%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM713^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Thu Oct 9 02:11:55 PM UTC 2025
% Result : Theorem 1.12s 1.61s
% Output : Proof 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 87 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 243 ( 16 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 235 ( 74 ~; 62 |; 0 &; 96 @)
% ( 0 <=>; 2 =>; 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 : 33 ( 31 usr; 32 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz32a,conjecture,
~ ! [X1: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X1 ) ) ).
thf(h0,negated_conjecture,
! [X1: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X1 ) ),
inference(assume_negation,[status(cth)],[satz32a]) ).
thf(ax1396,axiom,
( ~ p14
| p21 ),
file('<stdin>',ax1396) ).
thf(ax1390,axiom,
( ~ p4
| p22 ),
file('<stdin>',ax1390) ).
thf(ax1395,axiom,
( ~ p21
| p20 ),
file('<stdin>',ax1395) ).
thf(ax1404,axiom,
p14,
file('<stdin>',ax1404) ).
thf(ax1391,axiom,
( ~ p22
| p17 ),
file('<stdin>',ax1391) ).
thf(ax1408,axiom,
p4,
file('<stdin>',ax1408) ).
thf(ax1394,axiom,
( ~ p20
| ~ p1
| p19 ),
file('<stdin>',ax1394) ).
thf(ax1392,axiom,
( ~ p18
| ~ p17
| p16 ),
file('<stdin>',ax1392) ).
thf(ax1393,axiom,
( ~ p19
| p18 ),
file('<stdin>',ax1393) ).
thf(ax1411,axiom,
p1,
file('<stdin>',ax1411) ).
thf(ax1403,axiom,
( ~ p14
| p13 ),
file('<stdin>',ax1403) ).
thf(ax1397,axiom,
( ~ p4
| p15 ),
file('<stdin>',ax1397) ).
thf(ax1313,axiom,
( ~ p13
| p84 ),
file('<stdin>',ax1313) ).
thf(ax1398,axiom,
( ~ p15
| p9 ),
file('<stdin>',ax1398) ).
thf(ax1312,axiom,
( ~ p84
| ~ p16
| p83 ),
file('<stdin>',ax1312) ).
thf(ax1310,axiom,
( ~ p82
| ~ p9
| p81 ),
file('<stdin>',ax1310) ).
thf(ax1311,axiom,
( ~ p83
| p82 ),
file('<stdin>',ax1311) ).
thf(pax81,axiom,
( p81
=> ! [X1: nat] :
( ( fts @ fz @ fx )
!= ( fpl @ ( fts @ fz @ fy ) @ X1 ) ) ),
file('<stdin>',pax81) ).
thf(pax5,axiom,
( p5
=> ! [X1: nat,X2: nat,X3: nat] :
( ( fts @ X1 @ ( fpl @ X2 @ X3 ) )
= ( fpl @ ( fts @ X1 @ X2 ) @ ( fts @ X1 @ X3 ) ) ) ),
file('<stdin>',pax5) ).
thf(ax1407,axiom,
p5,
file('<stdin>',ax1407) ).
thf(nax2,axiom,
( p2
<= ! [X1: nat] :
( fx
!= ( fpl @ fy @ X1 ) ) ),
file('<stdin>',nax2) ).
thf(ax1410,axiom,
~ p2,
file('<stdin>',ax1410) ).
thf(c_0_22,plain,
( ~ p14
| p21 ),
inference(fof_simplification,[status(thm)],[ax1396]) ).
thf(c_0_23,plain,
( ~ p4
| p22 ),
inference(fof_simplification,[status(thm)],[ax1390]) ).
thf(c_0_24,plain,
( ~ p21
| p20 ),
inference(fof_simplification,[status(thm)],[ax1395]) ).
thf(c_0_25,plain,
( p21
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,plain,
p14,
inference(split_conjunct,[status(thm)],[ax1404]) ).
thf(c_0_27,plain,
( ~ p22
| p17 ),
inference(fof_simplification,[status(thm)],[ax1391]) ).
thf(c_0_28,plain,
( p22
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1408]) ).
thf(c_0_30,plain,
( ~ p20
| ~ p1
| p19 ),
inference(fof_simplification,[status(thm)],[ax1394]) ).
thf(c_0_31,plain,
( p20
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,plain,
p21,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_33,plain,
( ~ p18
| ~ p17
| p16 ),
inference(fof_simplification,[status(thm)],[ax1392]) ).
thf(c_0_34,plain,
( p17
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_35,plain,
p22,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_36,plain,
( ~ p19
| p18 ),
inference(fof_simplification,[status(thm)],[ax1393]) ).
thf(c_0_37,plain,
( p19
| ~ p20
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1411]) ).
thf(c_0_39,plain,
p20,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_40,plain,
( ~ p14
| p13 ),
inference(fof_simplification,[status(thm)],[ax1403]) ).
thf(c_0_41,plain,
( ~ p4
| p15 ),
inference(fof_simplification,[status(thm)],[ax1397]) ).
thf(c_0_42,plain,
( p16
| ~ p18
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_43,plain,
p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
thf(c_0_44,plain,
( p18
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_45,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
thf(c_0_46,plain,
( ~ p13
| p84 ),
inference(fof_simplification,[status(thm)],[ax1313]) ).
thf(c_0_47,plain,
( p13
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
( ~ p15
| p9 ),
inference(fof_simplification,[status(thm)],[ax1398]) ).
thf(c_0_49,plain,
( p15
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_50,plain,
( ~ p84
| ~ p16
| p83 ),
inference(fof_simplification,[status(thm)],[ax1312]) ).
thf(c_0_51,plain,
( p16
| ~ p18 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_52,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
thf(c_0_53,plain,
( p84
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_54,plain,
p13,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_26])]) ).
thf(c_0_55,plain,
( ~ p82
| ~ p9
| p81 ),
inference(fof_simplification,[status(thm)],[ax1310]) ).
thf(c_0_56,plain,
( p9
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_57,plain,
p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_29])]) ).
thf(c_0_58,plain,
( ~ p83
| p82 ),
inference(fof_simplification,[status(thm)],[ax1311]) ).
thf(c_0_59,plain,
( p83
| ~ p84
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_60,plain,
p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_61,plain,
p84,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
thf(c_0_62,plain,
( p81
| ~ p82
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_63,plain,
p9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_64,plain,
( p82
| ~ p83 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_65,plain,
p83,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
thf(c_0_66,plain,
! [X1602: nat] :
( ~ p81
| ( ( fts @ fz @ fx )
!= ( fpl @ ( fts @ fz @ fy ) @ X1602 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax81])])])]) ).
thf(c_0_67,plain,
( p81
| ~ p82 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
thf(c_0_68,plain,
p82,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
thf(c_0_69,plain,
! [X1720: nat,X1721: nat,X1722: nat] :
( ~ p5
| ( ( fts @ X1720 @ ( fpl @ X1721 @ X1722 ) )
= ( fpl @ ( fts @ X1720 @ X1721 ) @ ( fts @ X1720 @ X1722 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_70,plain,
! [X1: nat] :
( ~ p81
| ( ( fts @ fz @ fx )
!= ( fpl @ ( fts @ fz @ fy ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_71,plain,
p81,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
thf(c_0_72,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ( fts @ X1 @ ( fpl @ X2 @ X3 ) )
= ( fpl @ ( fts @ X1 @ X2 ) @ ( fts @ X1 @ X3 ) ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_73,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1407]) ).
thf(c_0_74,plain,
( ( fx
= ( fpl @ fy @ esk864_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_75,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax1410]) ).
thf(c_0_76,plain,
! [X1: nat] :
( ( fpl @ ( fts @ fz @ fy ) @ X1 )
!= ( fts @ fz @ fx ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
thf(c_0_77,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( fpl @ ( fts @ X1 @ X2 ) @ ( fts @ X1 @ X3 ) )
= ( fts @ X1 @ ( fpl @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_78,plain,
( ( fx
= ( fpl @ fy @ esk864_0 ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_79,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_80,plain,
! [X1: nat] :
( ( fts @ fz @ ( fpl @ fy @ X1 ) )
!= ( fts @ fz @ fx ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_81,plain,
( ( fpl @ fy @ esk864_0 )
= fx ),
inference(sr,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_82,plain,
$false,
inference(spm,[status(thm)],[c_0_80,c_0_81]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
~ ! [X1: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM713^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 22:26:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.12/1.61 % SZS status Theorem
% 1.12/1.61 % Mode: mode506
% 1.12/1.61 % Inferences: 19978
% 1.12/1.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------