TSTP Solution File: ALG298^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG298^5 : 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 17:57:58 EDT 2022
% Result : Theorem 44.07s 44.12s
% Output : Proof 44.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 40 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 288 ( 43 ~; 13 |; 4 &; 211 @)
% ( 0 <=>; 16 =>; 1 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 74 ( 0 ^ 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM270_pme,conjecture,
! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a] :
( ( X3 @ ( X1 @ X4 ) )
= ( X2 @ X4 ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
( ( X1 @ X5 )
!= X4 ) )
=> ~ ! [X4: a,X5: a] :
( ( X1 @ ( c_stara @ X4 @ X5 ) )
= ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ( X2 @ ( c_stara @ X4 @ X5 ) )
= ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) )
=> ! [X4: b,X5: b] :
( ( X3 @ ( c_starb @ X4 @ X5 ) )
= ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a] :
( ( X3 @ ( X1 @ X4 ) )
= ( X2 @ X4 ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
( ( X1 @ X5 )
!= X4 ) )
=> ~ ! [X4: a,X5: a] :
( ( X1 @ ( c_stara @ X4 @ X5 ) )
= ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ( X2 @ ( c_stara @ X4 @ X5 ) )
= ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) )
=> ! [X4: b,X5: b] :
( ( X3 @ ( c_starb @ X4 @ X5 ) )
= ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM270_pme]) ).
thf(ax120,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax120) ).
thf(ax121,axiom,
~ p1,
file('<stdin>',ax121) ).
thf(nax2,axiom,
( p2
<= ! [X60: a > c,X61: b > c] :
( ~ ( ~ ( ~ ( ! [X68: a] :
( ( X61 @ ( f__0 @ X68 ) )
= ( X60 @ X68 ) )
=> ~ ! [X69: b] :
~ ! [X70: a] :
( ( f__0 @ X70 )
!= X69 ) )
=> ~ ! [X71: a,X70: a] :
( ( f__0 @ ( fc_stara @ X71 @ X70 ) )
= ( fc_starb @ ( f__0 @ X71 ) @ ( f__0 @ X70 ) ) ) )
=> ~ ! [X71: a,X70: a] :
( ( X60 @ ( fc_stara @ X71 @ X70 ) )
= ( fc_starc @ ( X60 @ X71 ) @ ( X60 @ X70 ) ) ) )
=> ! [X72: b,X73: b] :
( ( X61 @ ( fc_starb @ X72 @ X73 ) )
= ( fc_starc @ ( X61 @ X72 ) @ ( X61 @ X73 ) ) ) ) ),
file('<stdin>',nax2) ).
thf(c_0_3,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax120]) ).
thf(c_0_4,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax121]) ).
thf(c_0_5,plain,
! [X298: a,X299: b,X301: a,X302: a,X303: a,X304: a] :
( ( ( ( esk106_0 @ ( f__0 @ X298 ) )
= ( esk105_0 @ X298 ) )
| p2 )
& ( ( ( f__0 @ ( esk107_1 @ X299 ) )
= X299 )
| p2 )
& ( ( ( f__0 @ ( fc_stara @ X301 @ X302 ) )
= ( fc_starb @ ( f__0 @ X301 ) @ ( f__0 @ X302 ) ) )
| p2 )
& ( ( ( esk105_0 @ ( fc_stara @ X303 @ X304 ) )
= ( fc_starc @ ( esk105_0 @ X303 ) @ ( esk105_0 @ X304 ) ) )
| p2 )
& ( ( ( esk106_0 @ ( fc_starb @ esk108_0 @ esk109_0 ) )
!= ( fc_starc @ ( esk106_0 @ esk108_0 ) @ ( esk106_0 @ esk109_0 ) ) )
| p2 ) ),
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)],[nax2])])])])])]) ).
thf(c_0_6,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,plain,
! [X5: a] :
( ( ( esk106_0 @ ( f__0 @ X5 ) )
= ( esk105_0 @ X5 ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
~ p2,
inference(sr,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,plain,
! [X2: b] :
( ( ( f__0 @ ( esk107_1 @ X2 ) )
= X2 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,plain,
! [X5: a,X7: a] :
( ( ( f__0 @ ( fc_stara @ X5 @ X7 ) )
= ( fc_starb @ ( f__0 @ X5 ) @ ( f__0 @ X7 ) ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,plain,
! [X5: a,X7: a] :
( ( ( esk105_0 @ ( fc_stara @ X5 @ X7 ) )
= ( fc_starc @ ( esk105_0 @ X5 ) @ ( esk105_0 @ X7 ) ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,plain,
! [X5: a] :
( ( esk106_0 @ ( f__0 @ X5 ) )
= ( esk105_0 @ X5 ) ),
inference(sr,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
! [X2: b] :
( ( f__0 @ ( esk107_1 @ X2 ) )
= X2 ),
inference(sr,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_15,plain,
! [X5: a,X7: a] :
( ( fc_starb @ ( f__0 @ X5 ) @ ( f__0 @ X7 ) )
= ( f__0 @ ( fc_stara @ X5 @ X7 ) ) ),
inference(sr,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_16,plain,
! [X5: a,X7: a] :
( ( fc_starc @ ( esk105_0 @ X5 ) @ ( esk105_0 @ X7 ) )
= ( esk105_0 @ ( fc_stara @ X5 @ X7 ) ) ),
inference(sr,[status(thm)],[c_0_12,c_0_9]) ).
thf(c_0_17,plain,
! [X2: b] :
( ( esk105_0 @ ( esk107_1 @ X2 ) )
= ( esk106_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X5: a,X2: b] :
( ( f__0 @ ( fc_stara @ X5 @ ( esk107_1 @ X2 ) ) )
= ( fc_starb @ ( f__0 @ X5 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
thf(c_0_19,plain,
! [X5: a,X2: b] :
( ( esk105_0 @ ( fc_stara @ X5 @ ( esk107_1 @ X2 ) ) )
= ( fc_starc @ ( esk105_0 @ X5 ) @ ( esk106_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,plain,
( p2
| ( ( esk106_0 @ ( fc_starb @ esk108_0 @ esk109_0 ) )
!= ( fc_starc @ ( esk106_0 @ esk108_0 ) @ ( esk106_0 @ esk109_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_21,plain,
! [X5: a,X2: b] :
( ( esk106_0 @ ( fc_starb @ ( f__0 @ X5 ) @ X2 ) )
= ( fc_starc @ ( esk105_0 @ X5 ) @ ( esk106_0 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19]) ).
thf(c_0_22,plain,
( esk106_0 @ ( fc_starb @ esk108_0 @ esk109_0 ) )
!= ( fc_starc @ ( esk106_0 @ esk108_0 ) @ ( esk106_0 @ esk109_0 ) ),
inference(sr,[status(thm)],[c_0_20,c_0_9]) ).
thf(c_0_23,plain,
! [X2: b,X3: b] :
( ( esk106_0 @ ( fc_starb @ X2 @ X3 ) )
= ( fc_starc @ ( esk106_0 @ X2 ) @ ( esk106_0 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_17]) ).
thf(c_0_24,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a] :
( ( X3 @ ( X1 @ X4 ) )
= ( X2 @ X4 ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
( ( X1 @ X5 )
!= X4 ) )
=> ~ ! [X4: a,X5: a] :
( ( X1 @ ( c_stara @ X4 @ X5 ) )
= ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ( X2 @ ( c_stara @ X4 @ X5 ) )
= ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) )
=> ! [X4: b,X5: b] :
( ( X3 @ ( c_starb @ X4 @ X5 ) )
= ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG298^5 : 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 : n022.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 : Thu Jun 9 02:21:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 44.07/44.12 % SZS status Theorem
% 44.07/44.12 % Mode: mode459
% 44.07/44.12 % Inferences: 77
% 44.07/44.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------