TSTP Solution File: ALG284^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG284^5 : 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 : n022.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 1.99s 2.48s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 264 ( 41 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 290 ( 46 ~; 27 |; 3 &; 199 @)
% ( 0 <=>; 13 =>; 2 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 58 ( 0 ^ 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM18_pme,conjecture,
( ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: $i,X2: $i] :
( ( cJ @ ( cP @ X1 @ X2 ) )
= ( cP @ ( cJ @ X2 ) @ ( cJ @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: $i,X2: $i] :
( ( cJ @ ( cP @ X1 @ X2 ) )
= ( cP @ ( cJ @ X2 ) @ ( cJ @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM18_pme]) ).
thf(ax1182,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1182) ).
thf(ax1183,axiom,
~ p1,
file('<stdin>',ax1183) ).
thf(ax1171,axiom,
( p2
| ~ p12 ),
file('<stdin>',ax1171) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
=> ~ ! [X1: $i] :
( ( fcP @ fcE @ X1 )
= X1 ) )
=> ~ ! [X1: $i] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) )
=> ! [X1: $i,X2: $i] :
( ( fcJ @ ( fcP @ X1 @ X2 ) )
= ( fcP @ ( fcJ @ X2 ) @ ( fcJ @ X1 ) ) ) ) ),
file('<stdin>',nax1) ).
thf(pax36,axiom,
( p36
=> ! [X1: $i] :
( ( fcP @ fcE @ X1 )
= X1 ) ),
file('<stdin>',pax36) ).
thf(ax1144,axiom,
( p12
| p36 ),
file('<stdin>',ax1144) ).
thf(ax1181,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1181) ).
thf(ax1180,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1180) ).
thf(ax1179,axiom,
( p4
| ~ p5 ),
file('<stdin>',ax1179) ).
thf(nax5,axiom,
( p5
<= ( ( fcJ @ ( fcP @ f__0 @ f__1 ) )
= ( fcP @ ( fcJ @ f__1 ) @ ( fcJ @ f__0 ) ) ) ),
file('<stdin>',nax5) ).
thf(c_0_10,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1182]) ).
thf(c_0_11,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1183]) ).
thf(c_0_12,plain,
( p2
| ~ p12 ),
inference(fof_simplification,[status(thm)],[ax1171]) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( p2
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
~ p2,
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
! [X1496: $i,X1497: $i,X1498: $i,X1499: $i,X1500: $i] :
( ( ( ( fcP @ ( fcP @ X1496 @ X1497 ) @ X1498 )
= ( fcP @ X1496 @ ( fcP @ X1497 @ X1498 ) ) )
| p1 )
& ( ( ( fcP @ fcE @ X1499 )
= X1499 )
| p1 )
& ( ( ( fcP @ ( fcJ @ X1500 ) @ X1500 )
= fcE )
| p1 )
& ( ( ( fcJ @ ( fcP @ esk748_0 @ esk749_0 ) )
!= ( fcP @ ( fcJ @ esk749_0 ) @ ( fcJ @ esk748_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_18,plain,
! [X1433: $i] :
( ~ p36
| ( ( fcP @ fcE @ X1433 )
= X1433 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax36])])]) ).
thf(c_0_19,plain,
( p12
| p36 ),
inference(split_conjunct,[status(thm)],[ax1144]) ).
thf(c_0_20,plain,
~ p12,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,plain,
! [X1: $i] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X1: $i] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| ~ p36 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
p36,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_21,c_0_14]) ).
thf(c_0_26,plain,
! [X1: $i] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(sr,[status(thm)],[c_0_22,c_0_14]) ).
thf(c_0_27,plain,
! [X1: $i] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
thf(c_0_28,plain,
! [X1: $i,X2: $i] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_29,plain,
! [X1: $i] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ fcE )
= X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
thf(c_0_30,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1181]) ).
thf(c_0_31,plain,
! [X1: $i] :
( ( fcP @ ( fcJ @ ( fcJ @ ( fcJ @ X1 ) ) ) @ X1 )
= fcE ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1180]) ).
thf(c_0_33,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,plain,
! [X1: $i] :
( ( fcJ @ ( fcJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_29]) ).
thf(c_0_35,plain,
( p4
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1179]) ).
thf(c_0_36,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
~ p3,
inference(sr,[status(thm)],[c_0_33,c_0_14]) ).
thf(c_0_38,plain,
! [X1: $i] :
( ( fcP @ X1 @ ( fcJ @ X1 ) )
= fcE ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
thf(c_0_39,plain,
( ( ( fcJ @ ( fcP @ f__0 @ f__1 ) )
!= ( fcP @ ( fcJ @ f__1 ) @ ( fcJ @ f__0 ) ) )
| p5 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax5])]) ).
thf(c_0_40,plain,
( p4
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_41,plain,
~ p4,
inference(sr,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_42,plain,
! [X1: $i,X2: $i] :
( ( fcP @ X1 @ ( fcP @ X2 @ ( fcJ @ ( fcP @ X1 @ X2 ) ) ) )
= fcE ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
thf(c_0_43,plain,
! [X1: $i] :
( ( fcP @ X1 @ fcE )
= X1 ),
inference(rw,[status(thm)],[c_0_29,c_0_34]) ).
thf(c_0_44,plain,
( p5
| ( ( fcJ @ ( fcP @ f__0 @ f__1 ) )
!= ( fcP @ ( fcJ @ f__1 ) @ ( fcJ @ f__0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_45,plain,
~ p5,
inference(sr,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_46,plain,
! [X1: $i,X2: $i] :
( ( fcP @ X1 @ ( fcJ @ ( fcP @ X2 @ X1 ) ) )
= ( fcJ @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_42]),c_0_43]) ).
thf(c_0_47,plain,
( fcP @ ( fcJ @ f__1 ) @ ( fcJ @ f__0 ) )
!= ( fcJ @ ( fcP @ f__0 @ f__1 ) ),
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,plain,
! [X2: $i,X1: $i] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcJ @ X2 ) )
= ( fcJ @ ( fcP @ X2 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
thf(c_0_49,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X1: $i,X2: $i] :
( ( cJ @ ( cP @ X1 @ X2 ) )
= ( cP @ ( cJ @ X2 ) @ ( cJ @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG284^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 15:35:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.48 % SZS status Theorem
% 1.99/2.48 % Mode: mode506
% 1.99/2.48 % Inferences: 38
% 1.99/2.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------