TSTP Solution File: NUM827^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM827^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 : 600s
% DateTime : Mon Jul 18 13:56:54 EDT 2022
% Result : Theorem 2.33s 2.58s
% Output : Proof 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 61 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 362 ( 67 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 396 ( 75 ~; 50 |; 5 &; 234 @)
% ( 0 <=>; 31 =>; 1 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 24 con; 0-2 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_cPA_1,definition,
( cPA_1
= ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ) ) ).
thf(def_cPA_2,definition,
( cPA_2
= ( ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) ) ) ).
thf(def_cPA_IND_EQ,definition,
( cPA_IND_EQ
= ( ! [X1: n > n,X2: n > n] :
( ~ ( ( ( X1 @ c0 )
= ( X2 @ c0 ) )
=> ~ ! [X3: n] :
( ( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( ( X1 @ ( cS @ X3 ) )
= ( X2 @ ( cS @ X3 ) ) ) ) )
=> ! [X3: n] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ) ).
thf(cPA_THM2,conjecture,
( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n > n,X2: n > n] :
( ~ ( ( ( X1 @ c0 )
= ( X2 @ c0 ) )
=> ~ ! [X3: n] :
( ( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( ( X1 @ ( cS @ X3 ) )
= ( X2 @ ( cS @ X3 ) ) ) ) )
=> ! [X3: n] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n > n,X2: n > n] :
( ~ ( ( ( X1 @ c0 )
= ( X2 @ c0 ) )
=> ~ ! [X3: n] :
( ( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( ( X1 @ ( cS @ X3 ) )
= ( X2 @ ( cS @ X3 ) ) ) ) )
=> ! [X3: n] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPA_THM2]) ).
thf(ax1474,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1474) ).
thf(ax1475,axiom,
~ p1,
file('<stdin>',ax1475) ).
thf(ax1452,axiom,
( ~ p18
| p23 ),
file('<stdin>',ax1452) ).
thf(ax1456,axiom,
( p2
| p18 ),
file('<stdin>',ax1456) ).
thf(ax1457,axiom,
( p2
| ~ p17 ),
file('<stdin>',ax1457) ).
thf(ax1453,axiom,
( ~ p23
| p22 ),
file('<stdin>',ax1453) ).
thf(ax1473,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1473) ).
thf(pax21,axiom,
( p21
=> ( ( ( fc_plus @ fc0 @ fc0 )
= ( fc_plus @ fc0 @ fc0 ) )
=> ~ ! [X101: n] :
( ( ( fc_plus @ X101 @ fc0 )
= ( fc_plus @ fc0 @ X101 ) )
=> ( ( fc_plus @ ( fcS @ X101 ) @ fc0 )
= ( fc_plus @ fc0 @ ( fcS @ X101 ) ) ) ) ) ),
file('<stdin>',pax21) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ! [X116: n] :
( ( fc_plus @ X116 @ fc0 )
= X116 )
=> ~ ! [X116: n,X117: n] :
( ( fc_plus @ X116 @ ( fcS @ X117 ) )
= ( fcS @ ( fc_plus @ X116 @ X117 ) ) ) )
=> ~ ! [X118: n > n,X119: n > n] :
( ~ ( ( ( X118 @ fc0 )
= ( X119 @ fc0 ) )
=> ~ ! [X6: n] :
( ( ( X118 @ X6 )
= ( X119 @ X6 ) )
=> ( ( X118 @ ( fcS @ X6 ) )
= ( X119 @ ( fcS @ X6 ) ) ) ) )
=> ! [X6: n] :
( ( X118 @ X6 )
= ( X119 @ X6 ) ) ) )
=> ! [X120: n] :
( ( fc_plus @ X120 @ fc0 )
= ( fc_plus @ fc0 @ X120 ) ) ) ),
file('<stdin>',nax1) ).
thf(ax1454,axiom,
( ~ p22
| p21
| p3 ),
file('<stdin>',ax1454) ).
thf(ax1138,axiom,
( ~ p290
| p298 ),
file('<stdin>',ax1138) ).
thf(ax1146,axiom,
( p17
| p290 ),
file('<stdin>',ax1146) ).
thf(pax298,axiom,
( p298
=> ! [X69: n] :
( ( fc_plus @ fc0 @ ( fcS @ X69 ) )
= ( fcS @ ( fc_plus @ fc0 @ X69 ) ) ) ),
file('<stdin>',pax298) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1474]) ).
thf(c_0_14,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1475]) ).
thf(c_0_15,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
( ~ p18
| p23 ),
inference(fof_simplification,[status(thm)],[ax1452]) ).
thf(c_0_18,plain,
( p2
| p18 ),
inference(split_conjunct,[status(thm)],[ax1456]) ).
thf(c_0_19,plain,
~ p2,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
( p2
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax1457]) ).
thf(c_0_21,plain,
( ~ p23
| p22 ),
inference(fof_simplification,[status(thm)],[ax1453]) ).
thf(c_0_22,plain,
( p23
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
p18,
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1473]) ).
thf(c_0_25,plain,
( p2
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
( ( ( ( fc_plus @ esk1243_0 @ fc0 )
= ( fc_plus @ fc0 @ esk1243_0 ) )
| ( ( fc_plus @ fc0 @ fc0 )
!= ( fc_plus @ fc0 @ fc0 ) )
| ~ p21 )
& ( ( ( fc_plus @ ( fcS @ esk1243_0 ) @ fc0 )
!= ( fc_plus @ fc0 @ ( fcS @ esk1243_0 ) ) )
| ( ( fc_plus @ fc0 @ fc0 )
!= ( fc_plus @ fc0 @ fc0 ) )
| ~ p21 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax21])])])]) ).
thf(c_0_27,plain,
! [X2659: n,X2660: n,X2661: n,X2662: n > n,X2663: n > n,X2665: n] :
( ( ( ( fc_plus @ X2659 @ fc0 )
= X2659 )
| p1 )
& ( ( ( fc_plus @ X2660 @ ( fcS @ X2661 ) )
= ( fcS @ ( fc_plus @ X2660 @ X2661 ) ) )
| p1 )
& ( ( ( X2662 @ ( esk1272_2 @ X2662 @ X2663 ) )
= ( X2663 @ ( esk1272_2 @ X2662 @ X2663 ) ) )
| ( ( X2662 @ fc0 )
!= ( X2663 @ fc0 ) )
| ( ( X2662 @ X2665 )
= ( X2663 @ X2665 ) )
| p1 )
& ( ( ( X2662 @ ( fcS @ ( esk1272_2 @ X2662 @ X2663 ) ) )
!= ( X2663 @ ( fcS @ ( esk1272_2 @ X2662 @ X2663 ) ) ) )
| ( ( X2662 @ fc0 )
!= ( X2663 @ fc0 ) )
| ( ( X2662 @ X2665 )
= ( X2663 @ X2665 ) )
| p1 )
& ( ( ( fc_plus @ esk1273_0 @ fc0 )
!= ( fc_plus @ fc0 @ esk1273_0 ) )
| p1 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])]) ).
thf(c_0_28,plain,
( ~ p22
| p21
| p3 ),
inference(fof_simplification,[status(thm)],[ax1454]) ).
thf(c_0_29,plain,
( p22
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,plain,
p23,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_31,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,plain,
( ~ p290
| p298 ),
inference(fof_simplification,[status(thm)],[ax1138]) ).
thf(c_0_33,plain,
( p17
| p290 ),
inference(split_conjunct,[status(thm)],[ax1146]) ).
thf(c_0_34,plain,
~ p17,
inference(sr,[status(thm)],[c_0_25,c_0_19]) ).
thf(c_0_35,plain,
( ( ( fc_plus @ ( fcS @ esk1243_0 ) @ fc0 )
!= ( fc_plus @ fc0 @ ( fcS @ esk1243_0 ) ) )
| ( ( fc_plus @ fc0 @ fc0 )
!= ( fc_plus @ fc0 @ fc0 ) )
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_36,plain,
! [X1: n] :
( ( ( fc_plus @ X1 @ fc0 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_37,plain,
( p21
| p3
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,plain,
p22,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
thf(c_0_39,plain,
~ p3,
inference(sr,[status(thm)],[c_0_31,c_0_16]) ).
thf(c_0_40,plain,
! [X2063: n] :
( ~ p298
| ( ( fc_plus @ fc0 @ ( fcS @ X2063 ) )
= ( fcS @ ( fc_plus @ fc0 @ X2063 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax298])])]) ).
thf(c_0_41,plain,
( p298
| ~ p290 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,plain,
p290,
inference(sr,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_43,plain,
( ( ( fc_plus @ esk1243_0 @ fc0 )
= ( fc_plus @ fc0 @ esk1243_0 ) )
| ( ( fc_plus @ fc0 @ fc0 )
!= ( fc_plus @ fc0 @ fc0 ) )
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_44,plain,
( ( ( fc_plus @ ( fcS @ esk1243_0 ) @ fc0 )
!= ( fc_plus @ fc0 @ ( fcS @ esk1243_0 ) ) )
| ~ p21 ),
inference(cn,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
! [X1: n] :
( ( fc_plus @ X1 @ fc0 )
= X1 ),
inference(sr,[status(thm)],[c_0_36,c_0_16]) ).
thf(c_0_46,plain,
p21,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),c_0_39]) ).
thf(c_0_47,plain,
! [X1: n] :
( ( ( fc_plus @ fc0 @ ( fcS @ X1 ) )
= ( fcS @ ( fc_plus @ fc0 @ X1 ) ) )
| ~ p298 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
p298,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_49,plain,
( ( ( fc_plus @ esk1243_0 @ fc0 )
= ( fc_plus @ fc0 @ esk1243_0 ) )
| ~ p21 ),
inference(cn,[status(thm)],[c_0_43]) ).
thf(c_0_50,plain,
( fc_plus @ fc0 @ ( fcS @ esk1243_0 ) )
!= ( fcS @ esk1243_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
thf(c_0_51,plain,
! [X1: n] :
( ( fc_plus @ fc0 @ ( fcS @ X1 ) )
= ( fcS @ ( fc_plus @ fc0 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_52,plain,
( ( fc_plus @ fc0 @ esk1243_0 )
= esk1243_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_45]),c_0_46])]) ).
thf(c_0_53,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n > n,X2: n > n] :
( ~ ( ( ( X1 @ c0 )
= ( X2 @ c0 ) )
=> ~ ! [X3: n] :
( ( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( ( X1 @ ( cS @ X3 ) )
= ( X2 @ ( cS @ X3 ) ) ) ) )
=> ! [X3: n] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM827^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 05:54:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.33/2.58 % SZS status Theorem
% 2.33/2.58 % Mode: mode506
% 2.33/2.58 % Inferences: 39166
% 2.33/2.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------