TSTP Solution File: NUM692^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM692^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 01:15:37 EDT 2024
% Result : Theorem 0.36s 0.64s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 33
% Syntax : Number of formulae : 78 ( 33 unt; 19 typ; 0 def)
% Number of atoms : 283 ( 47 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 673 ( 70 ~; 53 |; 10 &; 491 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 113 ( 72 ^ 41 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_72,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_152,type,
lessis: $i > $i > $o ).
thf(decl_155,type,
esk1_0: $i ).
thf(decl_156,type,
esk2_0: $i ).
thf(decl_157,type,
esk3_0: $i ).
thf(decl_158,type,
esk4_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_iii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lessis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
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/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(satz23a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X321: $i] : ( in @ X321 @ nat )
@ ^ [X322: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( lessis @ X1 @ X322 )
=> ( ( lessis @ X4 @ X13 )
=> ( lessis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X322 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23a) ).
thf(satz22d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X317: $i] : ( in @ X317 @ nat )
@ ^ [X318: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X318 )
=> ( ( lessis @ X4 @ X13 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X318 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22d) ).
thf(satz19c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X271: $i] : ( in @ X271 @ nat )
@ ^ [X272: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X272 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X272 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19c) ).
thf(satz19f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X277: $i] : ( in @ X277 @ nat )
@ ^ [X278: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X278 )
=> ( iii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X278 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19f) ).
thf(c_0_14,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_15,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_16,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_17,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_18,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_20,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_21,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,def_n_some]) ).
thf(c_0_22,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).
thf(c_0_23,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_19]) ).
thf(c_0_24,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_25,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_26,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_27,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
~ ! [X393: $i] :
( ( in @ X393 @ nat )
=> ! [X392: $i] :
( ( in @ X392 @ nat )
=> ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X392 @ X393 ) )
=> ~ $true )
=> ( X393 = X392 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X390 @ X391 ) )
=> ~ $true )
=> ( X391 = X390 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X392 @ X390 ) @ ( n_pl @ X393 @ X391 ) ) )
=> ~ $true )
=> ( ( n_pl @ X393 @ X391 )
= ( n_pl @ X392 @ X390 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz23a])]),c_0_26]),c_0_27]) ).
thf(c_0_29,plain,
! [X488: $i] :
( ( in @ X488 @ nat )
=> ! [X487: $i] :
( ( in @ X487 @ nat )
=> ! [X486: $i] :
( ( in @ X486 @ nat )
=> ! [X485: $i] :
( ( in @ X485 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X487 @ X488 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X485 @ X486 ) )
=> ~ $true )
=> ( X486 = X485 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X487 @ X485 ) @ ( n_pl @ X488 @ X486 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22d]),c_0_26]),c_0_27]),c_0_21]) ).
thf(c_0_30,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_0 ) )
& ( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
| ( esk3_0 = esk4_0 ) )
& ( $true
| ( esk3_0 = esk4_0 ) )
& ( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) )
| ~ $true )
& ( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).
thf(c_0_31,plain,
! [X692: $i,X693: $i,X694: $i,X695: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X695 @ X694 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X693 @ X695 ) @ ( n_pl @ X692 @ X694 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X693 @ X692 ) )
| ~ ( in @ X695 @ nat )
| ~ ( in @ X694 @ nat )
| ~ ( in @ X693 @ nat )
| ~ ( in @ X692 @ nat ) )
& ( ( X694 != X695 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X693 @ X695 ) @ ( n_pl @ X692 @ X694 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X693 @ X692 ) )
| ~ ( in @ X695 @ nat )
| ~ ( in @ X694 @ nat )
| ~ ( in @ X693 @ nat )
| ~ ( in @ X692 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])]) ).
thf(c_0_32,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_33,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X6 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(cn,[status(thm)],[c_0_32]) ).
thf(c_0_35,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_33]) ).
thf(c_0_36,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_40,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ~ ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) ) ),
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_34,c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39])]) ).
thf(c_0_41,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
| ( esk3_0 = esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,plain,
! [X423: $i] :
( ( in @ X423 @ nat )
=> ! [X422: $i] :
( ( in @ X422 @ nat )
=> ! [X421: $i] :
( ( in @ X421 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X422 @ X423 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X422 @ X421 ) @ ( n_pl @ X423 @ X421 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19c]),c_0_27]),c_0_21]) ).
thf(c_0_43,negated_conjecture,
( ( esk4_0 = esk3_0 )
| ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,plain,
! [X628: $i,X629: $i,X630: $i] :
( ~ ( in @ X628 @ nat )
| ~ ( in @ X629 @ nat )
| ~ ( in @ X630 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X629 @ X628 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X629 @ X630 ) @ ( n_pl @ X628 @ X630 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
thf(c_0_45,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
thf(c_0_46,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X4 @ X5 ) @ ( n_pl @ X1 @ X5 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_47,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_48,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38]),c_0_37]),c_0_36])]) ).
thf(c_0_49,plain,
! [X429: $i] :
( ( in @ X429 @ nat )
=> ! [X428: $i] :
( ( in @ X428 @ nat )
=> ! [X427: $i] :
( ( in @ X427 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X428 @ X429 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X427 @ X428 ) @ ( n_pl @ X427 @ X429 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_27]),c_0_21]) ).
thf(c_0_50,negated_conjecture,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_51,plain,
! [X634: $i,X635: $i,X636: $i] :
( ~ ( in @ X634 @ nat )
| ~ ( in @ X635 @ nat )
| ~ ( in @ X636 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X635 @ X634 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X636 @ X635 ) @ ( n_pl @ X636 @ X634 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
thf(c_0_52,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
thf(c_0_53,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X4 ) @ ( n_pl @ X5 @ X1 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_54,negated_conjecture,
( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_55,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_36]),c_0_39]),c_0_38])]) ).
thf(c_0_56,negated_conjecture,
( ( n_pl @ esk1_0 @ esk4_0 )
!= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_54,c_0_50]) ).
thf(c_0_57,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_41,c_0_55]) ).
thf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM692^4 : TPTP v8.2.0. Released v7.1.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 04:36:38 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.21/0.50 Running higher-order theorem proving
% 0.21/0.50 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/benchmark/theBenchmark.p
% 0.36/0.64 # Version: 3.1.0-ho
% 0.36/0.64 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.36/0.64 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.64 # Starting lpo1_fix with 900s (3) cores
% 0.36/0.64 # Starting full_lambda_9 with 300s (1) cores
% 0.36/0.64 # Starting almost_fo_4 with 300s (1) cores
% 0.36/0.64 # Starting new_ho_9 with 300s (1) cores
% 0.36/0.64 # Starting pre_casc_4 with 300s (1) cores
% 0.36/0.64 # Starting ho_unfolding_6 with 300s (1) cores
% 0.36/0.64 # full_lambda_9 with pid 11938 completed with status 0
% 0.36/0.64 # Result found by full_lambda_9
% 0.36/0.64 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.36/0.64 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.64 # Starting lpo1_fix with 900s (3) cores
% 0.36/0.64 # Starting full_lambda_9 with 300s (1) cores
% 0.36/0.64 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.36/0.64 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.36/0.64 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.36/0.64 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.64 # Starting full_lambda_5 with 25s (1) cores
% 0.36/0.64 # full_lambda_5 with pid 11944 completed with status 0
% 0.36/0.64 # Result found by full_lambda_5
% 0.36/0.64 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.36/0.64 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.64 # Starting lpo1_fix with 900s (3) cores
% 0.36/0.64 # Starting full_lambda_9 with 300s (1) cores
% 0.36/0.64 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.36/0.64 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.36/0.64 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.36/0.64 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.64 # Starting full_lambda_5 with 25s (1) cores
% 0.36/0.64 # Preprocessing time : 0.006 s
% 0.36/0.64 # Presaturation interreduction done
% 0.36/0.64
% 0.36/0.64 # Proof found!
% 0.36/0.64 # SZS status Theorem
% 0.36/0.64 # SZS output start CNFRefutation
% See solution above
% 0.36/0.64 # Parsed axioms : 396
% 0.36/0.64 # Removed by relevancy pruning/SinE : 263
% 0.36/0.64 # Initial clauses : 358
% 0.36/0.64 # Removed in clause preprocessing : 181
% 0.36/0.64 # Initial clauses in saturation : 177
% 0.36/0.64 # Processed clauses : 388
% 0.36/0.64 # ...of these trivial : 5
% 0.36/0.64 # ...subsumed : 96
% 0.36/0.64 # ...remaining for further processing : 287
% 0.36/0.64 # Other redundant clauses eliminated : 26
% 0.36/0.64 # Clauses deleted for lack of memory : 0
% 0.36/0.64 # Backward-subsumed : 5
% 0.36/0.64 # Backward-rewritten : 6
% 0.36/0.64 # Generated clauses : 780
% 0.36/0.64 # ...of the previous two non-redundant : 750
% 0.36/0.64 # ...aggressively subsumed : 0
% 0.36/0.64 # Contextual simplify-reflections : 1
% 0.36/0.64 # Paramodulations : 582
% 0.36/0.64 # Factorizations : 2
% 0.36/0.64 # NegExts : 2
% 0.36/0.64 # Equation resolutions : 32
% 0.36/0.64 # Disequality decompositions : 0
% 0.36/0.64 # Total rewrite steps : 126
% 0.36/0.64 # ...of those cached : 109
% 0.36/0.64 # Propositional unsat checks : 0
% 0.36/0.64 # Propositional check models : 0
% 0.36/0.64 # Propositional check unsatisfiable : 0
% 0.36/0.64 # Propositional clauses : 0
% 0.36/0.64 # Propositional clauses after purity: 0
% 0.36/0.64 # Propositional unsat core size : 0
% 0.36/0.64 # Propositional preprocessing time : 0.000
% 0.36/0.64 # Propositional encoding time : 0.000
% 0.36/0.64 # Propositional solver time : 0.000
% 0.36/0.64 # Success case prop preproc time : 0.000
% 0.36/0.64 # Success case prop encoding time : 0.000
% 0.36/0.64 # Success case prop solver time : 0.000
% 0.36/0.64 # Current number of processed clauses : 143
% 0.36/0.64 # Positive orientable unit clauses : 20
% 0.36/0.64 # Positive unorientable unit clauses: 0
% 0.36/0.64 # Negative unit clauses : 16
% 0.36/0.64 # Non-unit-clauses : 107
% 0.36/0.64 # Current number of unprocessed clauses: 650
% 0.36/0.64 # ...number of literals in the above : 3289
% 0.36/0.64 # Current number of archived formulas : 0
% 0.36/0.64 # Current number of archived clauses : 126
% 0.36/0.64 # Clause-clause subsumption calls (NU) : 5112
% 0.36/0.64 # Rec. Clause-clause subsumption calls : 1193
% 0.36/0.64 # Non-unit clause-clause subsumptions : 91
% 0.36/0.64 # Unit Clause-clause subsumption calls : 124
% 0.36/0.64 # Rewrite failures with RHS unbound : 0
% 0.36/0.64 # BW rewrite match attempts : 6
% 0.36/0.64 # BW rewrite match successes : 2
% 0.36/0.64 # Condensation attempts : 0
% 0.36/0.64 # Condensation successes : 0
% 0.36/0.64 # Termbank termtop insertions : 67723
% 0.36/0.64 # Search garbage collected termcells : 18326
% 0.36/0.64
% 0.36/0.64 # -------------------------------------------------
% 0.36/0.64 # User time : 0.078 s
% 0.36/0.64 # System time : 0.012 s
% 0.36/0.64 # Total time : 0.090 s
% 0.36/0.64 # Maximum resident set size: 5048 pages
% 0.36/0.64
% 0.36/0.64 # -------------------------------------------------
% 0.36/0.64 # User time : 0.091 s
% 0.36/0.64 # System time : 0.014 s
% 0.36/0.64 # Total time : 0.106 s
% 0.36/0.64 # Maximum resident set size: 2380 pages
% 0.36/0.64 % E---3.1 exiting
% 0.36/0.64 % E exiting
%------------------------------------------------------------------------------