TSTP Solution File: NUM651^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM651^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 13:54:38 EDT 2022
% Result : Theorem 38.77s 37.16s
% Output : Proof 38.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 483 ( 100 equ; 0 cnn)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 394 ( 102 ~; 76 |; 10 &; 174 @)
% ( 0 <=>; 27 =>; 5 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 28 con; 0-2 aty)
% Number of variables : 60 ( 0 ^ 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz9b,conjecture,
~ ( ( ( x = y )
=> ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ) )
=> ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ) )
=> ~ ( ~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) )
=> ( x != y ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ( x = y )
=> ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ) )
=> ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ) )
=> ~ ( ~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) )
=> ( x != y ) ) ) ),
inference(assume_negation,[status(cth)],[satz9b]) ).
thf(pax2,axiom,
( p2
=> ! [X1: nat,X2: nat] :
( X2
!= ( fpl @ X1 @ X2 ) ) ),
file('<stdin>',pax2) ).
thf(pax3,axiom,
( p3
=> ! [X1: nat,X2: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ) ),
file('<stdin>',pax3) ).
thf(ax1254,axiom,
p2,
file('<stdin>',ax1254) ).
thf(ax1253,axiom,
p3,
file('<stdin>',ax1253) ).
thf(nax19,axiom,
( p19
<= ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) ) ),
file('<stdin>',nax19) ).
thf(ax1236,axiom,
( p11
| ~ p19 ),
file('<stdin>',ax1236) ).
thf(nax11,axiom,
( p11
<= ( ~ ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) )
=> ( fx != fy ) ) ),
file('<stdin>',nax11) ).
thf(nax9,axiom,
( p9
<= ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) ) ),
file('<stdin>',nax9) ).
thf(ax1247,axiom,
( ~ p7
| ~ p10
| ~ p11 ),
file('<stdin>',ax1247) ).
thf(ax1237,axiom,
( p10
| ~ p19 ),
file('<stdin>',ax1237) ).
thf(ax1250,axiom,
( ~ p1
| ~ p6
| p7 ),
file('<stdin>',ax1250) ).
thf(ax1248,axiom,
( p6
| ~ p9 ),
file('<stdin>',ax1248) ).
thf(nax6,axiom,
( p6
<= ( ( fx = fy )
=> ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) ) ) ),
file('<stdin>',nax6) ).
thf(pax5,axiom,
( p5
=> ! [X1: nat,X2: nat,X3: nat] :
( ( fpl @ ( fpl @ X1 @ X2 ) @ X3 )
= ( fpl @ X1 @ ( fpl @ X2 @ X3 ) ) ) ),
file('<stdin>',pax5) ).
thf(pax1,axiom,
( p1
=> ( ( ( fx = fy )
=> ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) ) )
=> ( ( ~ ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) )
=> ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) ) )
=> ~ ( ~ ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) )
=> ( fx != fy ) ) ) ) ),
file('<stdin>',pax1) ).
thf(ax1255,axiom,
p1,
file('<stdin>',ax1255) ).
thf(ax1251,axiom,
p5,
file('<stdin>',ax1251) ).
thf(nax10,axiom,
( p10
<= ( ~ ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) )
=> ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) ) ) ),
file('<stdin>',nax10) ).
thf(c_0_18,plain,
! [X238: nat,X239: nat] :
( ~ p2
| ( X239
!= ( fpl @ X238 @ X239 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])]) ).
thf(c_0_19,plain,
! [X234: nat,X235: nat] :
( ~ p3
| ( ( fpl @ X234 @ X235 )
= ( fpl @ X235 @ X234 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).
thf(c_0_20,plain,
! [X2: nat,X1: nat] :
( ~ p2
| ( X1
!= ( fpl @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
p2,
inference(split_conjunct,[status(thm)],[ax1254]) ).
thf(c_0_22,plain,
! [X2: nat,X1: nat] :
( ( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
p3,
inference(split_conjunct,[status(thm)],[ax1253]) ).
thf(c_0_24,plain,
! [X1: nat,X2: nat] :
( ( fpl @ X1 @ X2 )
!= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_25,plain,
! [X2: nat,X1: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_26,plain,
( ( fy
= ( fpl @ fx @ esk100_0 ) )
| p19 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax19])])])]) ).
thf(c_0_27,plain,
( p11
| ~ p19 ),
inference(fof_simplification,[status(thm)],[ax1236]) ).
thf(c_0_28,plain,
! [X2: nat,X1: nat] :
( ( fpl @ X1 @ X2 )
!= X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,plain,
( ( fy
= ( fpl @ fx @ esk100_0 ) )
| p19 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_30,plain,
( ( ( fy
= ( fpl @ fx @ esk105_0 ) )
| p11 )
& ( ( fx = fy )
| p11 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax11])])])])]) ).
thf(c_0_31,plain,
( ( fx
= ( fpl @ fy @ esk108_0 ) )
| p9 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax9])])])]) ).
thf(c_0_32,plain,
( ~ p7
| ~ p10
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1247]) ).
thf(c_0_33,plain,
( p11
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,plain,
( p19
| ( fx != fy ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_35,plain,
( ( fx = fy )
| p11 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
( p10
| ~ p19 ),
inference(fof_simplification,[status(thm)],[ax1237]) ).
thf(c_0_37,plain,
( ~ p1
| ~ p6
| p7 ),
inference(fof_simplification,[status(thm)],[ax1250]) ).
thf(c_0_38,plain,
( p6
| ~ p9 ),
inference(fof_simplification,[status(thm)],[ax1248]) ).
thf(c_0_39,plain,
( ( fx
= ( fpl @ fy @ esk108_0 ) )
| p9 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
( ( ( fx = fy )
| p6 )
& ( ( fx
= ( fpl @ fy @ esk112_0 ) )
| p6 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6])])])])]) ).
thf(c_0_41,plain,
! [X228: nat,X229: nat,X230: nat] :
( ~ p5
| ( ( fpl @ ( fpl @ X228 @ X229 ) @ X230 )
= ( fpl @ X228 @ ( fpl @ X229 @ X230 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_42,plain,
( ( ( fy
= ( fpl @ fx @ esk123_0 ) )
| ( fx
= ( fpl @ fy @ esk121_0 ) )
| ( fx = fy )
| ~ p1 )
& ( ( fx = fy )
| ( fx
= ( fpl @ fy @ esk121_0 ) )
| ( fx = fy )
| ~ p1 )
& ( ( fy
= ( fpl @ fx @ esk123_0 ) )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ( fx = fy )
| ~ p1 )
& ( ( fx = fy )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ( fx = fy )
| ~ p1 )
& ( ( fy
= ( fpl @ fx @ esk123_0 ) )
| ( fx
= ( fpl @ fy @ esk121_0 ) )
| ( fx
= ( fpl @ fy @ esk120_0 ) )
| ~ p1 )
& ( ( fx = fy )
| ( fx
= ( fpl @ fy @ esk121_0 ) )
| ( fx
= ( fpl @ fy @ esk120_0 ) )
| ~ p1 )
& ( ( fy
= ( fpl @ fx @ esk123_0 ) )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ( fx
= ( fpl @ fy @ esk120_0 ) )
| ~ p1 )
& ( ( fx = fy )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ( fx
= ( fpl @ fy @ esk120_0 ) )
| ~ p1 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])]) ).
thf(c_0_43,plain,
( ~ p7
| ~ p10
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_44,plain,
p11,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
thf(c_0_45,plain,
( p10
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_46,plain,
( p7
| ~ p1
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_47,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1255]) ).
thf(c_0_48,plain,
( p6
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_49,plain,
( p9
| ( fx != fy ) ),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
thf(c_0_50,plain,
( ( fx = fy )
| p6 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_51,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ( fpl @ ( fpl @ X1 @ X2 ) @ X3 )
= ( fpl @ X1 @ ( fpl @ X2 @ X3 ) ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_52,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1251]) ).
thf(c_0_53,plain,
( ( fx = fy )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ( fx = fy )
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_54,plain,
( ~ p7
| ~ p10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
thf(c_0_55,plain,
( p10
| ( fx != fy ) ),
inference(spm,[status(thm)],[c_0_45,c_0_34]) ).
thf(c_0_56,plain,
( p7
| ~ p6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_57,plain,
p6,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
thf(c_0_58,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( fpl @ ( fpl @ X1 @ X2 ) @ X3 )
= ( fpl @ X1 @ ( fpl @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_59,plain,
( ( fx = fy )
| ( fy
= ( fpl @ fx @ esk122_0 ) )
| ~ p1 ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_60,plain,
( ( fx != fy )
| ~ p7 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_61,plain,
p7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_62,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( fpl @ X1 @ ( fpl @ X2 @ X3 ) )
!= X3 ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
thf(c_0_63,plain,
( ( ( fpl @ fx @ esk122_0 )
= fy )
| ( fx = fy ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_47])]) ).
thf(c_0_64,plain,
fx != fy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
thf(c_0_65,plain,
( ( ( fx
= ( fpl @ fy @ esk106_0 ) )
| p10 )
& ( ( fy
= ( fpl @ fx @ esk107_0 ) )
| p10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax10])])])])]) ).
thf(c_0_66,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( fpl @ X1 @ ( fpl @ X2 @ X3 ) )
!= X2 ),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
thf(c_0_67,plain,
( ( fpl @ fx @ esk122_0 )
= fy ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_68,plain,
( ( fx
= ( fpl @ fy @ esk106_0 ) )
| p10 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_69,plain,
~ p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_61])]) ).
thf(c_0_70,plain,
! [X1: nat] :
( ( fpl @ X1 @ fy )
!= fx ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_71,plain,
( ( fpl @ fy @ esk106_0 )
= fx ),
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_72,plain,
! [X1: nat] :
( ( fpl @ fy @ X1 )
!= fx ),
inference(spm,[status(thm)],[c_0_70,c_0_25]) ).
thf(c_0_73,plain,
$false,
inference(sr,[status(thm)],[c_0_71,c_0_72]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
~ ( ( ( x = y )
=> ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ) )
=> ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) ) )
=> ~ ( ~ ! [X1: nat] :
( y
!= ( pl @ x @ X1 ) )
=> ( x != y ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM651^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n008.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 13:00:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 38.77/37.16 % SZS status Theorem
% 38.77/37.16 % Mode: mode485
% 38.77/37.16 % Inferences: 171
% 38.77/37.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------