%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PHI005^2 : 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 08:20:10 AM UTC 2026
% Result : Theorem 0.29s 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 26 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 529 ( 31 ~; 33 |; 9 &; 423 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-4 aty)
% Number of variables : 201 ( 93 ^; 93 !; 15 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_29,type,
mimplies: ( $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_36,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_39,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_40,type,
mdia_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_43,type,
mdia: ( $i > $o ) > $i > $o ).
thf(decl_44,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_46,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(decl_47,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(decl_48,type,
god: mu > $i > $o ).
thf(decl_49,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(decl_50,type,
necessary_existence: mu > $i > $o ).
thf(decl_51,type,
esk1_1: $i > $i ).
thf(decl_52,type,
esk2_1: $i > mu ).
thf(decl_53,type,
epred1_2: $i > mu > mu > $i > $o ).
thf(decl_54,type,
esk3_0: $i ).
thf(decl_55,type,
esk4_0: $i ).
thf(decl_56,type,
epred2_1: mu > mu > $i > $o ).
thf(decl_57,type,
esk5_3: $i > ( mu > $i > $o ) > $i > 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.ofZ5ZIpVjz/E---3.1_2631918.p',mbox_generic) ).
thf(mdia_generic,axiom,
( mdia_generic
= ( ^ [X15: $i > $i > $o,X4: $i > $o,X3: $i] :
? [X16: $i] :
( ( X15 @ X3 @ X16 )
& ( X4 @ X16 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mdia_generic) ).
thf(defD1,axiom,
( god
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X19: mu > $i > $o] : ( mimplies @ ( positive @ X19 ) @ ( X19 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',defD1) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.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.ofZ5ZIpVjz/E---3.1_2631918.p',mforall_indset) ).
thf(defD3,axiom,
( necessary_existence
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X20: mu > $i > $o] :
( mimplies @ ( essence @ X20 @ X1 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X20 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',defD3) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
? [X1: mu] : ( X11 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mexists_ind) ).
thf(mbox,axiom,
( mbox
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X21: $i] :
( ~ ( rel @ Z1 @ X21 )
| ( Z0 @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mbox) ).
thf(mdia,axiom,
( mdia
= ( ^ [Z0: $i > $o,Z1: $i] :
? [X22: $i] :
( ( rel @ Z1 @ X22 )
& ( Z0 @ X22 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mdia) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mvalid) ).
thf(corC,lemma,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X1: mu] : ( god @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',corC) ).
thf(axA5,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',axA5) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X6: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X6 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',mforall_ind) ).
thf(thmT2,lemma,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( god @ X1 ) @ ( essence @ god @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',thmT2) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [X15: $i > $i > $o] :
! [X17: $i,X18: $i] :
( ( X15 @ X17 @ X18 )
=> ( X15 @ X18 @ X17 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',msymmetric) ).
thf(sym,axiom,
msymmetric @ rel,
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',sym) ).
thf(thmT3,conjecture,
( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X1: mu] : ( god @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ofZ5ZIpVjz/E---3.1_2631918.p',thmT3) ).
thf(c_0_17,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_18,plain,
( mdia_generic
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
? [X16: $i] :
( ( Z0 @ Z2 @ X16 )
& ( Z1 @ X16 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_generic]) ).
thf(c_0_19,plain,
( god
= ( ^ [Z0: mu,Z1: $i] :
! [X23: mu > $i > $o] :
( ( positive @ X23 @ Z1 )
=> ( X23 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[defD1]) ).
thf(c_0_20,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_21,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_22,plain,
( necessary_existence
= ( ^ [Z0: mu,Z1: $i] :
! [X26: mu > $i > $o] :
( ( essence @ X26 @ Z0 @ Z1 )
=> ! [X25: $i] :
( ~ ( rel @ Z1 @ X25 )
| ? [X24: mu] : ( X26 @ X24 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[defD3]) ).
thf(c_0_23,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
? [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_24,axiom,
( mbox
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X21: $i] :
( ~ ( rel @ Z1 @ X21 )
| ( Z0 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[mbox,c_0_17]) ).
thf(c_0_25,axiom,
( mdia
= ( ^ [Z0: $i > $o,Z1: $i] :
? [X22: $i] :
( ( rel @ Z1 @ X22 )
& ( Z0 @ X22 ) ) ) ),
inference(apply_def,[status(thm)],[mdia,c_0_18]) ).
thf(c_0_26,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_27,plain,
( god
= ( ^ [Z0: mu,Z1: $i] :
! [X23: mu > $i > $o] :
( ( positive @ X23 @ Z1 )
=> ( X23 @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
thf(c_0_28,plain,
( necessary_existence
= ( ^ [Z0: mu,Z1: $i] :
! [X26: mu > $i > $o] :
( ( essence @ X26 @ Z0 @ Z1 )
=> ! [X25: $i] :
( ~ ( rel @ Z1 @ X25 )
| ? [X24: mu] : ( X26 @ X24 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_20]),c_0_21]),c_0_23]),c_0_24]) ).
thf(c_0_29,lemma,
! [X36: $i] :
? [X35: $i] :
( ( rel @ X36 @ X35 )
& ? [X34: mu] :
! [X33: mu > $i > $o] :
( ( positive @ X33 @ X35 )
=> ( X33 @ X34 @ X35 ) ) ),
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)],[corC]),c_0_23]),c_0_25]),c_0_26]),c_0_27]) ).
thf(c_0_30,plain,
! [X32: $i] :
( positive
@ ^ [Z0: mu,Z1: $i] :
! [X29: mu > $i > $o] :
( ( essence @ X29 @ Z0 @ Z1 )
=> ! [X30: $i] :
( ~ ( rel @ Z1 @ X30 )
| ? [X31: mu] : ( X29 @ X31 @ X30 ) ) )
@ X32 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axA5,c_0_26]),c_0_28]) ).
thf(c_0_31,lemma,
! [X48: $i,X51: mu > $i > $o] :
( ( rel @ X48 @ ( esk1_1 @ X48 ) )
& ( ~ ( positive @ X51 @ ( esk1_1 @ X48 ) )
| ( X51 @ ( esk2_1 @ X48 ) @ ( esk1_1 @ X48 ) ) ) ),
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_32,plain,
! [X47: $i] :
( positive
@ ^ [Z0: mu,Z1: $i] :
! [X29: mu > $i > $o] :
( ( essence @ X29 @ Z0 @ Z1 )
=> ! [X30: $i] :
( ~ ( rel @ Z1 @ X30 )
| ? [X31: mu] : ( X29 @ X31 @ X30 ) ) )
@ X47 ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
thf(c_0_33,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_34,lemma,
! [X6: mu > $i > $o,X3: $i] :
( ( X6 @ ( esk2_1 @ X3 ) @ ( esk1_1 @ X3 ) )
| ~ ( positive @ X6 @ ( esk1_1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,plain,
! [X16: $i] :
( positive
@ ^ [Z0: mu,Z1: $i] :
! [X78: mu > $i > $o] :
( ( essence @ X78 @ Z0 @ Z1 )
=> ! [X79: $i] :
( ~ ( rel @ Z1 @ X79 )
| ? [X80: mu] : ( X78 @ X80 @ X79 ) ) )
@ X16 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_36,lemma,
! [X40: $i,X39: mu] :
( ! [X37: mu > $i > $o] :
( ( positive @ X37 @ X40 )
=> ( X37 @ X39 @ X40 ) )
=> ( essence
@ ^ [Z0: mu,Z1: $i] :
! [X38: mu > $i > $o] :
( ( positive @ X38 @ Z1 )
=> ( X38 @ Z0 @ Z1 ) )
@ X39
@ X40 ) ),
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)],[thmT2]),c_0_20]),c_0_33]),c_0_26]),c_0_27]) ).
thf(c_0_37,plain,
( msymmetric
= ( ^ [Z0: $i > $i > $o] :
! [X17: $i,X18: $i] :
( ( Z0 @ X17 @ X18 )
=> ( Z0 @ X18 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[msymmetric]) ).
thf(c_0_38,lemma,
! [X3: $i,X81: mu > $i > $o] :
( ( essence @ X81 @ ( esk2_1 @ X3 ) @ ( esk1_1 @ X3 ) )
=> ! [X82: $i] :
( ~ ( rel @ ( esk1_1 @ X3 ) @ X82 )
| ? [X83: mu] : ( X81 @ X83 @ X82 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,lemma,
! [X52: $i,X53: mu] :
( ( ( positive @ ( epred1_2 @ X52 @ X53 ) @ X52 )
| ( essence
@ ^ [Z0: mu,Z1: $i] :
! [X38: mu > $i > $o] :
( ( positive @ X38 @ Z1 )
=> ( X38 @ Z0 @ Z1 ) )
@ X53
@ X52 ) )
& ( ~ ( epred1_2 @ X52 @ X53 @ X53 @ X52 )
| ( essence
@ ^ [Z0: mu,Z1: $i] :
! [X38: mu > $i > $o] :
( ( positive @ X38 @ Z1 )
=> ( X38 @ Z0 @ Z1 ) )
@ X53
@ X52 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])]) ).
thf(c_0_40,plain,
! [X27: $i,X28: $i] :
( ( rel @ X27 @ X28 )
=> ( rel @ X28 @ X27 ) ),
inference(apply_def,[status(thm)],[sym,c_0_37]) ).
thf(c_0_41,lemma,
! [X3: $i,X6: mu > $i > $o,X16: $i] :
( ( X6 @ ( esk5_3 @ X3 @ X6 @ X16 ) @ X16 )
| ~ ( essence @ X6 @ ( esk2_1 @ X3 ) @ ( esk1_1 @ X3 ) )
| ~ ( rel @ ( esk1_1 @ X3 ) @ X16 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_38]) ).
thf(c_0_42,lemma,
! [X1: mu,X3: $i] :
( ( positive @ ( epred1_2 @ X3 @ X1 ) @ X3 )
| ( essence
@ ^ [Z0: mu,Z1: $i] :
! [X84: mu > $i > $o] :
( ( positive @ X84 @ Z1 )
=> ( X84 @ Z0 @ Z1 ) )
@ X1
@ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_43,plain,
! [X45: $i,X46: $i] :
( ~ ( rel @ X45 @ X46 )
| ( rel @ X46 @ X45 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
thf(c_0_44,negated_conjecture,
~ ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X1: mu] : ( god @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[thmT3]) ).
thf(c_0_45,lemma,
! [X16: $i,X3: $i] :
( ! [X85: mu > $i > $o] :
( ( positive @ X85 @ X3 )
=> ( X85
@ ( esk5_3 @ X16
@ ^ [Z0: mu,Z1: $i] :
! [X86: mu > $i > $o] :
( ( positive @ X86 @ Z1 )
=> ( X86 @ Z0 @ Z1 ) )
@ X3 )
@ X3 ) )
| ( positive @ ( epred1_2 @ ( esk1_1 @ X16 ) @ ( esk2_1 @ X16 ) ) @ ( esk1_1 @ X16 ) )
| ~ ( rel @ ( esk1_1 @ X16 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_46,plain,
! [X3: $i,X16: $i] :
( ( rel @ X16 @ X3 )
| ~ ( rel @ X3 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_47,lemma,
! [X3: $i] : ( rel @ X3 @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_48,negated_conjecture,
~ ! [X44: $i,X43: $i] :
( ~ ( rel @ X44 @ X43 )
| ? [X42: mu] :
! [X41: mu > $i > $o] :
( ( positive @ X41 @ X43 )
=> ( X41 @ X42 @ X43 ) ) ),
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)],[c_0_44]),c_0_23]),c_0_24]),c_0_26]),c_0_27])]) ).
thf(c_0_49,lemma,
! [X3: $i,X6: mu > $i > $o,X16: $i] :
( ( X6
@ ( esk5_3 @ X3
@ ^ [Z0: mu,Z1: $i] :
! [X87: mu > $i > $o] :
( ( positive @ X87 @ Z1 )
=> ( X87 @ Z0 @ Z1 ) )
@ X16 )
@ X16 )
| ( positive @ ( epred1_2 @ ( esk1_1 @ X3 ) @ ( esk2_1 @ X3 ) ) @ ( esk1_1 @ X3 ) )
| ~ ( rel @ ( esk1_1 @ X3 ) @ X16 )
| ~ ( positive @ X6 @ X16 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_45]) ).
thf(c_0_50,lemma,
! [X3: $i] : ( rel @ ( esk1_1 @ X3 ) @ X3 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_51,negated_conjecture,
! [X57: mu] :
( ( rel @ esk3_0 @ esk4_0 )
& ( positive @ ( epred2_1 @ X57 ) @ esk4_0 )
& ~ ( epred2_1 @ X57 @ X57 @ esk4_0 ) ),
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_48])])])])]) ).
thf(c_0_52,lemma,
! [X6: mu > $i > $o,X3: $i] :
( ( X6
@ ( esk5_3 @ X3
@ ^ [Z0: mu,Z1: $i] :
! [X88: mu > $i > $o] :
( ( positive @ X88 @ Z1 )
=> ( X88 @ Z0 @ Z1 ) )
@ X3 )
@ X3 )
| ( positive @ ( epred1_2 @ ( esk1_1 @ X3 ) @ ( esk2_1 @ X3 ) ) @ ( esk1_1 @ X3 ) )
| ~ ( positive @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X1: mu] : ( positive @ ( epred2_1 @ X1 ) @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_54,negated_conjecture,
! [X1: mu] :
~ ( epred2_1 @ X1 @ X1 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X1: mu] :
( ( epred2_1 @ X1
@ ( esk5_3 @ esk4_0
@ ^ [Z0: mu,Z1: $i] :
! [X89: mu > $i > $o] :
( ( positive @ X89 @ Z1 )
=> ( X89 @ Z0 @ Z1 ) )
@ esk4_0 )
@ esk4_0 )
| ( positive @ ( epred1_2 @ ( esk1_1 @ esk4_0 ) @ ( esk2_1 @ esk4_0 ) ) @ ( esk1_1 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_56,negated_conjecture,
positive @ ( epred1_2 @ ( esk1_1 @ esk4_0 ) @ ( esk2_1 @ esk4_0 ) ) @ ( esk1_1 @ esk4_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_57,lemma,
! [X1: mu,X3: $i] :
( ( essence
@ ^ [Z0: mu,Z1: $i] :
! [X90: mu > $i > $o] :
( ( positive @ X90 @ Z1 )
=> ( X90 @ Z0 @ Z1 ) )
@ X1
@ X3 )
| ~ ( epred1_2 @ X3 @ X1 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_58,lemma,
epred1_2 @ ( esk1_1 @ esk4_0 ) @ ( esk2_1 @ esk4_0 ) @ ( esk2_1 @ esk4_0 ) @ ( esk1_1 @ esk4_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
thf(c_0_59,lemma,
( essence
@ ^ [Z0: mu,Z1: $i] :
! [X91: mu > $i > $o] :
( ( positive @ X91 @ Z1 )
=> ( X91 @ Z0 @ Z1 ) )
@ ( esk2_1 @ esk4_0 )
@ ( esk1_1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_60,lemma,
! [X3: $i] :
( ! [X92: mu > $i > $o] :
( ( positive @ X92 @ X3 )
=> ( X92
@ ( esk5_3 @ esk4_0
@ ^ [Z0: mu,Z1: $i] :
! [X93: mu > $i > $o] :
( ( positive @ X93 @ Z1 )
=> ( X93 @ Z0 @ Z1 ) )
@ X3 )
@ X3 ) )
| ~ ( rel @ ( esk1_1 @ esk4_0 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_59]) ).
thf(c_0_61,lemma,
! [X6: mu > $i > $o,X3: $i] :
( ( X6
@ ( esk5_3 @ esk4_0
@ ^ [Z0: mu,Z1: $i] :
! [X94: mu > $i > $o] :
( ( positive @ X94 @ Z1 )
=> ( X94 @ Z0 @ Z1 ) )
@ X3 )
@ X3 )
| ~ ( rel @ ( esk1_1 @ esk4_0 ) @ X3 )
| ~ ( positive @ X6 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_60]) ).
thf(c_0_62,lemma,
! [X6: mu > $i > $o] :
( ( X6
@ ( esk5_3 @ esk4_0
@ ^ [Z0: mu,Z1: $i] :
! [X95: mu > $i > $o] :
( ( positive @ X95 @ Z1 )
=> ( X95 @ Z0 @ Z1 ) )
@ esk4_0 )
@ esk4_0 )
| ~ ( positive @ X6 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
thf(c_0_63,negated_conjecture,
! [X1: mu] :
( epred2_1 @ X1
@ ( esk5_3 @ esk4_0
@ ^ [Z0: mu,Z1: $i] :
! [X96: mu > $i > $o] :
( ( positive @ X96 @ Z1 )
=> ( X96 @ Z0 @ Z1 ) )
@ esk4_0 )
@ esk4_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
thf(c_0_64,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_54,c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI005^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:17:29 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.ofZ5ZIpVjz/E---3.1_2631918.p
% 0.29/0.29 % Version: 3.5.1-ho
% 0.29/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.29/0.29 % Starting almost_fo_3_lam with 300s (1) cores
% 0.29/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.29/0.29 % almost_fo_3_lam with pid 2631933 completed with status 0
% 0.29/0.29 % Result found by almost_fo_3_lam
% 0.29/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.29/0.29 % Starting almost_fo_3_lam with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.29 % No SInE strategy applied
% 0.29/0.29 % Search class: HGUNS-FFSF11-DHSSMSBN
% 0.29/0.29 % partial match(3): HGUNF-FFSF11-SHSSMMBN
% 0.29/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.29 % SubtermCWHack with pid 2631935 completed with status 10
% 0.29/0.29 % Starting almost_fo_3_lam with 31s (1) cores
% 0.29/0.29 % almost_fo_3_lam with pid 2631937 completed with status 0
% 0.29/0.29 % Result found by almost_fo_3_lam
% 0.29/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.29/0.29 % Starting almost_fo_3_lam with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.29 % No SInE strategy applied
% 0.29/0.29 % Search class: HGUNS-FFSF11-DHSSMSBN
% 0.29/0.29 % partial match(3): HGUNF-FFSF11-SHSSMMBN
% 0.29/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.29 % SubtermCWHack with pid 2631935 completed with status 10
% 0.29/0.29 % Starting almost_fo_3_lam with 31s (1) cores
% 0.29/0.29 % Preprocessing time : 0.001 s
% 0.29/0.29 % Presaturation interreduction done
% 0.29/0.29
% 0.29/0.29 % Proof found!
% 0.29/0.29 % SZS status Theorem
% 0.29/0.29 % SZS output start CNFRefutation
% See solution above
% 0.29/0.29 % Parsed axioms : 59
% 0.29/0.29 % Removed by relevancy pruning/SinE : 0
% 0.29/0.29 % Initial clauses : 38
% 0.29/0.29 % Removed in clause preprocessing : 29
% 0.29/0.29 % Initial clauses in saturation : 9
% 0.29/0.29 % Processed clauses : 37
% 0.29/0.29 % ...of these trivial : 0
% 0.29/0.29 % ...subsumed : 1
% 0.29/0.29 % ...remaining for further processing : 36
% 0.29/0.29 % Other redundant clauses eliminated : 0
% 0.29/0.29 % Clauses deleted for lack of memory : 0
% 0.29/0.29 % Backward-subsumed : 0
% 0.29/0.29 % Backward-rewritten : 1
% 0.29/0.29 % Generated clauses : 28
% 0.29/0.29 % ...of the previous two non-redundant : 24
% 0.29/0.29 % ...aggressively subsumed : 0
% 0.29/0.29 % Contextual simplify-reflections : 0
% 0.29/0.29 % Paramodulations : 22
% 0.29/0.29 % Factorizations : 0
% 0.29/0.29 % NegExts : 0
% 0.29/0.29 % Equation resolutions : 0
% 0.29/0.29 % Disequality decompositions : 0
% 0.29/0.29 % Total rewrite steps : 3
% 0.29/0.29 % ...of those cached : 0
% 0.29/0.29 % Propositional unsat checks : 0
% 0.29/0.29 % Propositional check models : 0
% 0.29/0.29 % Propositional check unsatisfiable : 0
% 0.29/0.29 % Propositional clauses : 0
% 0.29/0.29 % Propositional clauses after purity: 0
% 0.29/0.29 % Propositional unsat core size : 0
% 0.29/0.29 % Propositional preprocessing time : 0.000
% 0.29/0.29 % Propositional encoding time : 0.000
% 0.29/0.29 % Propositional solver time : 0.000
% 0.29/0.29 % Success case prop preproc time : 0.000
% 0.29/0.29 % Success case prop encoding time : 0.000
% 0.29/0.29 % Success case prop solver time : 0.000
% 0.29/0.29 % Current number of processed clauses : 22
% 0.29/0.29 % Positive orientable unit clauses : 10
% 0.29/0.29 % Positive unorientable unit clauses: 0
% 0.29/0.29 % Negative unit clauses : 1
% 0.29/0.29 % Non-unit-clauses : 11
% 0.29/0.29 % Current number of unprocessed clauses: 5
% 0.29/0.29 % ...number of literals in the above : 8
% 0.29/0.29 % Current number of archived formulas : 0
% 0.29/0.29 % Current number of archived clauses : 14
% 0.29/0.29 % Clause-clause subsumption calls (NU) : 22
% 0.29/0.29 % Rec. Clause-clause subsumption calls : 18
% 0.29/0.29 % Non-unit clause-clause subsumptions : 1
% 0.29/0.29 % Unit Clause-clause subsumption calls : 0
% 0.29/0.29 % Rewrite failures with RHS unbound : 0
% 0.29/0.29 % BW rewrite match attempts : 2
% 0.29/0.29 % BW rewrite match successes : 1
% 0.29/0.29 % Condensation attempts : 0
% 0.29/0.29 % Condensation successes : 0
% 0.29/0.29 % Termbank termtop insertions : 5885
% 0.29/0.29 % Search garbage collected termcells : 602
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.008 s
% 0.29/0.29 % System time : 0.001 s
% 0.29/0.29 % Total time : 0.009 s
% 0.29/0.29 % Maximum resident set size: 3688 pages
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.010 s
% 0.29/0.29 % System time : 0.006 s
% 0.29/0.29 % Total time : 0.016 s
% 0.29/0.29 % Maximum resident set size: 4864 pages
% 0.29/0.29 % E exiting
%------------------------------------------------------------------------------