%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : AGT027^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 07:44:27 AM UTC 2026
% Result : Theorem 0.95s 0.42s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 87 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 262 ( 24 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 754 ( 123 ~; 112 |; 5 &; 514 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 3 con; 0-3 aty)
% Number of variables : 220 ( 64 ^; 156 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $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_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_34,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
a1: $i > $i > $o ).
thf(decl_55,type,
a2: $i > $i > $o ).
thf(decl_56,type,
a: mu ).
thf(decl_58,type,
p: mu > $i > $o ).
thf(decl_59,type,
q: mu > $i > $o ).
thf(decl_60,type,
r: mu > $i > $o ).
thf(decl_61,type,
s: mu > $i > $o ).
thf(decl_62,type,
esk1_1: $i > $i ).
thf(decl_67,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_72,type,
esk11_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_73,type,
esk12_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_74,type,
esk13_0: $i ).
thf(decl_75,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.B8QFtAdTQi/E---3.1_2410558.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mor) ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.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.B8QFtAdTQi/E---3.1_2410558.p',mbox) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mexists_ind) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mforall_ind) ).
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.B8QFtAdTQi/E---3.1_2410558.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mvalid) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( p @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',conj) ).
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.B8QFtAdTQi/E---3.1_2410558.p',axiom_5_for_a1) ).
thf(axiom_a4,axiom,
mvalid @ ( mdia @ a1 @ ( s @ a ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',axiom_a4) ).
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.B8QFtAdTQi/E---3.1_2410558.p',axiom_I_for_a2_a1) ).
thf(axiom_a3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X1 ) @ ( mbox @ a1 @ ( r @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',axiom_a3) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',mand) ).
thf(axiom_5_for_a2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a2 @ X6 ) ) @ ( mbox @ a2 @ ( mnot @ ( mbox @ a2 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B8QFtAdTQi/E---3.1_2410558.p',axiom_5_for_a2) ).
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.B8QFtAdTQi/E---3.1_2410558.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.B8QFtAdTQi/E---3.1_2410558.p',axiom_a1) ).
thf(c_0_18,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_19,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_20,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_21,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_22,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_23,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_24,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_25,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_18,c_0_19]),c_0_20]) ).
thf(c_0_26,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_27,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_28,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_21,c_0_19]),c_0_22]) ).
thf(c_0_29,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( p @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_30,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_23,c_0_19]),c_0_24]) ).
thf(c_0_31,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_19]),c_0_25]),c_0_26]),c_0_22]),c_0_27])]) ).
thf(c_0_32,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_28]),c_0_27])]) ).
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_25]),c_0_26]),c_0_22]),c_0_27])]) ).
thf(c_0_34,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)],[c_0_29]),c_0_30]),c_0_22]),c_0_27])]) ).
thf(c_0_35,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_31])])])])])]) ).
thf(c_0_36,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_32])])]) ).
thf(c_0_37,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_38,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_34])])])]) ).
thf(c_0_39,plain,
! [X4: $i > $o,X3: $i,X14: $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_35]) ).
thf(c_0_40,plain,
! [X3: $i] : ( a1 @ X3 @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,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_37]) ).
thf(c_0_42,negated_conjecture,
! [X1: mu] : ( a1 @ esk13_0 @ ( esk14_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_43,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_25]),c_0_24]),c_0_22]),c_0_27])]) ).
thf(c_0_44,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk11_3 @ X3 @ X4 @ X14 ) )
| ~ ( a1 @ X3 @ X14 )
| ~ ( a1 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,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_39,c_0_40]) ).
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_37]) ).
thf(c_0_47,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_41,c_0_42]) ).
thf(c_0_48,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_49,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_43])])]) ).
thf(c_0_50,plain,
! [X15: $i,X14: $i,X3: $i] :
( ( a1 @ X3 @ ( esk1_1 @ X14 ) )
| ( a1 @ X3 @ X15 )
| ~ ( a1 @ X14 @ X15 )
| ~ ( a1 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_51,plain,
! [X75: $i,X74: $i > $o] :
( ~ ~ ! [X71: $i] :
( ~ ( a2 @ X75 @ X71 )
| ( X74 @ X71 ) )
| ! [X73: $i] :
( ~ ( a2 @ X75 @ X73 )
| ~ ! [X72: $i] :
( ~ ( a2 @ X73 @ X72 )
| ( X74 @ X72 ) ) ) ),
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_a2]),c_0_19]),c_0_25]),c_0_26]),c_0_22]),c_0_27])]) ).
thf(c_0_52,negated_conjecture,
! [X1: mu,X3: $i] :
( ( a2 @ esk13_0 @ ( esk14_1 @ X1 ) )
| ( a2 @ esk13_0 @ X3 )
| ~ ( a1 @ esk13_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_53,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_48,c_0_19]),c_0_20]) ).
thf(c_0_54,plain,
! [X3: $i,X1: mu,X14: $i,X15: $i] :
( ( r @ X1 @ X15 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( s @ X1 @ X14 )
| ~ ( a1 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_55,plain,
! [X14: $i,X3: $i] :
( ( a1 @ X3 @ ( esk1_1 @ X14 ) )
| ~ ( a1 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_40]) ).
thf(c_0_56,plain,
! [X129: $i,X130: $i > $o,X131: $i,X132: $i] :
( ( ( a2 @ X132 @ ( esk12_3 @ X129 @ X130 @ X132 ) )
| ~ ( a2 @ X129 @ X132 )
| ~ ( a2 @ X129 @ X131 )
| ( X130 @ X131 ) )
& ( ~ ( X130 @ ( esk12_3 @ X129 @ X130 @ X132 ) )
| ~ ( a2 @ X129 @ X132 )
| ~ ( a2 @ X129 @ X131 )
| ( X130 @ X131 ) ) ),
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_51])])])])])]) ).
thf(c_0_57,negated_conjecture,
! [X1: mu,X2: mu] :
( ( a2 @ esk13_0 @ ( esk14_1 @ X1 ) )
| ( a2 @ esk13_0 @ ( esk14_1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
thf(c_0_58,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_53]),c_0_25]),c_0_24]),c_0_22]),c_0_27])]) ).
thf(c_0_59,plain,
! [X1: mu,X3: $i,X14: $i,X15: $i] :
( ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a1 @ X14 @ X15 )
| ~ ( s @ X1 @ X15 )
| ~ ( a1 @ X3 @ X15 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_60,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( a2 @ X3 @ ( esk12_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( a2 @ X14 @ X3 )
| ~ ( a2 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_61,negated_conjecture,
! [X1: mu] : ( a2 @ esk13_0 @ ( esk14_1 @ X1 ) ),
inference(ef,[status(thm)],[c_0_57]) ).
thf(c_0_62,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_25]),c_0_24]),c_0_22]),c_0_28]),c_0_27])]) ).
thf(c_0_63,plain,
! [X4: $i > $o,X3: $i] :
( ( a2 @ X3 @ ( esk6_2 @ X3 @ X4 ) )
| ( X4 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
thf(c_0_64,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_58])])]) ).
thf(c_0_65,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( s @ X1 @ ( esk1_1 @ X14 ) )
| ~ ( a1 @ X3 @ ( esk1_1 @ X14 ) ) ),
inference(spm,[status(thm)],[c_0_59,c_0_40]) ).
thf(c_0_66,plain,
! [X3: $i] : ( s @ a @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_67,negated_conjecture,
! [X1: mu,X4: $i > $o,X3: $i] :
( ( a2 @ X3 @ ( esk12_3 @ esk13_0 @ X4 @ X3 ) )
| ( X4 @ ( esk14_1 @ X1 ) )
| ~ ( a2 @ esk13_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_68,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_62])])])]) ).
thf(c_0_69,plain,
! [X3: $i,X14: $i] :
( ( a2 @ X3 @ ( esk1_1 @ X3 ) )
| ( a2 @ X3 @ X14 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_63]) ).
thf(c_0_70,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_64]) ).
thf(c_0_71,plain,
! [X3: $i,X14: $i] :
( ( r @ a @ ( esk1_1 @ X3 ) )
| ~ ( a1 @ X3 @ ( esk1_1 @ X14 ) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_72,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk12_3 @ X3 @ X4 @ X14 ) )
| ~ ( a2 @ X3 @ X14 )
| ~ ( a2 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_73,negated_conjecture,
! [X1: mu,X4: $i > $o,X2: mu] :
( ( a2 @ ( esk14_1 @ X1 ) @ ( esk12_3 @ esk13_0 @ X4 @ ( esk14_1 @ X1 ) ) )
| ( X4 @ ( esk14_1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_67,c_0_61]) ).
thf(c_0_74,plain,
! [X3: $i,X1: mu,X14: $i,X15: $i] :
( ( p @ X1 @ X14 )
| ~ ( a2 @ X3 @ X14 )
| ~ ( a2 @ X14 @ X15 )
| ~ ( q @ X1 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_75,plain,
! [X3: $i] : ( a2 @ X3 @ ( esk1_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_40]) ).
thf(c_0_76,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_70,c_0_40]) ).
thf(c_0_77,plain,
! [X3: $i] : ( r @ a @ ( esk1_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_40]) ).
thf(c_0_78,negated_conjecture,
! [X1: mu,X2: mu,X3: $i] :
( ( a2 @ ( esk14_1 @ X1 ) @ ( esk14_1 @ X2 ) )
| ( a2 @ ( esk14_1 @ X1 ) @ X3 )
| ~ ( a2 @ esk13_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_61])]) ).
thf(c_0_79,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( p @ X1 @ X3 )
| ~ ( q @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
thf(c_0_80,plain,
! [X3: $i] : ( q @ a @ ( esk1_1 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_66])]) ).
thf(c_0_81,negated_conjecture,
! [X1: mu,X2: mu,X18: mu] :
( ( a2 @ ( esk14_1 @ X1 ) @ ( esk14_1 @ X2 ) )
| ( a2 @ ( esk14_1 @ X1 ) @ ( esk14_1 @ X18 ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_61]) ).
thf(c_0_82,plain,
! [X14: $i,X3: $i] :
( ( p @ a @ X3 )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_83,negated_conjecture,
! [X1: mu,X2: mu] : ( a2 @ ( esk14_1 @ X1 ) @ ( esk14_1 @ X2 ) ),
inference(ef,[status(thm)],[c_0_81]) ).
thf(c_0_84,negated_conjecture,
! [X1: mu] :
~ ( p @ X1 @ ( esk14_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_85,negated_conjecture,
! [X1: mu] : ( p @ a @ ( esk14_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_86,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_84,c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT027^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:28:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.B8QFtAdTQi/E---3.1_2410558.p
% 0.95/0.42 % Version: 3.5.1-ho
% 0.95/0.42 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.95/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.95/0.42 % Starting post_as_ho3 with 300s (1) cores
% 0.95/0.42 % Starting new_ho_12 with 300s (1) cores
% 0.95/0.42 % Starting new_bool_2 with 300s (1) cores
% 0.95/0.42 % new_bool_2 with pid 2410574 completed with status 9
% 0.95/0.42 % new_ho_10_cnf2 with pid 2410571 completed with status 0
% 0.95/0.42 % Result found by new_ho_10_cnf2
% 0.95/0.42 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.95/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.95/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.95/0.42 % No SInE strategy applied
% 0.95/0.42 % Search class: HGUNS-FFMF32-SHSSMMBN
% 0.95/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.95/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.95/0.42 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.95/0.42 % Starting sh5l with 169s (1) cores
% 0.95/0.42 % Starting ehoh_best_sine_rwall with 169s (1) cores
% 0.95/0.42 % Starting lpo1_def_fix with 169s (1) cores
% 0.95/0.42 % SubtermCWHack with pid 2410577 completed with status 0
% 0.95/0.42 % Result found by SubtermCWHack
% 0.95/0.42 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.95/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.95/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.95/0.42 % No SInE strategy applied
% 0.95/0.42 % Search class: HGUNS-FFMF32-SHSSMMBN
% 0.95/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.95/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.95/0.42 % Preprocessing time : 0.001 s
% 0.95/0.42
% 0.95/0.42 % Proof found!
% 0.95/0.42 % SZS status Theorem
% 0.95/0.42 % SZS output start CNFRefutation
% See solution above
% 0.95/0.42 % Parsed axioms : 85
% 0.95/0.42 % Removed by relevancy pruning/SinE : 0
% 0.95/0.42 % Initial clauses : 69
% 0.95/0.42 % Removed in clause preprocessing : 40
% 0.95/0.42 % Initial clauses in saturation : 29
% 0.95/0.42 % Processed clauses : 527
% 0.95/0.42 % ...of these trivial : 20
% 0.95/0.42 % ...subsumed : 48
% 0.95/0.42 % ...remaining for further processing : 459
% 0.95/0.42 % Other redundant clauses eliminated : 0
% 0.95/0.42 % Clauses deleted for lack of memory : 0
% 0.95/0.42 % Backward-subsumed : 41
% 0.95/0.42 % Backward-rewritten : 11
% 0.95/0.42 % Generated clauses : 16832
% 0.95/0.42 % ...of the previous two non-redundant : 16700
% 0.95/0.42 % ...aggressively subsumed : 0
% 0.95/0.42 % Contextual simplify-reflections : 0
% 0.95/0.42 % Paramodulations : 16820
% 0.95/0.42 % Factorizations : 12
% 0.95/0.42 % NegExts : 0
% 0.95/0.42 % Equation resolutions : 0
% 0.95/0.42 % Disequality decompositions : 0
% 0.95/0.42 % Total rewrite steps : 175
% 0.95/0.42 % ...of those cached : 114
% 0.95/0.42 % Propositional unsat checks : 0
% 0.95/0.42 % Propositional check models : 0
% 0.95/0.42 % Propositional check unsatisfiable : 0
% 0.95/0.42 % Propositional clauses : 0
% 0.95/0.42 % Propositional clauses after purity: 0
% 0.95/0.42 % Propositional unsat core size : 0
% 0.95/0.42 % Propositional preprocessing time : 0.000
% 0.95/0.42 % Propositional encoding time : 0.000
% 0.95/0.42 % Propositional solver time : 0.000
% 0.95/0.42 % Success case prop preproc time : 0.000
% 0.95/0.42 % Success case prop encoding time : 0.000
% 0.95/0.42 % Success case prop solver time : 0.000
% 0.95/0.42 % Current number of processed clauses : 407
% 0.95/0.42 % Positive orientable unit clauses : 53
% 0.95/0.42 % Positive unorientable unit clauses: 0
% 0.95/0.42 % Negative unit clauses : 1
% 0.95/0.42 % Non-unit-clauses : 353
% 0.95/0.42 % Current number of unprocessed clauses: 16142
% 0.95/0.42 % ...number of literals in the above : 56124
% 0.95/0.42 % Current number of archived formulas : 0
% 0.95/0.42 % Current number of archived clauses : 52
% 0.95/0.42 % Clause-clause subsumption calls (NU) : 8168
% 0.95/0.42 % Rec. Clause-clause subsumption calls : 5298
% 0.95/0.42 % Non-unit clause-clause subsumptions : 56
% 0.95/0.42 % Unit Clause-clause subsumption calls : 779
% 0.95/0.42 % Rewrite failures with RHS unbound : 0
% 0.95/0.42 % BW rewrite match attempts : 32
% 0.95/0.42 % BW rewrite match successes : 32
% 0.95/0.42 % Condensation attempts : 0
% 0.95/0.42 % Condensation successes : 0
% 0.95/0.42 % Termbank termtop insertions : 328035
% 0.95/0.42 % Search garbage collected termcells : 2951
% 0.95/0.42
% 0.95/0.42 % -------------------------------------------------
% 0.95/0.42 % User time : 0.149 s
% 0.95/0.42 % System time : 0.009 s
% 0.95/0.42 % Total time : 0.159 s
% 0.95/0.42 % Maximum resident set size: 4224 pages
% 0.95/0.42
% 0.95/0.42 % -------------------------------------------------
% 0.95/0.42 % User time : 0.761 s
% 0.95/0.42 % System time : 0.070 s
% 0.95/0.42 % Total time : 0.831 s
% 0.95/0.42 % Maximum resident set size: 4864 pages
% 0.95/0.42 % E exiting
%------------------------------------------------------------------------------