%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM738^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:16:58 AM UTC 2026
% Result : Theorem 36.40s 5.78s
% Output : CNFRefutation 36.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 71 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 599 ( 22 ~; 18 |; 7 &; 526 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 125 ( 104 ^; 21 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_190,type,
frac: $i ).
thf(decl_192,type,
num: $i > $i ).
thf(decl_193,type,
den: $i > $i ).
thf(decl_194,type,
n_eq: $i > $i > $o ).
thf(decl_195,type,
moref: $i > $i > $o ).
thf(decl_196,type,
lessf: $i > $i > $o ).
thf(decl_198,type,
esk1_0: $i ).
thf(decl_199,type,
esk2_0: $i ).
thf(decl_200,type,
esk3_0: $i ).
thf(decl_201,type,
esk4_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_e_is) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_n_is) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_d_29_ii) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_iii) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_moref) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_n_some) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_n_eq) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_is_of) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',def_lessf) ).
thf(satz45,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X463: $i] : ( in @ X463 @ frac )
@ ^ [X464: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( lessf @ X1 @ X464 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X464 @ X13 )
=> ( lessf @ X4 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',satz45) ).
thf(satz44,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X461: $i] : ( in @ X461 @ frac )
@ ^ [X462: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moref @ X1 @ X462 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X462 @ X13 )
=> ( moref @ X4 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p',satz44) ).
thf(c_0_13,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_14,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_15,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_13]) ).
thf(c_0_16,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_17,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_19,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_20,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_17]),def_n_some]) ).
thf(c_0_21,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_22,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_23,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_24,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_25,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_17]),def_n_some]) ).
thf(c_0_26,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_27,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_15]) ).
thf(c_0_28,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_29,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X463: $i] : ( in @ X463 @ frac )
@ ^ [X464: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( lessf @ X1 @ X464 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X464 @ X13 )
=> ( lessf @ X4 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz45]) ).
thf(c_0_30,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_31,plain,
! [X599: $i] :
( ( in @ X599 @ frac )
=> ! [X598: $i] :
( ( in @ X598 @ frac )
=> ! [X597: $i] :
( ( in @ X597 @ frac )
=> ! [X596: $i] :
( ( in @ X596 @ frac )
=> ( ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X599 ) @ ( den @ X598 ) )
= ( n_pl @ ( n_ts @ ( num @ X598 ) @ ( den @ X599 ) ) @ Z0 ) ) )
=> ( ( ( n_ts @ ( num @ X599 ) @ ( den @ X597 ) )
= ( n_ts @ ( num @ X597 ) @ ( den @ X599 ) ) )
=> ( ( ( n_ts @ ( num @ X598 ) @ ( den @ X596 ) )
= ( n_ts @ ( num @ X596 ) @ ( den @ X598 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X597 ) @ ( den @ X596 ) )
= ( n_pl @ ( n_ts @ ( num @ X596 ) @ ( den @ X597 ) ) @ Z0 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz44]),c_0_26]),c_0_27]),c_0_28]) ).
thf(c_0_32,negated_conjecture,
~ ! [X508: $i] :
( ( in @ X508 @ frac )
=> ! [X507: $i] :
( ( in @ X507 @ frac )
=> ! [X506: $i] :
( ( in @ X506 @ frac )
=> ! [X505: $i] :
( ( in @ X505 @ frac )
=> ( ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X507 ) @ ( den @ X508 ) )
= ( n_pl @ ( n_ts @ ( num @ X508 ) @ ( den @ X507 ) ) @ Z0 ) ) )
=> ( ( ( n_ts @ ( num @ X508 ) @ ( den @ X506 ) )
= ( n_ts @ ( num @ X506 ) @ ( den @ X508 ) ) )
=> ( ( ( n_ts @ ( num @ X507 ) @ ( den @ X505 ) )
= ( n_ts @ ( num @ X505 ) @ ( den @ X507 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X505 ) @ ( den @ X506 ) )
= ( n_pl @ ( n_ts @ ( num @ X506 ) @ ( den @ X505 ) ) @ Z0 ) ) ) ) ) ) ) ) ) ),
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_27]),c_0_30]),c_0_28]) ).
thf(c_0_33,plain,
! [X811: $i,X812: $i,X813: $i,X814: $i] :
( ~ ( in @ X811 @ frac )
| ~ ( in @ X812 @ frac )
| ~ ( in @ X813 @ frac )
| ~ ( in @ X814 @ frac )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X811 ) @ ( den @ X812 ) )
= ( n_pl @ ( n_ts @ ( num @ X812 ) @ ( den @ X811 ) ) @ Z0 ) ) )
| ( ( n_ts @ ( num @ X811 ) @ ( den @ X813 ) )
!= ( n_ts @ ( num @ X813 ) @ ( den @ X811 ) ) )
| ( ( n_ts @ ( num @ X812 ) @ ( den @ X814 ) )
!= ( n_ts @ ( num @ X814 ) @ ( den @ X812 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X813 ) @ ( den @ X814 ) )
= ( n_pl @ ( n_ts @ ( num @ X814 ) @ ( den @ X813 ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
thf(c_0_34,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( in @ esk4_0 @ frac )
& ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) )
= ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
& ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) )
= ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) )
& ( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk4_0 ) )
= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk2_0 ) ) )
& ~ ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) )
= ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
thf(c_0_35,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) )
= ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ frac )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
= ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ Z0 ) ) )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) )
!= ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
!= ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_36,negated_conjecture,
( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) )
= ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_37,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_38,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_39,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) )
= ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_40,negated_conjecture,
! [X4: $i,X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] :
( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
= ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ Z0 ) ) )
| ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ X4 ) )
!= ( n_ts @ ( num @ X4 ) @ ( den @ esk1_0 ) ) )
| ( ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) )
!= ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
thf(c_0_41,negated_conjecture,
( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) )
= ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_42,negated_conjecture,
( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk4_0 ) )
= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_43,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_44,negated_conjecture,
in @ esk4_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM738^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n001.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 12:52:50 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 Running higher-order theorem proving
% 0.32/0.41 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.kfcUAhUtup/E---3.1_1187074.p
% 36.40/5.77 % Version: 3.5.1-ho
% 36.40/5.77 % Preprocessing class: HSLMSMSMLLLCHSA.
% 36.40/5.77 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 36.40/5.77 % Starting pre_casc_4 with 1200s (4) cores
% 36.40/5.77 % Starting full_lambda_6 with 300s (1) cores
% 36.40/5.77 % Starting sh10 with 300s (1) cores
% 36.40/5.77 % Starting post_as_ho9 with 300s (1) cores
% 36.40/5.77 % Starting post_as_ho8 with 300s (1) cores
% 36.40/5.77 % pre_casc_4 with pid 1187098 completed with status 0
% 36.40/5.77 % Result found by pre_casc_4
% 36.40/5.77 % Preprocessing class: HSLMSMSMLLLCHSA.
% 36.40/5.77 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 36.40/5.77 % Starting pre_casc_4 with 1200s (4) cores
% 36.40/5.77 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 36.40/5.77 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 36.40/5.77 % Search class: HGUSM-FFLM31-DHSMMFBN
% 36.40/5.77 % partial match(3): HGUSM-FSLM31-DHSFFFBN
% 36.40/5.77 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 36.40/5.77 % Starting SubtermCWHack with 109s (1) cores
% 36.40/5.77 % Starting pre_casc_4 with 121s (1) cores
% 36.40/5.77 % Starting sh5l with 135s (1) cores
% 36.40/5.78 % Starting ehoh_best8_lambda with 135s (1) cores
% 36.40/5.78 % pre_casc_4 with pid 1187108 completed with status 0
% 36.40/5.78 % Result found by pre_casc_4
% 36.40/5.78 % Preprocessing class: HSLMSMSMLLLCHSA.
% 36.40/5.78 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 36.40/5.78 % Starting pre_casc_4 with 1200s (4) cores
% 36.40/5.78 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 36.40/5.78 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 36.40/5.78 % Search class: HGUSM-FFLM31-DHSMMFBN
% 36.40/5.78 % partial match(3): HGUSM-FSLM31-DHSFFFBN
% 36.40/5.78 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 36.40/5.78 % Starting SubtermCWHack with 109s (1) cores
% 36.40/5.78 % Starting pre_casc_4 with 121s (1) cores
% 36.40/5.78 % Preprocessing time : 0.005 s
% 36.40/5.78 % Presaturation interreduction done
% 36.40/5.78
% 36.40/5.78 % Proof found!
% 36.40/5.78 % SZS status Theorem
% 36.40/5.78 % SZS output start CNFRefutation
% See solution above
% 36.40/5.78 % Parsed axioms : 547
% 36.40/5.78 % Removed by relevancy pruning/SinE : 424
% 36.40/5.78 % Initial clauses : 133
% 36.40/5.78 % Removed in clause preprocessing : 14
% 36.40/5.78 % Initial clauses in saturation : 119
% 36.40/5.78 % Processed clauses : 7497
% 36.40/5.78 % ...of these trivial : 315
% 36.40/5.78 % ...subsumed : 3050
% 36.40/5.78 % ...remaining for further processing : 4132
% 36.40/5.78 % Other redundant clauses eliminated : 27
% 36.40/5.78 % Clauses deleted for lack of memory : 0
% 36.40/5.78 % Backward-subsumed : 2
% 36.40/5.78 % Backward-rewritten : 344
% 36.40/5.78 % Generated clauses : 199797
% 36.40/5.78 % ...of the previous two non-redundant : 187810
% 36.40/5.78 % ...aggressively subsumed : 0
% 36.40/5.78 % Contextual simplify-reflections : 35
% 36.40/5.78 % Paramodulations : 187446
% 36.40/5.78 % Factorizations : 0
% 36.40/5.78 % NegExts : 501
% 36.40/5.78 % Equation resolutions : 67
% 36.40/5.78 % Disequality decompositions : 0
% 36.40/5.78 % Total rewrite steps : 65018
% 36.40/5.78 % ...of those cached : 64912
% 36.40/5.78 % Propositional unsat checks : 0
% 36.40/5.78 % Propositional check models : 0
% 36.40/5.78 % Propositional check unsatisfiable : 0
% 36.40/5.78 % Propositional clauses : 0
% 36.40/5.78 % Propositional clauses after purity: 0
% 36.40/5.78 % Propositional unsat core size : 0
% 36.40/5.78 % Propositional preprocessing time : 0.000
% 36.40/5.78 % Propositional encoding time : 0.000
% 36.40/5.78 % Propositional solver time : 0.000
% 36.40/5.78 % Success case prop preproc time : 0.000
% 36.40/5.78 % Success case prop encoding time : 0.000
% 36.40/5.78 % Success case prop solver time : 0.000
% 36.40/5.78 % Current number of processed clauses : 3596
% 36.40/5.78 % Positive orientable unit clauses : 116
% 36.40/5.78 % Positive unorientable unit clauses: 0
% 36.40/5.78 % Negative unit clauses : 416
% 36.40/5.78 % Non-unit-clauses : 3064
% 36.40/5.78 % Current number of unprocessed clauses: 180027
% 36.40/5.78 % ...number of literals in the above : 610439
% 36.40/5.78 % Current number of archived formulas : 0
% 36.40/5.78 % Current number of archived clauses : 526
% 36.40/5.78 % Clause-clause subsumption calls (NU) : 2740769
% 36.40/5.78 % Rec. Clause-clause subsumption calls : 460526
% 36.40/5.78 % Non-unit clause-clause subsumptions : 585
% 36.40/5.78 % Unit Clause-clause subsumption calls : 30639
% 36.40/5.78 % Rewrite failures with RHS unbound : 0
% 36.40/5.78 % BW rewrite match attempts : 84
% 36.40/5.78 % BW rewrite match successes : 45
% 36.40/5.78 % Condensation attempts : 0
% 36.40/5.78 % Condensation successes : 0
% 36.40/5.78 % Termbank termtop insertions : 7320683
% 36.40/5.78 % Search garbage collected termcells : 14873
% 36.40/5.78
% 36.40/5.78 % -------------------------------------------------
% 36.40/5.78 % User time : 5.031 s
% 36.40/5.78 % System time : 0.166 s
% 36.40/5.78 % Total time : 5.197 s
% 36.40/5.78 % Maximum resident set size: 6628 pages
% 36.40/5.78
% 36.40/5.78 % -------------------------------------------------
% 36.40/5.78 % User time : 19.915 s
% 36.40/5.78 % System time : 0.554 s
% 36.40/5.78 % Total time : 20.469 s
% 36.40/5.78 % Maximum resident set size: 5632 pages
% 36.40/5.78 % E exiting
%------------------------------------------------------------------------------