TSTP Solution File: NUM670^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM670^1 : 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 : n029.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 13:54:58 EDT 2022
% Result : Theorem 2.03s 2.43s
% Output : Proof 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 212 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 205 ( 49 ~; 36 |; 0 &; 116 @)
% ( 0 <=>; 3 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 23 con; 0-2 aty)
% Number of variables : 31 ( 0 ^ 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz19a,conjecture,
~ ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ) ).
thf(h0,negated_conjecture,
! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
inference(assume_negation,[status(cth)],[satz19a]) ).
thf(ax1388,axiom,
( ~ p14
| p13 ),
file('<stdin>',ax1388) ).
thf(ax1382,axiom,
( ~ p4
| p15 ),
file('<stdin>',ax1382) ).
thf(ax1387,axiom,
( ~ p13
| p12 ),
file('<stdin>',ax1387) ).
thf(ax1389,axiom,
p14,
file('<stdin>',ax1389) ).
thf(ax1383,axiom,
( ~ p15
| p9 ),
file('<stdin>',ax1383) ).
thf(ax1393,axiom,
p4,
file('<stdin>',ax1393) ).
thf(ax1386,axiom,
( ~ p12
| ~ p1
| p11 ),
file('<stdin>',ax1386) ).
thf(ax1384,axiom,
( ~ p10
| ~ p9
| p8 ),
file('<stdin>',ax1384) ).
thf(ax1385,axiom,
( ~ p11
| p10 ),
file('<stdin>',ax1385) ).
thf(ax1396,axiom,
p1,
file('<stdin>',ax1396) ).
thf(pax8,axiom,
( p8
=> ! [X1: nat] :
( ( fpl @ fz @ fx )
!= ( fpl @ ( fpl @ fy @ fz ) @ X1 ) ) ),
file('<stdin>',pax8) ).
thf(pax5,axiom,
( p5
=> ! [X1: nat,X2: nat,X3: nat] :
( ( fpl @ ( fpl @ X1 @ X2 ) @ X3 )
= ( fpl @ X1 @ ( fpl @ X2 @ X3 ) ) ) ),
file('<stdin>',pax5) ).
thf(ax1392,axiom,
p5,
file('<stdin>',ax1392) ).
thf(pax4,axiom,
( p4
=> ! [X1: nat,X2: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ) ),
file('<stdin>',pax4) ).
thf(nax2,axiom,
( p2
<= ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) ) ),
file('<stdin>',nax2) ).
thf(ax1395,axiom,
~ p2,
file('<stdin>',ax1395) ).
thf(c_0_16,plain,
( ~ p14
| p13 ),
inference(fof_simplification,[status(thm)],[ax1388]) ).
thf(c_0_17,plain,
( ~ p4
| p15 ),
inference(fof_simplification,[status(thm)],[ax1382]) ).
thf(c_0_18,plain,
( ~ p13
| p12 ),
inference(fof_simplification,[status(thm)],[ax1387]) ).
thf(c_0_19,plain,
( p13
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
p14,
inference(split_conjunct,[status(thm)],[ax1389]) ).
thf(c_0_21,plain,
( ~ p15
| p9 ),
inference(fof_simplification,[status(thm)],[ax1383]) ).
thf(c_0_22,plain,
( p15
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1393]) ).
thf(c_0_24,plain,
( ~ p12
| ~ p1
| p11 ),
inference(fof_simplification,[status(thm)],[ax1386]) ).
thf(c_0_25,plain,
( p12
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,plain,
p13,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_27,plain,
( ~ p10
| ~ p9
| p8 ),
inference(fof_simplification,[status(thm)],[ax1384]) ).
thf(c_0_28,plain,
( p9
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,plain,
p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_30,plain,
( ~ p11
| p10 ),
inference(fof_simplification,[status(thm)],[ax1385]) ).
thf(c_0_31,plain,
( p11
| ~ p12
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1396]) ).
thf(c_0_33,plain,
p12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_34,plain,
( p8
| ~ p10
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_35,plain,
p9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_36,plain,
( p10
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,plain,
p11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
thf(c_0_38,plain,
! [X1636: nat] :
( ~ p8
| ( ( fpl @ fz @ fx )
!= ( fpl @ ( fpl @ fy @ fz ) @ X1636 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax8])])])]) ).
thf(c_0_39,plain,
( p8
| ~ p10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
thf(c_0_40,plain,
p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_41,plain,
! [X1642: nat,X1643: nat,X1644: nat] :
( ~ p5
| ( ( fpl @ ( fpl @ X1642 @ X1643 ) @ X1644 )
= ( fpl @ X1642 @ ( fpl @ X1643 @ X1644 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_42,plain,
! [X1: nat] :
( ~ p8
| ( ( fpl @ fz @ fx )
!= ( fpl @ ( fpl @ fy @ fz ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_43,plain,
p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_44,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_45,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1392]) ).
thf(c_0_46,plain,
! [X1648: nat,X1649: nat] :
( ~ p4
| ( ( fpl @ X1648 @ X1649 )
= ( fpl @ X1649 @ X1648 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_47,plain,
( ( fx
= ( fpl @ fy @ esk825_0 ) )
| p2 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])])]) ).
thf(c_0_48,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax1395]) ).
thf(c_0_49,plain,
! [X1: nat] :
( ( fpl @ ( fpl @ fy @ fz ) @ X1 )
!= ( fpl @ fz @ fx ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_50,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_44,c_0_45])]) ).
thf(c_0_51,plain,
! [X2: nat,X1: nat] :
( ( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_52,plain,
( ( fx
= ( fpl @ fy @ esk825_0 ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_53,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_54,plain,
! [X1: nat] :
( ( fpl @ fy @ ( fpl @ fz @ X1 ) )
!= ( fpl @ fz @ fx ) ),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_55,plain,
! [X2: nat,X1: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_23])]) ).
thf(c_0_56,plain,
( ( fpl @ fy @ esk825_0 )
= fx ),
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_57,plain,
! [X1: nat] :
( ( fpl @ fy @ ( fpl @ X1 @ fz ) )
!= ( fpl @ fz @ fx ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_58,plain,
! [X1: nat] :
( ( fpl @ fy @ ( fpl @ esk825_0 @ X1 ) )
= ( fpl @ fx @ X1 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
thf(c_0_59,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_55])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
~ ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM670^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jul 6 20:54:13 EDT 2022
% 0.11/0.33 % CPUTime :
% 2.03/2.43 % SZS status Theorem
% 2.03/2.43 % Mode: mode506
% 2.03/2.43 % Inferences: 19973
% 2.03/2.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------