TSTP Solution File: ALG282^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG282^5 : 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 : n032.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 37.49s 37.13s
% Output : Proof 37.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 51 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 324 ( 72 ~; 41 |; 6 &; 185 @)
% ( 0 <=>; 19 =>; 1 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 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 : 83 ( 0 ^ 83 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM21_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,X2: a] :
~ ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ) ).
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,X2: a] :
~ ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ),
inference(assume_negation,[status(cth)],[cTHM21_pme]) ).
thf(ax1075,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1075) ).
thf(ax1076,axiom,
~ p1,
file('<stdin>',ax1076) ).
thf(ax1066,axiom,
( ~ p16
| p15 ),
file('<stdin>',ax1066) ).
thf(ax1073,axiom,
( p2
| ~ p4 ),
file('<stdin>',ax1073) ).
thf(ax1038,axiom,
( ~ p15
| p42 ),
file('<stdin>',ax1038) ).
thf(ax1067,axiom,
p16,
file('<stdin>',ax1067) ).
thf(ax1037,axiom,
( ~ p42
| p1
| p41 ),
file('<stdin>',ax1037) ).
thf(pax7,axiom,
( p7
=> ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ) ),
file('<stdin>',pax7) ).
thf(ax1070,axiom,
( p4
| p7 ),
file('<stdin>',ax1070) ).
thf(pax5,axiom,
( p5
=> ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) ),
file('<stdin>',pax5) ).
thf(ax1072,axiom,
( p2
| p5 ),
file('<stdin>',ax1072) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) )
=> ! [X1: a,X2: a] :
~ ! [X3: a] :
( ( fcP @ X3 @ X1 )
!= X2 ) ) ),
file('<stdin>',nax1) ).
thf(pax41,axiom,
( p41
=> ! [X1: a] :
( ( X1 = fcE )
=> ~ ( ~ ( ~ ( ! [X2: a,X3: a,X4: a] :
( ( fcP @ ( fcP @ X2 @ X3 ) @ X4 )
= ( fcP @ X2 @ ( fcP @ X3 @ X4 ) ) )
=> ~ ! [X2: a] :
( ( fcP @ X1 @ X2 )
= X2 ) )
=> ~ ! [X2: a] :
( ( fcP @ ( fcJ @ X2 ) @ X2 )
= fcE ) )
=> ! [X2: a,X3: a] :
~ ! [X4: a] :
( ( fcP @ X4 @ X2 )
!= X3 ) ) ) ),
file('<stdin>',pax41) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1075]) ).
thf(c_0_14,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1076]) ).
thf(c_0_15,plain,
( ~ p16
| p15 ),
inference(fof_simplification,[status(thm)],[ax1066]) ).
thf(c_0_16,plain,
( p2
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1073]) ).
thf(c_0_17,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
( ~ p15
| p42 ),
inference(fof_simplification,[status(thm)],[ax1038]) ).
thf(c_0_20,plain,
( p15
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
p16,
inference(split_conjunct,[status(thm)],[ax1067]) ).
thf(c_0_22,plain,
( p2
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,plain,
~ p2,
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_24,plain,
( ~ p42
| p1
| p41 ),
inference(fof_simplification,[status(thm)],[ax1037]) ).
thf(c_0_25,plain,
( p42
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_27,plain,
! [X1677: a,X1678: a,X1679: a] :
( ~ p7
| ( ( fcP @ ( fcP @ X1677 @ X1678 ) @ X1679 )
= ( fcP @ X1677 @ ( fcP @ X1678 @ X1679 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])]) ).
thf(c_0_28,plain,
( p4
| p7 ),
inference(split_conjunct,[status(thm)],[ax1070]) ).
thf(c_0_29,plain,
~ p4,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_30,plain,
! [X1687: a] :
( ~ p5
| ( ( fcP @ ( fcJ @ X1687 ) @ X1687 )
= fcE ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_31,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax1072]) ).
thf(c_0_32,plain,
! [X1721: a,X1722: a,X1723: a,X1724: a,X1725: a,X1728: a] :
( ( ( ( fcP @ ( fcP @ X1721 @ X1722 ) @ X1723 )
= ( fcP @ X1721 @ ( fcP @ X1722 @ X1723 ) ) )
| p1 )
& ( ( ( fcP @ fcE @ X1724 )
= X1724 )
| p1 )
& ( ( ( fcP @ ( fcJ @ X1725 ) @ X1725 )
= fcE )
| p1 )
& ( ( ( fcP @ X1728 @ esk861_0 )
!= esk862_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_33,plain,
! [X1419: a,X1420: a,X1421: a,X1422: a,X1423: a,X1424: a,X1427: a] :
( ( ( ( fcP @ ( fcP @ X1420 @ X1421 ) @ X1422 )
= ( fcP @ X1420 @ ( fcP @ X1421 @ X1422 ) ) )
| ( X1419 != fcE )
| ~ p41 )
& ( ( ( fcP @ X1419 @ X1423 )
= X1423 )
| ( X1419 != fcE )
| ~ p41 )
& ( ( ( fcP @ ( fcJ @ X1424 ) @ X1424 )
= fcE )
| ( X1419 != fcE )
| ~ p41 )
& ( ( ( fcP @ X1427 @ ( esk708_1 @ X1419 ) )
!= ( esk709_1 @ X1419 ) )
| ( X1419 != fcE )
| ~ p41 ) ),
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)],[pax41])])])])])]) ).
thf(c_0_34,plain,
( p1
| p41
| ~ p42 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_35,plain,
p42,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_36,plain,
! [X1: a,X2: a,X3: a] :
( ( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_37,plain,
p7,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_38,plain,
! [X1: a] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,plain,
p5,
inference(sr,[status(thm)],[c_0_31,c_0_23]) ).
thf(c_0_40,plain,
! [X1: a] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,plain,
! [X1: a,X2: a] :
( ( ( fcP @ X1 @ ( esk708_1 @ X2 ) )
!= ( esk709_1 @ X2 ) )
| ( X2 != fcE )
| ~ p41 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_42,plain,
p41,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),c_0_18]) ).
thf(c_0_43,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_36,c_0_37])]) ).
thf(c_0_44,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
thf(c_0_45,plain,
! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_40,c_0_18]) ).
thf(c_0_46,plain,
! [X1: a] :
( ( fcP @ X1 @ ( esk708_1 @ fcE ) )
!= ( esk709_1 @ fcE ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])])]) ).
thf(c_0_47,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
thf(c_0_48,plain,
! [X1: a,X2: a] :
( ( fcP @ X1 @ ( fcP @ X2 @ ( esk708_1 @ fcE ) ) )
!= ( esk709_1 @ fcE ) ),
inference(spm,[status(thm)],[c_0_46,c_0_43]) ).
thf(c_0_49,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ X2 )
= ( fcP @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_47]) ).
thf(c_0_50,plain,
! [X1: a] :
( ( fcP @ X1 @ fcE )
!= ( esk709_1 @ fcE ) ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
thf(c_0_51,plain,
! [X1: a] :
( ( fcP @ X1 @ fcE )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_44]),c_0_49]) ).
thf(c_0_52,plain,
$false,
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),
[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,X2: a] :
~ ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : ALG282^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Wed Jun 8 10:41:21 EDT 2022
% 0.09/0.30 % CPUTime :
% 37.49/37.13 % SZS status Theorem
% 37.49/37.13 % Mode: mode485
% 37.49/37.13 % Inferences: 42
% 37.49/37.13 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------