TSTP Solution File: PHI004^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:18:05 EDT 2024
% Result : Theorem 0.40s 0.58s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 37
% Syntax : Number of formulae : 84 ( 34 unt; 21 typ; 0 def)
% Number of atoms : 185 ( 25 equ; 0 cnn)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 454 ( 51 ~; 51 |; 15 &; 318 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 131 ( 68 ^ 63 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $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_30,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_40,type,
rel: $i > $i > $o ).
thf(decl_41,type,
mbox: ( $i > $o ) > $i > $o ).
thf(decl_43,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_45,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(decl_46,type,
god: mu > $i > $o ).
thf(decl_47,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(decl_51,type,
esk3_0: $i ).
thf(decl_52,type,
esk4_0: mu ).
thf(decl_53,type,
epred1_0: mu > $i > $o ).
thf(decl_54,type,
epred2_0: mu > $i > $o ).
thf(decl_55,type,
esk5_0: $i ).
thf(decl_56,type,
esk6_0: mu ).
thf(decl_57,type,
epred3_1: ( mu > $i > $o ) > mu > $i > $o ).
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/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(defD1,axiom,
( god
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X20: mu > $i > $o] : ( mimplies @ ( positive @ X20 ) @ ( X20 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',defD1) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',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/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(defD2,axiom,
( essence
= ( ^ [X22: mu > $i > $o,X1: mu] :
( mand @ ( X22 @ X1 )
@ ( mforall_indset
@ ^ [X23: mu > $i > $o] :
( mimplies @ ( X23 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X22 @ X2 ) @ ( X23 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',defD2) ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
& ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X6: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X6 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_ind) ).
thf(mbox,axiom,
( mbox
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X25: $i] :
( ~ ( rel @ Z1 @ X25 )
| ( Z0 @ X25 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
<=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(axA1,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X17: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X17 @ X1 ) ) )
@ ( mnot @ ( positive @ X17 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',axA1) ).
thf(thmT2,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( god @ X1 ) @ ( essence @ god @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT2) ).
thf(axA4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X21: mu > $i > $o] : ( mimplies @ ( positive @ X21 ) @ ( mbox @ ( positive @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',axA4) ).
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] :
! [X27: mu > $i > $o] :
( ( positive @ X27 @ Z1 )
=> ( X27 @ 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 )
& ! [X30: mu > $i > $o] :
( ( X30 @ Z1 @ Z2 )
=> ! [X29: $i] :
( ~ ( rel @ Z2 @ X29 )
| ! [X28: mu] :
( ( Z0 @ X28 @ X29 )
=> ( X30 @ X28 @ X29 ) ) ) ) ) ) ),
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] :
! [X25: $i] :
( ~ ( rel @ Z1 @ X25 )
| ( Z0 @ X25 ) ) ) ),
inference(apply_def,[status(thm)],[mbox,c_0_14]) ).
thf(c_0_22,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_23,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_24,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_25,plain,
( god
= ( ^ [Z0: mu,Z1: $i] :
! [X27: mu > $i > $o] :
( ( positive @ X27 @ Z1 )
=> ( X27 @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_26,plain,
( essence
= ( ^ [Z0: mu > $i > $o,Z1: mu,Z2: $i] :
( ( Z0 @ Z1 @ Z2 )
& ! [X30: mu > $i > $o] :
( ( X30 @ Z1 @ Z2 )
=> ! [X29: $i] :
( ~ ( rel @ Z2 @ X29 )
| ! [X28: mu] :
( ( Z0 @ X28 @ X29 )
=> ( X30 @ X28 @ X29 ) ) ) ) ) ) ),
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_27,plain,
! [X38: $i,X37: mu > $i > $o] :
( ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X37 @ Z0 @ Z1 )
@ X38 )
<=> ~ ( positive @ X37 @ X38 ) ),
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_22]),c_0_23]),c_0_17]),c_0_24])]) ).
thf(c_0_28,negated_conjecture,
~ ! [X62: $i,X61: mu] :
( ! [X56: mu > $i > $o] :
( ( positive @ X56 @ X62 )
=> ( X56 @ X61 @ X62 ) )
=> ( ! [X57: mu > $i > $o] :
( ( positive @ X57 @ X62 )
=> ( X57 @ X61 @ X62 ) )
& ! [X58: mu > $i > $o] :
( ( X58 @ X61 @ X62 )
=> ! [X59: $i] :
( ~ ( rel @ X62 @ X59 )
| ! [X60: mu] :
( ! [X57: mu > $i > $o] :
( ( positive @ X57 @ X59 )
=> ( X57 @ X60 @ X59 ) )
=> ( X58 @ X60 @ X59 ) ) ) ) ) ),
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)],[inference(assume_negation,[status(cth)],[thmT2])]),c_0_16]),c_0_20]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_29,plain,
! [X63: $i,X64: mu > $i > $o] :
( ( ~ ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X64 @ Z0 @ Z1 )
@ X63 )
| ~ ( positive @ X64 @ X63 ) )
& ( ( positive @ X64 @ X63 )
| ( positive
@ ^ [Z0: mu,Z1: $i] :
~ ( X64 @ Z0 @ Z1 )
@ X63 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
thf(c_0_30,plain,
! [X84: $i,X83: mu,X6: mu > $i > $o] :
( ( epred3_1 @ X6 @ X83 @ X84 )
<=> ~ ( X6 @ X83 @ X84 ) ),
introduced(definition) ).
thf(c_0_31,negated_conjecture,
! [X77: mu > $i > $o,X82: mu > $i > $o] :
( ( ~ ( positive @ X77 @ esk3_0 )
| ( X77 @ esk4_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk4_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk3_0 ) )
& ( ( rel @ esk3_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 ) )
& ( ~ ( positive @ X82 @ esk5_0 )
| ( X82 @ esk6_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 ) )
& ( ~ ( epred2_0 @ esk6_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) )
& ( ( rel @ esk3_0 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) )
& ( ~ ( positive @ X82 @ esk5_0 )
| ( X82 @ esk6_0 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) )
& ( ~ ( epred2_0 @ esk6_0 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_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_28])])])])])]) ).
thf(c_0_32,plain,
! [X6: mu > $i > $o,X3: $i] :
( ( positive @ X6 @ X3 )
| ( ( positive @ ( epred3_1 @ X6 ) @ X3 )
= $true ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_29]),c_0_30]) ).
thf(c_0_33,plain,
! [X48: $i,X47: mu > $i > $o] :
( ( positive @ X47 @ X48 )
=> ! [X46: $i] :
( ~ ( rel @ X48 @ X46 )
| ( positive @ X47 @ X46 ) ) ),
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_24])]) ).
thf(c_0_34,plain,
! [X98: $i,X99: mu,X100: mu > $i > $o] :
( ( ~ ( epred3_1 @ X100 @ X99 @ X98 )
| ~ ( X100 @ X99 @ X98 ) )
& ( ( X100 @ X99 @ X98 )
| ( epred3_1 @ X100 @ X99 @ X98 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_35,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk4_0 @ esk3_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,plain,
! [X6: mu > $i > $o,X3: $i] :
( ( positive @ ( epred3_1 @ X6 ) @ X3 )
| ( positive @ X6 @ X3 ) ),
inference(cn,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
! [X71: $i,X72: mu > $i > $o,X73: $i] :
( ~ ( positive @ X72 @ X71 )
| ~ ( rel @ X71 @ X73 )
| ( positive @ X72 @ X73 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
thf(c_0_38,plain,
! [X1: mu,X6: mu > $i > $o,X3: $i] :
( ~ ( epred3_1 @ X6 @ X1 @ X3 )
| ~ ( X6 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_39,negated_conjecture,
! [X6: mu > $i > $o] :
( ( epred3_1 @ X6 @ esk4_0 @ esk3_0 )
| ( positive @ X6 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,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_37]) ).
thf(c_0_41,negated_conjecture,
( ( rel @ esk3_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,plain,
! [X6: mu > $i > $o] :
( ( positive @ X6 @ esk3_0 )
| ~ ( X6 @ esk4_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_43,negated_conjecture,
( ( epred2_0 @ esk4_0 @ esk3_0 )
| ( positive @ epred1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_44,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ epred1_0 @ esk3_0 )
| ( positive @ X6 @ esk5_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_45,negated_conjecture,
( ( positive @ epred1_0 @ esk3_0 )
| ( positive @ epred2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk6_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 )
| ~ ( positive @ X6 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_47,negated_conjecture,
( ( positive @ epred2_0 @ esk5_0 )
| ( positive @ epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,negated_conjecture,
( ( positive @ epred1_0 @ esk3_0 )
| ~ ( epred2_0 @ esk6_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_49,negated_conjecture,
positive @ epred1_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
thf(c_0_50,negated_conjecture,
( ( rel @ esk3_0 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_51,negated_conjecture,
epred1_0 @ esk4_0 @ esk3_0,
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
thf(c_0_52,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk6_0 @ esk5_0 )
| ~ ( positive @ X6 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_53,negated_conjecture,
rel @ esk3_0 @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
thf(c_0_54,negated_conjecture,
( ( epred2_0 @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_55,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk6_0 @ esk5_0 )
| ~ ( positive @ X6 @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_51])]) ).
thf(c_0_56,negated_conjecture,
! [X6: mu > $i > $o] :
( ( positive @ X6 @ esk5_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_53]) ).
thf(c_0_57,negated_conjecture,
( ( positive @ epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
thf(c_0_58,negated_conjecture,
( ~ ( epred2_0 @ esk6_0 @ esk5_0 )
| ~ ( epred1_0 @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_59,negated_conjecture,
! [X6: mu > $i > $o] :
( ( X6 @ esk6_0 @ esk5_0 )
| ~ ( positive @ X6 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_60,negated_conjecture,
positive @ epred2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_51])]) ).
thf(c_0_61,negated_conjecture,
~ ( epred2_0 @ esk6_0 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_51])]) ).
thf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% 0.13/0.15 % Command : run_E %s %d THM
% 0.17/0.37 % Computer : n011.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat May 18 14:47:38 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.23/0.53 Running higher-order theorem proving
% 0.23/0.53 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/benchmark/theBenchmark.p
% 0.40/0.58 # Version: 3.1.0-ho
% 0.40/0.58 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.40/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.58 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.40/0.58 # Starting post_as_ho3 with 300s (1) cores
% 0.40/0.58 # Starting new_ho_12 with 300s (1) cores
% 0.40/0.58 # Starting new_bool_2 with 300s (1) cores
% 0.40/0.58 # post_as_ho3 with pid 3935 completed with status 0
% 0.40/0.58 # Result found by post_as_ho3
% 0.40/0.58 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.40/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.58 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.40/0.58 # Starting post_as_ho3 with 300s (1) cores
% 0.40/0.58 # No SInE strategy applied
% 0.40/0.58 # Search class: HGHNS-FFMF33-SHSSMSBN
% 0.40/0.58 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.40/0.58 # Starting new_ho_10 with 163s (1) cores
% 0.40/0.58 # new_ho_10 with pid 3939 completed with status 0
% 0.40/0.58 # Result found by new_ho_10
% 0.40/0.58 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.40/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.58 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.40/0.58 # Starting post_as_ho3 with 300s (1) cores
% 0.40/0.58 # No SInE strategy applied
% 0.40/0.58 # Search class: HGHNS-FFMF33-SHSSMSBN
% 0.40/0.58 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.40/0.58 # Starting new_ho_10 with 163s (1) cores
% 0.40/0.58 # Preprocessing time : 0.003 s
% 0.40/0.58 # Presaturation interreduction done
% 0.40/0.58
% 0.40/0.58 # Proof found!
% 0.40/0.58 # SZS status Theorem
% 0.40/0.58 # SZS output start CNFRefutation
% See solution above
% 0.40/0.58 # Parsed axioms : 59
% 0.40/0.58 # Removed by relevancy pruning/SinE : 0
% 0.40/0.58 # Initial clauses : 58
% 0.40/0.58 # Removed in clause preprocessing : 28
% 0.40/0.58 # Initial clauses in saturation : 30
% 0.40/0.58 # Processed clauses : 97
% 0.40/0.58 # ...of these trivial : 1
% 0.40/0.58 # ...subsumed : 3
% 0.40/0.58 # ...remaining for further processing : 93
% 0.40/0.58 # Other redundant clauses eliminated : 0
% 0.40/0.58 # Clauses deleted for lack of memory : 0
% 0.40/0.58 # Backward-subsumed : 0
% 0.40/0.58 # Backward-rewritten : 14
% 0.40/0.58 # Generated clauses : 97
% 0.40/0.58 # ...of the previous two non-redundant : 80
% 0.40/0.58 # ...aggressively subsumed : 0
% 0.40/0.58 # Contextual simplify-reflections : 1
% 0.40/0.58 # Paramodulations : 97
% 0.40/0.58 # Factorizations : 0
% 0.40/0.58 # NegExts : 0
% 0.40/0.58 # Equation resolutions : 0
% 0.40/0.58 # Disequality decompositions : 0
% 0.40/0.58 # Total rewrite steps : 33
% 0.40/0.58 # ...of those cached : 19
% 0.40/0.58 # Propositional unsat checks : 0
% 0.40/0.58 # Propositional check models : 0
% 0.40/0.58 # Propositional check unsatisfiable : 0
% 0.40/0.58 # Propositional clauses : 0
% 0.40/0.58 # Propositional clauses after purity: 0
% 0.40/0.58 # Propositional unsat core size : 0
% 0.40/0.58 # Propositional preprocessing time : 0.000
% 0.40/0.58 # Propositional encoding time : 0.000
% 0.40/0.58 # Propositional solver time : 0.000
% 0.40/0.58 # Success case prop preproc time : 0.000
% 0.40/0.58 # Success case prop encoding time : 0.000
% 0.40/0.58 # Success case prop solver time : 0.000
% 0.40/0.58 # Current number of processed clauses : 49
% 0.40/0.58 # Positive orientable unit clauses : 11
% 0.40/0.58 # Positive unorientable unit clauses: 0
% 0.40/0.58 # Negative unit clauses : 1
% 0.40/0.58 # Non-unit-clauses : 37
% 0.40/0.58 # Current number of unprocessed clauses: 37
% 0.40/0.58 # ...number of literals in the above : 130
% 0.40/0.58 # Current number of archived formulas : 0
% 0.40/0.58 # Current number of archived clauses : 44
% 0.40/0.58 # Clause-clause subsumption calls (NU) : 540
% 0.40/0.58 # Rec. Clause-clause subsumption calls : 250
% 0.40/0.58 # Non-unit clause-clause subsumptions : 4
% 0.40/0.58 # Unit Clause-clause subsumption calls : 9
% 0.40/0.58 # Rewrite failures with RHS unbound : 0
% 0.40/0.58 # BW rewrite match attempts : 2
% 0.40/0.58 # BW rewrite match successes : 2
% 0.40/0.58 # Condensation attempts : 97
% 0.40/0.58 # Condensation successes : 0
% 0.40/0.58 # Termbank termtop insertions : 6794
% 0.40/0.58 # Search garbage collected termcells : 1892
% 0.40/0.58
% 0.40/0.58 # -------------------------------------------------
% 0.40/0.58 # User time : 0.013 s
% 0.40/0.58 # System time : 0.005 s
% 0.40/0.58 # Total time : 0.017 s
% 0.40/0.58 # Maximum resident set size: 2120 pages
% 0.40/0.58
% 0.40/0.58 # -------------------------------------------------
% 0.40/0.58 # User time : 0.014 s
% 0.40/0.58 # System time : 0.008 s
% 0.40/0.58 # Total time : 0.022 s
% 0.40/0.58 # Maximum resident set size: 1792 pages
% 0.40/0.58 % E---3.1 exiting
% 0.56/0.58 % E exiting
%------------------------------------------------------------------------------