 @ X11 )
=> ! [X14: qML_i] :
( ( qML_r @ X11 @ X14 )
=> ? [X15: qML_mu] : ( X13 @ X15 @ X14 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V370zp7NvY/E---3.1_1258747.p',fact_7_NE__def) ).
thf(c_0_8,plain,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 )
@ X1 )
=> ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_0_A1a])]) ).
thf(c_0_9,plain,
! [X44: qML_i,X45: qML_mu > qML_i > $o,X46: qML_mu > qML_i > $o] :
( ( ( qML_r @ X44 @ ( esk1_3 @ X44 @ X45 @ X46 ) )
| ~ ( inconsistency_P @ X45 @ X44 )
| ( inconsistency_P @ X46 @ X44 ) )
& ( ( X45 @ ( esk2_3 @ X44 @ X45 @ X46 ) @ ( esk1_3 @ X44 @ X45 @ X46 ) )
| ~ ( inconsistency_P @ X45 @ X44 )
| ( inconsistency_P @ X46 @ X44 ) )
& ( ~ ( X46 @ ( esk2_3 @ X44 @ X45 @ X46 ) @ ( esk1_3 @ X44 @ X45 @ X46 ) )
| ~ ( inconsistency_P @ X45 @ X44 )
| ( inconsistency_P @ X46 @ X44 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_A2])])])])]) ).
thf(c_0_10,plain,
! [X40: qML_i,X41: qML_mu > qML_i > $o] :
( ~ ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X41 @ Z0 @ Z1 )
@ X40 )
| ~ ( inconsistency_P @ X41 @ X40 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_11,plain,
! [X5: qML_mu > qML_i > $o,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P @ X2 @ X1 )
| ~ ( X2 @ ( esk2_3 @ X1 @ X5 @ X2 ) @ ( esk1_3 @ X1 @ X5 @ X2 ) )
| ~ ( inconsistency_P @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( inconsistency_P @ X2 @ X1 )
=> ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 )
@ X1 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_1_A1b])]) ).
thf(c_0_13,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ~ ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 )
@ X1 )
| ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] : $true
@ X1 )
| ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X42: qML_i,X43: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X43 @ X42 )
| ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X43 @ Z0 @ Z1 )
@ X42 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
thf(c_0_16,plain,
! [X5: qML_mu > qML_i > $o,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 ) )
!= ( ^ [Z0: qML_mu,Z1: qML_i] : $true ) )
| ~ ( inconsistency_P @ X2 @ X1 )
| ~ ( inconsistency_P @ X5 @ X1 ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_17,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P @ X2 @ X1 )
| ( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 )
@ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X53: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ X53 ),
inference(variable_rename,[status(thm)],[fact_5_A5]) ).
thf(c_0_19,plain,
! [X5: qML_mu > qML_i > $o,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P @ X2 @ X1 )
| ( ( ^ [Z0: qML_mu,Z1: qML_i] : ( X2 @ Z0 @ Z1 ) )
!= ( ^ [Z0: qML_mu,Z1: qML_i] : $true ) )
| ~ ( inconsistency_P @ X5 @ X1 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_20,plain,
! [X1: qML_i] : ( inconsistency_P @ incons1905966852QML_mu @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
! [X37: qML_mu > qML_i > $o,X38: qML_mu,X39: qML_i] :
( ( incons1389517216QML_mu @ X37 @ X38 @ X39 )
<=> ! [X17: qML_mu > qML_i > $o] :
( ( X17 @ X38 @ X39 )
=> ! [X14: qML_i] :
( ( qML_r @ X39 @ X14 )
=> ! [X18: qML_mu] :
( ( X37 @ X18 @ X14 )
=> ( X17 @ X18 @ X14 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_8_ess__def])]) ).
thf(c_0_22,plain,
! [X5: qML_mu > qML_i > $o,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P @ X2 @ X1 )
| ( ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X5 @ Z0 @ Z1 ) )
!= ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 ) ) )
| ~ ( inconsistency_P @ X5 @ X1 ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_13,c_0_17])]) ).
thf(c_0_23,plain,
! [X1: qML_i] :
( inconsistency_P
@ ^ [Z0: qML_mu,Z1: qML_i] : $true
@ X1 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_24,plain,
! [X70: qML_mu > qML_i > $o,X71: qML_mu,X72: qML_i,X73: qML_mu > qML_i > $o,X74: qML_i,X75: qML_mu,X76: qML_mu > qML_i > $o,X77: qML_mu,X78: qML_i] :
( ( ~ ( incons1389517216QML_mu @ X70 @ X71 @ X72 )
| ~ ( X73 @ X71 @ X72 )
| ~ ( qML_r @ X72 @ X74 )
| ~ ( X70 @ X75 @ X74 )
| ( X73 @ X75 @ X74 ) )
& ( ( epred3_3 @ X76 @ X77 @ X78 @ X77 @ X78 )
| ( incons1389517216QML_mu @ X76 @ X77 @ X78 ) )
& ( ( qML_r @ X78 @ ( esk5_3 @ X76 @ X77 @ X78 ) )
| ( incons1389517216QML_mu @ X76 @ X77 @ X78 ) )
& ( ( X76 @ ( esk6_3 @ X76 @ X77 @ X78 ) @ ( esk5_3 @ X76 @ X77 @ X78 ) )
| ( incons1389517216QML_mu @ X76 @ X77 @ X78 ) )
& ( ~ ( epred3_3 @ X76 @ X77 @ X78 @ ( esk6_3 @ X76 @ X77 @ X78 ) @ ( esk5_3 @ X76 @ X77 @ X78 ) )
| ( incons1389517216QML_mu @ X76 @ X77 @ X78 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])])]) ).
thf(c_0_25,plain,
! [X49: qML_i] : ( inconsistency_P @ inconsistency_G @ X49 ),
inference(variable_rename,[status(thm)],[fact_3_A3]) ).
thf(c_0_26,plain,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X2 @ X1 )
| ( ( ^ [Z0: qML_mu,Z1: qML_i] : ~ $true )
!= ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 ) ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_27,plain,
! [X3: qML_mu,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( X2 @ ( esk6_3 @ X2 @ X3 @ X1 ) @ ( esk5_3 @ X2 @ X3 @ X1 ) )
| ( incons1389517216QML_mu @ X2 @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,plain,
! [X33: qML_mu,X34: qML_i] :
( ( inconsistency_G @ X33 @ X34 )
<=> ! [X12: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X12 @ X34 )
=> ( X12 @ X33 @ X34 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_6_G__def])]) ).
thf(c_0_29,plain,
! [X1: qML_i] : ( inconsistency_P @ inconsistency_G @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,plain,
! [X1: qML_i,X2: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X2 @ X1 )
| ~ ( X2 @ ( esk71_1 @ X2 ) @ ( esk72_1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_26])]) ).
thf(c_0_31,plain,
! [X3: qML_mu,X1: qML_i] :
( incons1389517216QML_mu
@ ^ [Z0: qML_mu,Z1: qML_i] : ~ $true
@ X3
@ X1 ),
inference(primitive_enumeration,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
! [X35: qML_mu,X36: qML_i] :
( ( incons1905966852QML_mu @ X35 @ X36 )
<=> ! [X13: qML_mu > qML_i > $o] :
( ( incons1389517216QML_mu @ X13 @ X35 @ X36 )
=> ! [X14: qML_i] :
( ( qML_r @ X36 @ X14 )
=> ? [X15: qML_mu] : ( X13 @ X15 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_7_NE__def])]) ).
thf(c_0_33,plain,
! [X54: qML_mu,X55: qML_i,X56: qML_mu > qML_i > $o,X57: qML_mu,X58: qML_i] :
( ( ~ ( inconsistency_G @ X54 @ X55 )
| ~ ( inconsistency_P @ X56 @ X55 )
| ( X56 @ X54 @ X55 ) )
& ( ( inconsistency_P @ ( epred1_2 @ X57 @ X58 ) @ X58 )
| ( inconsistency_G @ X57 @ X58 ) )
& ( ~ ( epred1_2 @ X57 @ X58 @ X57 @ X58 )
| ( inconsistency_G @ X57 @ X58 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])])]) ).
thf(c_0_34,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X2 @ Z0 @ Z1 ) )
!= inconsistency_G )
| ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_13,c_0_29])]) ).
thf(c_0_35,plain,
! [X1: qML_i] :
( inconsistency_P
@ ( incons1389517216QML_mu
@ ^ [Z0: qML_mu,Z1: qML_i] : ~ $true )
@ X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,plain,
! [X60: qML_mu,X61: qML_i,X62: qML_mu > qML_i > $o,X63: qML_i,X65: qML_mu,X66: qML_i,X69: qML_mu] :
( ( ~ ( incons1905966852QML_mu @ X60 @ X61 )
| ~ ( incons1389517216QML_mu @ X62 @ X60 @ X61 )
| ~ ( qML_r @ X61 @ X63 )
| ( X62 @ ( esk3_4 @ X60 @ X61 @ X62 @ X63 ) @ X63 ) )
& ( ( incons1389517216QML_mu @ ( epred2_2 @ X65 @ X66 ) @ X65 @ X66 )
| ( incons1905966852QML_mu @ X65 @ X66 ) )
& ( ( qML_r @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ( incons1905966852QML_mu @ X65 @ X66 ) )
& ( ~ ( epred2_2 @ X65 @ X66 @ X69 @ ( esk4_2 @ X65 @ X66 ) )
| ( incons1905966852QML_mu @ X65 @ X66 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])])]) ).
thf(c_0_37,plain,
! [X3: qML_mu,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( X2 @ X3 @ X1 )
| ~ ( inconsistency_G @ X3 @ X1 )
| ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_38,plain,
( ( ^ [Z0: qML_mu,Z1: qML_i] :
~ ( incons1389517216QML_mu
@ ^ [Z2: qML_mu,Z3: qML_i] : ~ $true
@ Z0
@ Z1 ) )
!= inconsistency_G ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,plain,
! [X1: qML_i,X3: qML_mu,X2: qML_mu > qML_i > $o,X4: qML_i] :
( ( X2 @ ( esk3_4 @ X3 @ X1 @ X2 @ X4 ) @ X4 )
| ~ ( incons1905966852QML_mu @ X3 @ X1 )
| ~ ( incons1389517216QML_mu @ X2 @ X3 @ X1 )
| ~ ( qML_r @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_40,plain,
! [X3: qML_mu,X1: qML_i] :
( ( incons1905966852QML_mu @ X3 @ X1 )
| ~ ( inconsistency_G @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
thf(c_0_41,plain,
inconsistency_G @ esk118_0 @ esk119_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_38]),c_0_31])]) ).
thf(c_0_42,plain,
! [X1: qML_i,X3: qML_mu,X4: qML_i] :
( ~ ( incons1905966852QML_mu @ X3 @ X1 )
| ~ ( qML_r @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
thf(c_0_43,plain,
incons1905966852QML_mu @ esk118_0 @ esk119_0,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,plain,
! [X3: qML_mu,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( inconsistency_P @ X2 @ X1 )
| ~ ( inconsistency_G @ X3 @ X1 )
| ~ ( X2 @ X3 @ X1 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_17])]) ).
thf(c_0_45,plain,
! [X1: qML_i] :
~ ( qML_r @ esk119_0 @ X1 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,plain,
! [X3: qML_mu,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( qML_r @ X1 @ ( esk5_3 @ X2 @ X3 @ X1 ) )
| ( incons1389517216QML_mu @ X2 @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_47,plain,
! [X2: qML_mu > qML_i > $o] :
( ( inconsistency_P @ X2 @ esk119_0 )
| ~ ( X2 @ esk118_0 @ esk119_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
thf(c_0_48,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu] : ( incons1389517216QML_mu @ X2 @ X3 @ esk119_0 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_49,plain,
! [X5: qML_mu > qML_i > $o,X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( qML_r @ X1 @ ( esk1_3 @ X1 @ X2 @ X5 ) )
| ( inconsistency_P @ X5 @ X1 )
| ~ ( inconsistency_P @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_50,plain,
! [X2: qML_mu > qML_i > $o] : ( inconsistency_P @ ( incons1389517216QML_mu @ X2 ) @ esk119_0 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_51,plain,
! [X2: qML_mu > qML_i > $o] : ( inconsistency_P @ X2 @ esk119_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]) ).
thf(c_0_52,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_51]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI007^5 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.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 13:19:36 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
% 0.09/0.25 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.V370zp7NvY/E---3.1_1258747.p
% 0.23/0.32 % Version: 3.5.1-ho
% 0.23/0.32 % Preprocessing class: HSMSSMSSSSMNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting ehoh_best_nonlift with 1500s (5) cores
% 0.23/0.32 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.23/0.32 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.23/0.32 % Starting ehoh_best3_fo with 300s (1) cores
% 0.23/0.32 % ehoh_best_nonlift with pid 1258760 completed with status 0
% 0.23/0.32 % Result found by ehoh_best_nonlift
% 0.23/0.32 % Preprocessing class: HSMSSMSSSSMNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting ehoh_best_nonlift with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHNS-FFMF33-MHFFFSBN
% 0.23/0.32 % partial match(3): HGHNS-FFMF32-SHSFFSBN
% 0.23/0.32 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.32 % Starting ho_unfolding_3 with 901s (1) cores
% 0.23/0.32 % Starting ehoh_best_nonlift_rwall with 151s (1) cores
% 0.23/0.32 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.23/0.32 % Starting ehoh_best8_lambda with 146s (1) cores
% 0.23/0.32 % ehoh_best_nonlift_nonlambdatoforall with pid 1258770 completed with status 0
% 0.23/0.32 % Result found by ehoh_best_nonlift_nonlambdatoforall
% 0.23/0.32 % Preprocessing class: HSMSSMSSSSMNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting ehoh_best_nonlift with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHNS-FFMF33-MHFFFSBN
% 0.23/0.32 % partial match(3): HGHNS-FFMF32-SHSFFSBN
% 0.23/0.32 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.32 % Starting ho_unfolding_3 with 901s (1) cores
% 0.23/0.32 % Starting ehoh_best_nonlift_rwall with 151s (1) cores
% 0.23/0.32 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.23/0.32 % Preprocessing time : 0.002 s
% 0.23/0.32 % Presaturation interreduction done
% 0.23/0.32
% 0.23/0.32 % Proof found!
% 0.23/0.32 % SZS status ContradictoryAxioms
% 0.23/0.32 % SZS output start CNFRefutation
% See solution above
% 0.23/0.32 % Parsed axioms : 17
% 0.23/0.32 % Removed by relevancy pruning/SinE : 0
% 0.23/0.32 % Initial clauses : 28
% 0.23/0.32 % Removed in clause preprocessing : 8
% 0.23/0.32 % Initial clauses in saturation : 20
% 0.23/0.32 % Processed clauses : 445
% 0.23/0.32 % ...of these trivial : 1
% 0.23/0.32 % ...subsumed : 88
% 0.23/0.32 % ...remaining for further processing : 356
% 0.23/0.32 % Other redundant clauses eliminated : 44
% 0.23/0.32 % Clauses deleted for lack of memory : 0
% 0.23/0.32 % Backward-subsumed : 26
% 0.23/0.32 % Backward-rewritten : 62
% 0.23/0.32 % Generated clauses : 1037
% 0.23/0.32 % ...of the previous two non-redundant : 862
% 0.23/0.32 % ...aggressively subsumed : 0
% 0.23/0.32 % Contextual simplify-reflections : 0
% 0.23/0.32 % Paramodulations : 773
% 0.23/0.32 % Factorizations : 0
% 0.23/0.32 % NegExts : 125
% 0.23/0.32 % Equation resolutions : 53
% 0.23/0.32 % Disequality decompositions : 0
% 0.23/0.32 % Total rewrite steps : 156
% 0.23/0.32 % ...of those cached : 59
% 0.23/0.32 % Propositional unsat checks : 0
% 0.23/0.32 % Propositional check models : 0
% 0.23/0.32 % Propositional check unsatisfiable : 0
% 0.23/0.32 % Propositional clauses : 0
% 0.23/0.32 % Propositional clauses after purity: 0
% 0.23/0.32 % Propositional unsat core size : 0
% 0.23/0.32 % Propositional preprocessing time : 0.000
% 0.23/0.32 % Propositional encoding time : 0.000
% 0.23/0.32 % Propositional solver time : 0.000
% 0.23/0.32 % Success case prop preproc time : 0.000
% 0.23/0.32 % Success case prop encoding time : 0.000
% 0.23/0.32 % Success case prop solver time : 0.000
% 0.23/0.32 % Current number of processed clauses : 229
% 0.23/0.32 % Positive orientable unit clauses : 57
% 0.23/0.32 % Positive unorientable unit clauses: 0
% 0.23/0.32 % Negative unit clauses : 36
% 0.23/0.32 % Non-unit-clauses : 136
% 0.23/0.32 % Current number of unprocessed clauses: 350
% 0.23/0.32 % ...number of literals in the above : 926
% 0.23/0.32 % Current number of archived formulas : 0
% 0.23/0.32 % Current number of archived clauses : 127
% 0.23/0.32 % Clause-clause subsumption calls (NU) : 2401
% 0.23/0.32 % Rec. Clause-clause subsumption calls : 2009
% 0.23/0.32 % Non-unit clause-clause subsumptions : 63
% 0.23/0.32 % Unit Clause-clause subsumption calls : 1025
% 0.23/0.32 % Rewrite failures with RHS unbound : 0
% 0.23/0.32 % BW rewrite match attempts : 288
% 0.23/0.32 % BW rewrite match successes : 44
% 0.23/0.32 % Condensation attempts : 0
% 0.23/0.32 % Condensation successes : 0
% 0.23/0.32 % Termbank termtop insertions : 30814
% 0.23/0.32 % Search garbage collected termcells : 616
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.047 s
% 0.23/0.32 % System time : 0.007 s
% 0.23/0.32 % Total time : 0.054 s
% 0.23/0.32 % Maximum resident set size: 3652 pages
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.192 s
% 0.23/0.32 % System time : 0.024 s
% 0.23/0.32 % Total time : 0.216 s
% 0.23/0.32 % Maximum resident set size: 4864 pages
% 0.23/0.32 % E exiting
%------------------------------------------------------------------------------