TSTP Solution File: ALG280^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG280^5 : TPTP v8.1.0. Released v4.0.0.
% 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 : 600s
% DateTime : Thu Jul 14 17:57:55 EDT 2022
% Result : Theorem 2.00s 2.51s
% Output : Proof 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 68 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 220 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 228 ( 54 ~; 38 |; 0 &; 123 @)
% ( 0 <=>; 12 =>; 1 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 21 con; 0-2 aty)
% Number of variables : 44 ( 0 ^ 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM17_pme,conjecture,
( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: a] :
( ( cP @ X1 @ cE )
= X1 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: a] :
( ( cP @ X1 @ cE )
= X1 ) ),
inference(assume_negation,[status(cth)],[cTHM17_pme]) ).
thf(ax1188,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1188) ).
thf(ax1189,axiom,
~ p1,
file('<stdin>',ax1189) ).
thf(ax1178,axiom,
( p2
| ~ p11 ),
file('<stdin>',ax1178) ).
thf(pax34,axiom,
( p34
=> ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ) ),
file('<stdin>',pax34) ).
thf(ax1152,axiom,
( p11
| p34 ),
file('<stdin>',ax1152) ).
thf(pax12,axiom,
( p12
=> ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) ),
file('<stdin>',pax12) ).
thf(ax1177,axiom,
( p2
| p12 ),
file('<stdin>',ax1177) ).
thf(pax35,axiom,
( p35
=> ! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ) ),
file('<stdin>',pax35) ).
thf(ax1151,axiom,
( p11
| p35 ),
file('<stdin>',ax1151) ).
thf(ax1181,axiom,
( ~ p6
| p9 ),
file('<stdin>',ax1181) ).
thf(ax1187,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1187) ).
thf(ax1180,axiom,
( ~ p9
| p10 ),
file('<stdin>',ax1180) ).
thf(ax1185,axiom,
p6,
file('<stdin>',ax1185) ).
thf(ax1186,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1186) ).
thf(ax1179,axiom,
( ~ p10
| ~ p5
| p4 ),
file('<stdin>',ax1179) ).
thf(nax5,axiom,
( p5
<= ( f__0
= ( fcP @ f__0 @ fcE ) ) ),
file('<stdin>',nax5) ).
thf(c_0_16,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1188]) ).
thf(c_0_17,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1189]) ).
thf(c_0_18,plain,
( p2
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1178]) ).
thf(c_0_19,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
( p2
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
~ p2,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,plain,
! [X1475: a,X1476: a,X1477: a] :
( ~ p34
| ( ( fcP @ ( fcP @ X1475 @ X1476 ) @ X1477 )
= ( fcP @ X1475 @ ( fcP @ X1476 @ X1477 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax34])])]) ).
thf(c_0_24,plain,
( p11
| p34 ),
inference(split_conjunct,[status(thm)],[ax1152]) ).
thf(c_0_25,plain,
~ p11,
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,plain,
! [X1495: a] :
( ~ p12
| ( ( fcP @ ( fcJ @ X1495 ) @ X1495 )
= fcE ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax12])])]) ).
thf(c_0_27,plain,
( p2
| p12 ),
inference(split_conjunct,[status(thm)],[ax1177]) ).
thf(c_0_28,plain,
! [X1473: a] :
( ~ p35
| ( ( fcP @ fcE @ X1473 )
= X1473 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax35])])]) ).
thf(c_0_29,plain,
( p11
| p35 ),
inference(split_conjunct,[status(thm)],[ax1151]) ).
thf(c_0_30,plain,
! [X1: a,X2: a,X3: a] :
( ( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
| ~ p34 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_31,plain,
p34,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_32,plain,
! [X1: a] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_33,plain,
p12,
inference(sr,[status(thm)],[c_0_27,c_0_22]) ).
thf(c_0_34,plain,
! [X1: a] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| ~ p35 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_35,plain,
p35,
inference(sr,[status(thm)],[c_0_29,c_0_25]) ).
thf(c_0_36,plain,
( ~ p6
| p9 ),
inference(fof_simplification,[status(thm)],[ax1181]) ).
thf(c_0_37,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1187]) ).
thf(c_0_38,plain,
! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
thf(c_0_39,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
thf(c_0_40,plain,
! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
thf(c_0_41,plain,
( ~ p9
| p10 ),
inference(fof_simplification,[status(thm)],[ax1180]) ).
thf(c_0_42,plain,
( p9
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_43,plain,
p6,
inference(split_conjunct,[status(thm)],[ax1185]) ).
thf(c_0_44,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1186]) ).
thf(c_0_45,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_46,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
thf(c_0_47,plain,
( ~ p10
| ~ p5
| p4 ),
inference(fof_simplification,[status(thm)],[ax1179]) ).
thf(c_0_48,plain,
( p10
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_49,plain,
p9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_50,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_51,plain,
~ p3,
inference(sr,[status(thm)],[c_0_45,c_0_20]) ).
thf(c_0_52,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ fcE )
= X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
thf(c_0_53,plain,
( ( f__0
!= ( fcP @ f__0 @ fcE ) )
| p5 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax5])]) ).
thf(c_0_54,plain,
( p4
| ~ p10
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_55,plain,
p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
thf(c_0_56,plain,
~ p4,
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_57,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ ( fcJ @ ( fcJ @ X1 ) ) ) @ X1 )
= fcE ),
inference(spm,[status(thm)],[c_0_46,c_0_52]) ).
thf(c_0_58,plain,
( p5
| ( f__0
!= ( fcP @ f__0 @ fcE ) ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_59,plain,
~ p5,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),c_0_56]) ).
thf(c_0_60,plain,
! [X1: a] :
( ( fcJ @ ( fcJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_52]) ).
thf(c_0_61,plain,
( fcP @ f__0 @ fcE )
!= f__0,
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_62,plain,
! [X1: a] :
( ( fcP @ X1 @ fcE )
= X1 ),
inference(rw,[status(thm)],[c_0_52,c_0_60]) ).
thf(c_0_63,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: a] :
( ( cP @ X1 @ cE )
= X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG280^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 15:30:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.51 % SZS status Theorem
% 2.00/2.51 % Mode: mode506
% 2.00/2.51 % Inferences: 37
% 2.00/2.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------