TSTP Solution File: ALG281^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG281^5 : 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 : 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 : Thu Jul 14 17:57:55 EDT 2022
% Result : Theorem 2.94s 3.12s
% Output : Proof 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 72 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 271 ( 39 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 290 ( 75 ~; 55 |; 3 &; 141 @)
% ( 0 <=>; 13 =>; 3 <=; 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 : 23 ( 21 usr; 22 con; 0-2 aty)
% Number of variables : 47 ( 0 ^ 47 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM16_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] :
( ( cP @ X1 @ ( cJ @ X1 ) )
= cE ) ) ).
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] :
( ( cP @ X1 @ ( cJ @ X1 ) )
= cE ) ),
inference(assume_negation,[status(cth)],[cTHM16_pme]) ).
thf(ax1117,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1117) ).
thf(ax1118,axiom,
~ p1,
file('<stdin>',ax1118) ).
thf(ax1116,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1116) ).
thf(ax984,axiom,
( ~ p39
| p4
| ~ p98
| ~ p39 ),
file('<stdin>',ax984) ).
thf(ax1073,axiom,
( ~ p12
| p39 ),
file('<stdin>',ax1073) ).
thf(ax1106,axiom,
( p2
| p12 ),
file('<stdin>',ax1106) ).
thf(ax1115,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1115) ).
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] :
( ( fcP @ X1 @ ( fcJ @ X1 ) )
= fcE ) ) ),
file('<stdin>',nax1) ).
thf(pax12,axiom,
( p12
=> ! [X1: $i] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) ),
file('<stdin>',pax12) ).
thf(ax1069,axiom,
( ~ p6
| p43 ),
file('<stdin>',ax1069) ).
thf(nax107,axiom,
( p107
<= ( ( fcJ @ f__0 )
= ( fcJ @ f__0 ) ) ),
file('<stdin>',nax107) ).
thf(ax967,axiom,
( ~ p43
| p111 ),
file('<stdin>',ax967) ).
thf(ax1114,axiom,
p6,
file('<stdin>',ax1114) ).
thf(ax971,axiom,
( p98
| ~ p106
| ~ p107 ),
file('<stdin>',ax971) ).
thf(ax966,axiom,
( ~ p111
| ~ p108
| p106 ),
file('<stdin>',ax966) ).
thf(nax108,axiom,
( p108
<= ( f__0
= ( fcJ @ ( fcJ @ f__0 ) ) ) ),
file('<stdin>',nax108) ).
thf(c_0_16,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1117]) ).
thf(c_0_17,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1118]) ).
thf(c_0_18,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1116]) ).
thf(c_0_21,plain,
( ~ p39
| p4
| ~ p98
| ~ p39 ),
inference(fof_simplification,[status(thm)],[ax984]) ).
thf(c_0_22,plain,
( ~ p12
| p39 ),
inference(fof_simplification,[status(thm)],[ax1073]) ).
thf(c_0_23,plain,
( p2
| p12 ),
inference(split_conjunct,[status(thm)],[ax1106]) ).
thf(c_0_24,plain,
~ p2,
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1115]) ).
thf(c_0_26,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
! [X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i] :
( ( ( ( fcP @ ( fcP @ X1103 @ X1104 ) @ X1105 )
= ( fcP @ X1103 @ ( fcP @ X1104 @ X1105 ) ) )
| p1 )
& ( ( ( fcP @ fcE @ X1106 )
= X1106 )
| p1 )
& ( ( ( fcP @ ( fcJ @ X1107 ) @ X1107 )
= fcE )
| p1 )
& ( ( ( fcP @ esk552_0 @ ( fcJ @ esk552_0 ) )
!= fcE )
| 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_28,plain,
! [X1067: $i] :
( ~ p12
| ( ( fcP @ ( fcJ @ X1067 ) @ X1067 )
= fcE ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax12])])]) ).
thf(c_0_29,plain,
( ~ p6
| p43 ),
inference(fof_simplification,[status(thm)],[ax1069]) ).
thf(c_0_30,plain,
( ( ( fcJ @ f__0 )
!= ( fcJ @ f__0 ) )
| p107 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax107])]) ).
thf(c_0_31,plain,
( p4
| ~ p39
| ~ p98
| ~ p39 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_32,plain,
( p39
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_33,plain,
p12,
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_34,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_35,plain,
~ p3,
inference(sr,[status(thm)],[c_0_26,c_0_19]) ).
thf(c_0_36,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_27]) ).
thf(c_0_37,plain,
! [X1: $i] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,plain,
! [X1: $i] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_39,plain,
( ~ p43
| p111 ),
inference(fof_simplification,[status(thm)],[ax967]) ).
thf(c_0_40,plain,
( p43
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_41,plain,
p6,
inference(split_conjunct,[status(thm)],[ax1114]) ).
thf(c_0_42,plain,
( p98
| ~ p106
| ~ p107 ),
inference(fof_simplification,[status(thm)],[ax971]) ).
thf(c_0_43,plain,
( p107
| ( ( fcJ @ f__0 )
!= ( fcJ @ f__0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,plain,
( p4
| ~ p39
| ~ p98 ),
inference(cn,[status(thm)],[c_0_31]) ).
thf(c_0_45,plain,
p39,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
thf(c_0_46,plain,
~ p4,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_47,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_36,c_0_19]) ).
thf(c_0_48,plain,
! [X1: $i] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_33])]) ).
thf(c_0_49,plain,
! [X1: $i] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_38,c_0_19]) ).
thf(c_0_50,plain,
( ~ p111
| ~ p108
| p106 ),
inference(fof_simplification,[status(thm)],[ax966]) ).
thf(c_0_51,plain,
( p111
| ~ p43 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_52,plain,
p43,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
thf(c_0_53,plain,
( p98
| ~ p106
| ~ p107 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_54,plain,
p107,
inference(cn,[status(thm)],[c_0_43]) ).
thf(c_0_55,plain,
~ p98,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),c_0_46]) ).
thf(c_0_56,plain,
! [X1: $i,X2: $i] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
thf(c_0_57,plain,
( ( f__0
!= ( fcJ @ ( fcJ @ f__0 ) ) )
| p108 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax108])]) ).
thf(c_0_58,plain,
( p106
| ~ p111
| ~ p108 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_59,plain,
p111,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_60,plain,
~ p106,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),c_0_55]) ).
thf(c_0_61,plain,
! [X1: $i,X2: $i] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ X2 )
= ( fcP @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_56]) ).
thf(c_0_62,plain,
( p108
| ( f__0
!= ( fcJ @ ( fcJ @ f__0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_63,plain,
~ p108,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),c_0_60]) ).
thf(c_0_64,plain,
! [X1: $i] :
( ( fcP @ X1 @ fcE )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_61]) ).
thf(c_0_65,plain,
( fcJ @ ( fcJ @ f__0 ) )
!= f__0,
inference(sr,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_66,plain,
! [X1: $i] :
( ( fcJ @ ( fcJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_64]),c_0_64]) ).
thf(c_0_67,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]),
[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] :
( ( cP @ X1 @ ( cJ @ X1 ) )
= cE ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG281^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 23:37:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.94/3.12 % SZS status Theorem
% 2.94/3.12 % Mode: mode506
% 2.94/3.12 % Inferences: 19571
% 2.94/3.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------