%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PHI004^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:20:07 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 24 equ; 0 cnn)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 434 ( 51 ~; 49 |; 14 &; 302 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 125 ( 71 ^; 54 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_26,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_29,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_34,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_39,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_41,type,
rel: $i > $i > $o ).
thf(decl_42,type,
mbox: ( $i > $o ) > $i > $o ).
thf(decl_44,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_46,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(decl_47,type,
god: mu > $i > $o ).
thf(decl_48,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(decl_49,type,
esk1_0: $i ).
thf(decl_50,type,
esk2_0: mu ).
thf(decl_51,type,
epred1_0: mu > $i > $o ).
thf(decl_52,type,
epred2_0: mu > $i > $o ).
thf(decl_53,type,
esk3_0: $i ).
thf(decl_54,type,
esk4_0: mu ).
thf(mbox_generic,axiom,
( mbox_generic
= ( ^ [X15: $i > $i > $o,X4: $i > $o,X3: $i] :
! [X16: $i] :
( ~ ( X15 @ X3 @ X16 )
| ( X4 @ X16 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mbox_generic) ).
thf(defD1,axiom,
( god
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X18: mu > $i > $o] : ( mimplies @ ( positive @ X18 ) @ ( X18 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',defD1) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mimplies) ).
thf(mforall_indset,axiom,
( mforall_indset
= ( ^ [X7: ( mu > $i > $o ) > $i > $o,X3: $i] :
! [X8: mu > $i > $o] : ( X7 @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mforall_indset) ).
thf(defD2,axiom,
( essence
= ( ^ [X20: mu > $i > $o,X1: mu] :
( mand @ ( X20 @ X1 )
@ ( mforall_indset
@ ^ [X21: mu > $i > $o] :
( mimplies @ ( X21 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X20 @ X2 ) @ ( X21 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',defD2) ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
& ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mand) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X6: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X6 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mforall_ind) ).
thf(mbox,axiom,
( mbox
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X22: $i] :
( ~ ( rel @ Z1 @ X22 )
| ( Z0 @ X22 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mvalid) ).
thf(thmT2,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( god @ X1 ) @ ( essence @ god @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',thmT2) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mnot) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
<=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',mequiv) ).
thf(axA4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X19: mu > $i > $o] : ( mimplies @ ( positive @ X19 ) @ ( mbox @ ( positive @ X19 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',axA4) ).
thf(axA1,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X17: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X17 @ X1 ) ) )
@ ( mnot @ ( positive @ X17 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ENiBmGuWra/E---3.1_2631440.p',axA1) ).
thf(c_0_14,plain,
( mbox_generic
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X16: $i] :
( ~ ( Z0 @ Z2 @ X16 )
| ( Z1 @ X16 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_generic]) ).
thf(c_0_15,plain,
( god
= ( ^ [Z0: mu,Z1: $i] :
! [X24: mu > $i > $o] :
( ( positive @ X24 @ Z1 )
=> ( X24 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[defD1]) ).
thf(c_0_16,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_17,plain,
( mforall_indset
= ( ^ [Z0: ( mu > $i > $o ) > $i > $o,Z1: $i] :
! [X8: mu > $i > $o] : ( Z0 @ X8 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_indset]) ).
thf(c_0_18,plain,
( essence
= ( ^ [Z0: mu > $i > $o,Z1: mu,Z2: $i] :
( ( Z0 @ Z1 @ Z2 )
& ! [X27: mu > $i > $o] :
( ( X27 @ Z1 @ Z2 )
=> ! [X26: $i] :
( ~ ( rel @ Z2 @ X26 )
| ! [X25: mu] :
( ( Z0 @ X25 @ X26 )
=> ( X27 @ X25 @ X26 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[defD2]) ).
thf(c_0_19,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_20,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_21,axiom,
( mbox
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X22: $i] :
( ~ ( rel @ Z1 @ X22 )
| ( Z0 @ X22 ) ) ) ),
inference(apply_def,[status(thm)],[mbox,c_0_14]) ).
thf(c_0_22,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_23,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( god @ X1 ) @ ( essence @ god @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[thmT2]) ).
thf(c_0_24,plain,
( god
= ( ^ [Z0: mu,Z1: $i] :
! [X24: mu > $i > $o] :
( ( positive @ X24 @ Z1 )
=> ( X24 @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_25,plain,
( essence
= ( ^ [Z0: mu > $i > $o,Z1: mu,Z2: $i] :
( ( Z0 @ Z1 @ Z2 )
& ! [X27: mu > $i > $o] :
( ( X27 @ Z1 @ Z2 )
=> ! [X26: $i] :
( ~ ( rel @ Z2 @ X26 )
| ! [X25: mu] :
( ( Z0 @ X25 @ X26 )
=> ( X27 @ X25 @ X26 ) ) ) ) ) ) ),
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)],[c_0_18,c_0_19]),c_0_16]),c_0_20]),c_0_17]),c_0_21]) ).
thf(c_0_26,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_27,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_28,plain,
! [X32: $i,X31: mu > $i > $o] :
( ( positive @ X31 @ X32 )
=> ! [X30: $i] :
( ~ ( rel @ X32 @ X30 )
| ( positive @ X31 @ X30 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[axA4]),c_0_16]),c_0_17]),c_0_21]),c_0_22])]) ).
thf(c_0_29,negated_conjecture,
~ ! [X39: $i,X38: mu] :
( ! [X33: mu > $i > $o] :
( ( positive @ X33 @ X39 )
=> ( X33 @ X38 @ X39 ) )
=> ( ! [X34: mu > $i > $o] :
( ( positive @ X34 @ X39 )
=> ( X34 @ X38 @ X39 ) )
& ! [X35: mu > $i > $o] :
( ( X35 @ X38 @ X39 )
=> ! [X36: $i] :
( ~ ( rel @ X39 @ X36 )
| ! [X37: mu] :
( ! [X34: mu > $i > $o] :
( ( positive @ X34 @ X36 )
=> ( X34 @ X37 @ X36 ) )
=> ( X35 @ X37 @ X36 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_23]),c_0_16]),c_0_20]),c_0_22]),c_0_24]),c_0_25])]) ).
thf(c_0_30,plain,
! [X29: $i,X28: mu > $i > $o] :
( ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X28 @ Z0 @ Z1 )
@ X29 )
<=> ~ ( positive @ X28 @ X29 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[axA1]),c_0_26]),c_0_27]),c_0_17]),c_0_22])]) ).
thf(c_0_31,plain,
! [X42: $i,X43: mu > $i > $o,X44: $i] :
( ~ ( positive @ X43 @ X42 )
| ~ ( rel @ X42 @ X44 )
| ( positive @ X43 @ X44 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
thf(c_0_32,negated_conjecture,
! [X47: mu > $i > $o,X52: mu > $i > $o] :
( ( ~ ( positive @ X47 @ esk1_0 )
| ( X47 @ esk2_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk2_0 @ esk1_0 )
| ( positive @ epred1_0 @ esk1_0 ) )
& ( ( rel @ esk1_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 ) )
& ( ~ ( positive @ X52 @ esk3_0 )
| ( X52 @ esk4_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk4_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ( rel @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( positive @ X52 @ esk3_0 )
| ( X52 @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_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_29])])])])])]) ).
thf(c_0_33,plain,
! [X40: $i,X41: mu > $i > $o] :
( ( ~ ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X41 @ Z0 @ Z1 )
@ X40 )
| ~ ( positive @ X41 @ X40 ) )
& ( ( positive @ X41 @ X40 )
| ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X41 @ Z0 @ Z1 )
@ X40 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
thf(c_0_34,plain,
! [X3: $i,X6: mu > $i > $o,X16: $i] :
( ( positive @ X6 @ X16 )
| ~ ( positive @ X6 @ X3 )
| ~ ( rel @ X3 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,negated_conjecture,
( ( rel @ esk1_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk2_0 @ esk1_0 )
| ~ ( positive @ X6 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
! [X6: mu > $i > $o,X3: $i] :
( ( positive @ X6 @ X3 )
| ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X6 @ Z0 @ Z1 )
@ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_38,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ epred1_0 @ esk1_0 )
| ( positive @ X6 @ esk3_0 )
| ~ ( positive @ X6 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ X6 @ esk1_0 )
| ~ ( X6 @ esk2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_40,negated_conjecture,
( ( epred2_0 @ esk2_0 @ esk1_0 )
| ( positive @ epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,negated_conjecture,
( ( epred2_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ epred1_0 @ esk1_0 )
| ( positive @ X6 @ esk3_0 )
| ~ ( X6 @ esk2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_43,negated_conjecture,
epred2_0 @ esk2_0 @ esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_41]) ).
thf(c_0_44,negated_conjecture,
( ( positive @ epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,negated_conjecture,
( ~ ( epred2_0 @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_46,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_47,negated_conjecture,
( ( positive @ epred2_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,negated_conjecture,
~ ( epred2_0 @ esk4_0 @ esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_45]) ).
thf(c_0_49,negated_conjecture,
positive @ epred1_0 @ esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
thf(c_0_50,negated_conjecture,
( ( rel @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_51,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ~ ( positive @ X6 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_52,negated_conjecture,
epred1_0 @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
thf(c_0_53,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ X6 @ esk3_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 )
| ~ ( positive @ X6 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
thf(c_0_54,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_55,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ X6 @ esk3_0 )
| ~ ( positive @ X6 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_52])]) ).
thf(c_0_56,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ~ ( positive @ X6 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_57,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ~ ( X6 @ esk2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
thf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n014.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 13:17:15 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 Running higher-order theorem proving
% 0.12/0.25 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.ENiBmGuWra/E---3.1_2631440.p
% 0.12/0.28 % Version: 3.5.1-ho
% 0.12/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.12/0.28 % almost_fo_3_lam with pid 2631472 completed with status 0
% 0.12/0.28 % Result found by almost_fo_3_lam
% 0.12/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.28 % No SInE strategy applied
% 0.12/0.28 % Search class: HGHNF-FFSF00-MHSSMSBN
% 0.12/0.28 % partial match(3): HGHNF-FFSF00-SHSSMFNN
% 0.12/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.28 % SubtermCWHack with pid 2631474 completed with status 0
% 0.12/0.28 % Result found by SubtermCWHack
% 0.12/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.28 % No SInE strategy applied
% 0.12/0.28 % Search class: HGHNF-FFSF00-MHSSMSBN
% 0.12/0.28 % partial match(3): HGHNF-FFSF00-SHSSMFNN
% 0.12/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.28 % Preprocessing time : 0.001 s
% 0.12/0.28
% 0.12/0.28 % Proof found!
% 0.12/0.28 % SZS status Theorem
% 0.12/0.28 % SZS output start CNFRefutation
% See solution above
% 0.12/0.28 % Parsed axioms : 54
% 0.12/0.28 % Removed by relevancy pruning/SinE : 0
% 0.12/0.28 % Initial clauses : 39
% 0.12/0.28 % Removed in clause preprocessing : 27
% 0.12/0.28 % Initial clauses in saturation : 12
% 0.12/0.28 % Processed clauses : 39
% 0.12/0.28 % ...of these trivial : 0
% 0.12/0.28 % ...subsumed : 4
% 0.12/0.28 % ...remaining for further processing : 35
% 0.12/0.28 % Other redundant clauses eliminated : 0
% 0.12/0.28 % Clauses deleted for lack of memory : 0
% 0.12/0.28 % Backward-subsumed : 3
% 0.12/0.28 % Backward-rewritten : 12
% 0.12/0.28 % Generated clauses : 47
% 0.12/0.28 % ...of the previous two non-redundant : 43
% 0.12/0.28 % ...aggressively subsumed : 0
% 0.12/0.28 % Contextual simplify-reflections : 2
% 0.12/0.28 % Paramodulations : 47
% 0.12/0.28 % Factorizations : 0
% 0.12/0.28 % NegExts : 0
% 0.12/0.28 % Equation resolutions : 0
% 0.12/0.28 % Disequality decompositions : 0
% 0.12/0.28 % Total rewrite steps : 13
% 0.12/0.28 % ...of those cached : 10
% 0.12/0.28 % Propositional unsat checks : 0
% 0.12/0.28 % Propositional check models : 0
% 0.12/0.28 % Propositional check unsatisfiable : 0
% 0.12/0.28 % Propositional clauses : 0
% 0.12/0.28 % Propositional clauses after purity: 0
% 0.12/0.28 % Propositional unsat core size : 0
% 0.12/0.28 % Propositional preprocessing time : 0.000
% 0.12/0.28 % Propositional encoding time : 0.000
% 0.12/0.28 % Propositional solver time : 0.000
% 0.12/0.28 % Success case prop preproc time : 0.000
% 0.12/0.28 % Success case prop encoding time : 0.000
% 0.12/0.28 % Success case prop solver time : 0.000
% 0.12/0.28 % Current number of processed clauses : 20
% 0.12/0.28 % Positive orientable unit clauses : 5
% 0.12/0.28 % Positive unorientable unit clauses: 0
% 0.12/0.28 % Negative unit clauses : 1
% 0.12/0.28 % Non-unit-clauses : 14
% 0.12/0.28 % Current number of unprocessed clauses: 8
% 0.12/0.28 % ...number of literals in the above : 16
% 0.12/0.28 % Current number of archived formulas : 0
% 0.12/0.28 % Current number of archived clauses : 15
% 0.12/0.28 % Clause-clause subsumption calls (NU) : 27
% 0.12/0.28 % Rec. Clause-clause subsumption calls : 25
% 0.12/0.28 % Non-unit clause-clause subsumptions : 6
% 0.12/0.28 % Unit Clause-clause subsumption calls : 3
% 0.12/0.28 % Rewrite failures with RHS unbound : 0
% 0.12/0.28 % BW rewrite match attempts : 3
% 0.12/0.28 % BW rewrite match successes : 3
% 0.12/0.28 % Condensation attempts : 0
% 0.12/0.28 % Condensation successes : 0
% 0.12/0.28 % Termbank termtop insertions : 3330
% 0.12/0.28 % Search garbage collected termcells : 802
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.008 s
% 0.12/0.28 % System time : 0.000 s
% 0.12/0.28 % Total time : 0.008 s
% 0.12/0.28 % Maximum resident set size: 3688 pages
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.011 s
% 0.12/0.28 % System time : 0.004 s
% 0.12/0.28 % Total time : 0.015 s
% 0.12/0.28 % Maximum resident set size: 4608 pages
% 0.12/0.28 % E exiting
%------------------------------------------------------------------------------