TSTP Solution File: AGT027^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : AGT027^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 : Sat May 4 07:08:55 EDT 2024
% Result : Theorem 0.38s 0.70s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 40
% Syntax : Number of formulae : 97 ( 36 unt; 23 typ; 0 def)
% Number of atoms : 213 ( 24 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 605 ( 106 ~; 88 |; 4 &; 407 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-3 aty)
% Number of variables : 186 ( 62 ^ 124 !; 0 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_33,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_37,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_49,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
a1: $i > $i > $o ).
thf(decl_54,type,
a2: $i > $i > $o ).
thf(decl_55,type,
a: mu ).
thf(decl_57,type,
p: mu > $i > $o ).
thf(decl_58,type,
q: mu > $i > $o ).
thf(decl_59,type,
r: mu > $i > $o ).
thf(decl_60,type,
s: mu > $i > $o ).
thf(decl_61,type,
esk1_1: $i > $i ).
thf(decl_66,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_71,type,
esk11_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_73,type,
esk13_0: $i ).
thf(decl_74,type,
esk14_1: mu > $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mor) ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mdia) ).
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.fFYLkBOiI4/E---3.1_4605.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.fFYLkBOiI4/E---3.1_4605.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mvalid) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mforall_ind) ).
thf(axiom_5_for_a1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a1 @ X6 ) ) @ ( mbox @ a1 @ ( mnot @ ( mbox @ a1 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_5_for_a1) ).
thf(axiom_a4,axiom,
mvalid @ ( mdia @ a1 @ ( s @ a ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_a4) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mand) ).
thf(axiom_a3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X1 ) @ ( mbox @ a1 @ ( r @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_a3) ).
thf(axiom_I_for_a2_a1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ a2 @ X6 ) @ ( mbox @ a1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_I_for_a2_a1) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',mexists_ind) ).
thf(axiom_a2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X1 ) @ ( s @ X1 ) ) @ ( q @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_a2) ).
thf(axiom_a1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X1 ) ) @ ( p @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',axiom_a1) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( p @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fFYLkBOiI4/E---3.1_4605.p',conj) ).
thf(c_0_17,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_18,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_19,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_20,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X20: $i] :
( ~ ( Z0 @ Z2 @ X20 )
| ~ ( Z1 @ X20 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_21,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_22,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_17,c_0_18]),c_0_19]) ).
thf(c_0_23,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_24,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_25,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X20: $i] :
( ~ ( Z0 @ Z2 @ X20 )
| ~ ( Z1 @ X20 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
thf(c_0_26,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_27,plain,
! [X70: $i,X69: $i > $o] :
( ~ ~ ! [X66: $i] :
( ~ ( a1 @ X70 @ X66 )
| ( X69 @ X66 ) )
| ! [X68: $i] :
( ~ ( a1 @ X70 @ X68 )
| ~ ! [X67: $i] :
( ~ ( a1 @ X68 @ X67 )
| ( X69 @ X67 ) ) ) ),
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)],[axiom_5_for_a1]),c_0_18]),c_0_22]),c_0_23]),c_0_21]),c_0_24])]) ).
thf(c_0_28,plain,
! [X33: $i] :
~ ! [X32: $i] :
( ~ ( a1 @ X33 @ X32 )
| ~ ( s @ a @ X32 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a4,c_0_25]),c_0_24])]) ).
thf(c_0_29,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_30,plain,
! [X31: $i,X30: mu,X29: $i] :
( ~ ( a1 @ X31 @ X29 )
| ~ ( s @ X30 @ X29 )
| ! [X28: $i] :
( ~ ( a1 @ X29 @ X28 )
| ( r @ X30 @ X28 ) ) ),
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)],[axiom_a3]),c_0_22]),c_0_26]),c_0_21]),c_0_24])]) ).
thf(c_0_31,plain,
! [X124: $i,X125: $i > $o,X126: $i,X127: $i] :
( ( ( a1 @ X127 @ ( esk11_3 @ X124 @ X125 @ X127 ) )
| ~ ( a1 @ X124 @ X127 )
| ~ ( a1 @ X124 @ X126 )
| ( X125 @ X126 ) )
& ( ~ ( X125 @ ( esk11_3 @ X124 @ X125 @ X127 ) )
| ~ ( a1 @ X124 @ X127 )
| ~ ( a1 @ X124 @ X126 )
| ( X125 @ X126 ) ) ),
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_27])])])])])]) ).
thf(c_0_32,plain,
! [X90: $i] :
( ( a1 @ X90 @ ( esk1_1 @ X90 ) )
& ( s @ a @ ( esk1_1 @ X90 ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
thf(c_0_33,plain,
! [X45: $i,X44: $i > $o] :
( ~ ! [X42: $i] :
( ~ ( a2 @ X45 @ X42 )
| ( X44 @ X42 ) )
| ! [X43: $i] :
( ~ ( a1 @ X45 @ X43 )
| ( X44 @ 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)],[axiom_I_for_a2_a1]),c_0_22]),c_0_23]),c_0_21]),c_0_24])]) ).
thf(c_0_34,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_29,c_0_18]),c_0_19]) ).
thf(c_0_35,plain,
! [X86: $i,X87: mu,X88: $i,X89: $i] :
( ~ ( a1 @ X86 @ X88 )
| ~ ( s @ X87 @ X88 )
| ~ ( a1 @ X88 @ X89 )
| ( r @ X87 @ X89 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])])]) ).
thf(c_0_36,plain,
! [X14: $i,X4: $i > $o,X3: $i,X15: $i] :
( ( a1 @ X3 @ ( esk11_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( a1 @ X14 @ X3 )
| ~ ( a1 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
! [X3: $i] : ( a1 @ X3 @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_39,plain,
! [X100: $i,X101: $i > $o,X103: $i] :
( ( ( a2 @ X100 @ ( esk6_2 @ X100 @ X101 ) )
| ~ ( a1 @ X100 @ X103 )
| ( X101 @ X103 ) )
& ( ~ ( X101 @ ( esk6_2 @ X100 @ X101 ) )
| ~ ( a1 @ X100 @ X103 )
| ( X101 @ X103 ) ) ),
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_33])])])])])]) ).
thf(c_0_40,plain,
! [X27: $i,X26: mu,X25: $i] :
( ~ ( a1 @ X27 @ X25 )
| ~ ~ ( ~ ( r @ X26 @ X25 )
| ~ ( s @ X26 @ X25 ) )
| ( q @ X26 @ X25 ) ),
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)],[axiom_a2]),c_0_34]),c_0_22]),c_0_26]),c_0_21]),c_0_24])]) ).
thf(c_0_41,plain,
! [X14: $i,X3: $i,X4: $i > $o,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk11_3 @ X3 @ X4 @ X14 ) )
| ~ ( a1 @ X3 @ X14 )
| ~ ( a1 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,plain,
! [X14: $i,X3: $i,X1: mu,X15: $i] :
( ( r @ X1 @ X15 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( s @ X1 @ X14 )
| ~ ( a1 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_43,plain,
! [X14: $i,X4: $i > $o,X3: $i] :
( ( a1 @ X3 @ ( esk11_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ ( esk1_1 @ X14 ) )
| ~ ( a1 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_44,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38,c_0_18]),c_0_26]) ).
thf(c_0_45,plain,
! [X24: $i,X23: mu,X22: $i] :
( ~ ( a2 @ X24 @ X22 )
| ~ ~ ! [X21: $i] :
( ~ ( a2 @ X22 @ X21 )
| ~ ( q @ X23 @ X21 ) )
| ( p @ X23 @ X22 ) ),
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)],[axiom_a1]),c_0_22]),c_0_26]),c_0_21]),c_0_25]),c_0_24])]) ).
thf(c_0_46,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk6_2 @ X3 @ X4 ) )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_47,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( a2 @ X3 @ ( esk6_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_48,plain,
! [X83: $i,X84: mu,X85: $i] :
( ~ ( a1 @ X83 @ X85 )
| ~ ( r @ X84 @ X85 )
| ~ ( s @ X84 @ X85 )
| ( q @ X84 @ X85 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
thf(c_0_49,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ ( esk1_1 @ X3 ) )
| ~ ( X4 @ ( esk11_3 @ X3 @ X4 @ X14 ) )
| ~ ( a1 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
thf(c_0_50,plain,
! [X4: $i > $o,X3: $i,X1: mu,X14: $i] :
( ( r @ X1 @ ( esk11_3 @ X3 @ X4 @ X14 ) )
| ( X4 @ ( esk1_1 @ X3 ) )
| ~ ( a1 @ X3 @ X14 )
| ~ ( s @ X1 @ X14 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_51,negated_conjecture,
~ ! [X78: $i] :
~ ! [X77: mu] :
~ ! [X76: $i] :
( ~ ( a1 @ X78 @ X76 )
| ( p @ X77 @ X76 ) ),
inference(fof_simplification,[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)],[conj])]),c_0_44]),c_0_21]),c_0_24])]) ).
thf(c_0_52,plain,
! [X79: $i,X80: mu,X81: $i,X82: $i] :
( ~ ( a2 @ X79 @ X81 )
| ~ ( a2 @ X81 @ X82 )
| ~ ( q @ X80 @ X82 )
| ( p @ X80 @ X81 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
thf(c_0_53,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ ( esk1_1 @ X3 ) )
| ~ ( X4 @ ( esk6_2 @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
thf(c_0_54,plain,
! [X4: $i > $o,X3: $i] :
( ( a2 @ X3 @ ( esk6_2 @ X3 @ X4 ) )
| ( X4 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
thf(c_0_55,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( q @ X1 @ X14 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( r @ X1 @ X14 )
| ~ ( s @ X1 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_56,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a1 @ X3 @ X14 )
| ~ ( s @ X1 @ X14 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_57,negated_conjecture,
! [X135: mu] :
( ( a1 @ esk13_0 @ ( esk14_1 @ X135 ) )
& ~ ( p @ X135 @ ( esk14_1 @ X135 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
thf(c_0_58,plain,
! [X14: $i,X1: mu,X3: $i,X15: $i] :
( ( p @ X1 @ X14 )
| ~ ( a2 @ X3 @ X14 )
| ~ ( a2 @ X14 @ X15 )
| ~ ( q @ X1 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_59,plain,
! [X3: $i] : ( a2 @ X3 @ ( esk1_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_60,plain,
! [X1: mu,X3: $i] :
( ( q @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_55,c_0_37]) ).
thf(c_0_61,plain,
! [X1: mu,X3: $i] :
( ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
thf(c_0_62,negated_conjecture,
! [X1: mu] : ( a1 @ esk13_0 @ ( esk14_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_63,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( p @ X1 @ X3 )
| ~ ( q @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_64,plain,
! [X1: mu,X3: $i] :
( ( q @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_65,negated_conjecture,
! [X1: mu,X4: $i > $o] :
( ( X4 @ ( esk14_1 @ X1 ) )
| ~ ( X4 @ ( esk6_2 @ esk13_0 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_46,c_0_62]) ).
thf(c_0_66,negated_conjecture,
! [X4: $i > $o,X1: mu] :
( ( a2 @ esk13_0 @ ( esk6_2 @ esk13_0 @ X4 ) )
| ( X4 @ ( esk14_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
thf(c_0_67,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( p @ X1 @ X3 )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_68,negated_conjecture,
! [X1: mu] : ( a2 @ esk13_0 @ ( esk14_1 @ X1 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66])]) ).
thf(c_0_69,negated_conjecture,
! [X1: mu] :
~ ( p @ X1 @ ( esk14_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_70,negated_conjecture,
! [X1: mu,X2: mu] :
( ( p @ X1 @ ( esk14_1 @ X2 ) )
| ~ ( s @ X1 @ ( esk1_1 @ ( esk14_1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_71,negated_conjecture,
! [X1: mu] :
~ ( s @ X1 @ ( esk1_1 @ ( esk14_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_72,plain,
! [X3: $i] : ( s @ a @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_73,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_71,c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : AGT027^1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 3 12:56:58 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.23/0.51 Running higher-order theorem proving
% 0.23/0.51 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.fFYLkBOiI4/E---3.1_4605.p
% 0.38/0.70 # Version: 3.1.0-ho
% 0.38/0.70 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.38/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.70 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.38/0.70 # Starting post_as_ho3 with 300s (1) cores
% 0.38/0.70 # Starting new_ho_12 with 300s (1) cores
% 0.38/0.70 # Starting new_bool_2 with 300s (1) cores
% 0.38/0.70 # new_bool_2 with pid 4739 completed with status 8
% 0.38/0.70 # post_as_ho3 with pid 4737 completed with status 0
% 0.38/0.70 # Result found by post_as_ho3
% 0.38/0.70 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.38/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.70 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.38/0.70 # Starting post_as_ho3 with 300s (1) cores
% 0.38/0.70 # No SInE strategy applied
% 0.38/0.70 # Search class: HGUNS-FFMF32-SHSSMMBN
% 0.38/0.70 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.70 # Starting new_ho_10 with 135s (1) cores
% 0.38/0.70 # new_ho_10 with pid 4747 completed with status 0
% 0.38/0.70 # Result found by new_ho_10
% 0.38/0.70 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.38/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.70 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.38/0.70 # Starting post_as_ho3 with 300s (1) cores
% 0.38/0.70 # No SInE strategy applied
% 0.38/0.70 # Search class: HGUNS-FFMF32-SHSSMMBN
% 0.38/0.70 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.70 # Starting new_ho_10 with 135s (1) cores
% 0.38/0.70 # Preprocessing time : 0.003 s
% 0.38/0.70 # Presaturation interreduction done
% 0.38/0.70
% 0.38/0.70 # Proof found!
% 0.38/0.70 # SZS status Theorem
% 0.38/0.70 # SZS output start CNFRefutation
% See solution above
% 0.38/0.70 # Parsed axioms : 85
% 0.38/0.70 # Removed by relevancy pruning/SinE : 0
% 0.38/0.70 # Initial clauses : 69
% 0.38/0.70 # Removed in clause preprocessing : 40
% 0.38/0.70 # Initial clauses in saturation : 29
% 0.38/0.70 # Processed clauses : 410
% 0.38/0.70 # ...of these trivial : 7
% 0.38/0.70 # ...subsumed : 22
% 0.38/0.70 # ...remaining for further processing : 381
% 0.38/0.70 # Other redundant clauses eliminated : 0
% 0.38/0.70 # Clauses deleted for lack of memory : 0
% 0.38/0.70 # Backward-subsumed : 6
% 0.38/0.70 # Backward-rewritten : 0
% 0.38/0.70 # Generated clauses : 7037
% 0.38/0.70 # ...of the previous two non-redundant : 6840
% 0.38/0.70 # ...aggressively subsumed : 0
% 0.38/0.70 # Contextual simplify-reflections : 0
% 0.38/0.70 # Paramodulations : 7035
% 0.38/0.70 # Factorizations : 2
% 0.38/0.70 # NegExts : 0
% 0.38/0.70 # Equation resolutions : 0
% 0.38/0.70 # Disequality decompositions : 0
% 0.38/0.70 # Total rewrite steps : 264
% 0.38/0.70 # ...of those cached : 225
% 0.38/0.70 # Propositional unsat checks : 0
% 0.38/0.70 # Propositional check models : 0
% 0.38/0.70 # Propositional check unsatisfiable : 0
% 0.38/0.70 # Propositional clauses : 0
% 0.38/0.70 # Propositional clauses after purity: 0
% 0.38/0.70 # Propositional unsat core size : 0
% 0.38/0.70 # Propositional preprocessing time : 0.000
% 0.38/0.70 # Propositional encoding time : 0.000
% 0.38/0.70 # Propositional solver time : 0.000
% 0.38/0.70 # Success case prop preproc time : 0.000
% 0.38/0.70 # Success case prop encoding time : 0.000
% 0.38/0.70 # Success case prop solver time : 0.000
% 0.38/0.70 # Current number of processed clauses : 346
% 0.38/0.70 # Positive orientable unit clauses : 16
% 0.38/0.70 # Positive unorientable unit clauses: 0
% 0.38/0.70 # Negative unit clauses : 2
% 0.38/0.70 # Non-unit-clauses : 328
% 0.38/0.70 # Current number of unprocessed clauses: 6486
% 0.38/0.70 # ...number of literals in the above : 25581
% 0.38/0.70 # Current number of archived formulas : 0
% 0.38/0.70 # Current number of archived clauses : 35
% 0.38/0.70 # Clause-clause subsumption calls (NU) : 8276
% 0.38/0.70 # Rec. Clause-clause subsumption calls : 5612
% 0.38/0.70 # Non-unit clause-clause subsumptions : 25
% 0.38/0.70 # Unit Clause-clause subsumption calls : 65
% 0.38/0.70 # Rewrite failures with RHS unbound : 0
% 0.38/0.70 # BW rewrite match attempts : 4
% 0.38/0.70 # BW rewrite match successes : 4
% 0.38/0.70 # Condensation attempts : 410
% 0.38/0.70 # Condensation successes : 5
% 0.38/0.70 # Termbank termtop insertions : 152845
% 0.38/0.70 # Search garbage collected termcells : 2952
% 0.38/0.70
% 0.38/0.70 # -------------------------------------------------
% 0.38/0.70 # User time : 0.170 s
% 0.38/0.70 # System time : 0.007 s
% 0.38/0.70 # Total time : 0.177 s
% 0.38/0.70 # Maximum resident set size: 2352 pages
% 0.38/0.70
% 0.38/0.70 # -------------------------------------------------
% 0.38/0.70 # User time : 0.213 s
% 0.38/0.70 # System time : 0.034 s
% 0.38/0.70 # Total time : 0.247 s
% 0.38/0.70 # Maximum resident set size: 1800 pages
% 0.38/0.70 % E---3.1 exiting
% 0.38/0.70 % E exiting
%------------------------------------------------------------------------------