TSTP Solution File: SYO334^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO334^5 : 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 : n003.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 21 19:31:29 EDT 2022
% Result : Theorem 77.66s 77.58s
% Output : Proof 77.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 72
% Syntax : Number of formulae : 195 ( 67 unt; 12 typ; 0 def)
% Number of atoms : 485 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 854 ( 194 ~; 105 |; 0 &; 469 @)
% ( 0 <=>; 85 =>; 1 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 47 con; 0-2 aty)
% Number of variables : 141 ( 0 ^ 141 !; 0 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_eigen__2,type,
eigen__2: b > c ).
thf(ty_c_stara,type,
c_stara: a > a > a ).
thf(ty_c_starc,type,
c_starc: c > c > c ).
thf(ty_eigen__1,type,
eigen__1: a > c ).
thf(ty_c_starb,type,
c_starb: b > b > b ).
thf(ty_eigen__0,type,
eigen__0: a > b ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__5,type,
eigen__5: c > $o ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(cTHM270_INST,conjecture,
! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a,X5: c > $o] :
( ( X5 @ ( X3 @ ( X1 @ X4 ) ) )
=> ( X5 @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
~ ! [X6: b > $o] :
( ( X6 @ ( X1 @ X5 ) )
=> ( X6 @ X4 ) ) )
=> ~ ! [X4: a,X5: a,X6: b > $o] :
( ( X6 @ ( X1 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a,X6: c > $o] :
( ( X6 @ ( X2 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) ) )
=> ! [X4: b,X5: b,X6: c > $o] :
( ( X6 @ ( X3 @ ( c_starb @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a,X5: c > $o] :
( ( X5 @ ( X3 @ ( X1 @ X4 ) ) )
=> ( X5 @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
~ ! [X6: b > $o] :
( ( X6 @ ( X1 @ X5 ) )
=> ( X6 @ X4 ) ) )
=> ~ ! [X4: a,X5: a,X6: b > $o] :
( ( X6 @ ( X1 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a,X6: c > $o] :
( ( X6 @ ( X2 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) ) )
=> ! [X4: b,X5: b,X6: c > $o] :
( ( X6 @ ( X3 @ ( c_starb @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM270_INST]) ).
thf(h1,assumption,
~ ! [X1: a > c,X2: b > c] :
( ~ ( ~ ( ~ ( ! [X3: a,X4: c > $o] :
( ( X4 @ ( X2 @ ( eigen__0 @ X3 ) ) )
=> ( X4 @ ( X1 @ X3 ) ) )
=> ~ ! [X3: b] :
~ ! [X4: a] :
~ ! [X5: b > $o] :
( ( X5 @ ( eigen__0 @ X4 ) )
=> ( X5 @ X3 ) ) )
=> ~ ! [X3: a,X4: a,X5: b > $o] :
( ( X5 @ ( eigen__0 @ ( c_stara @ X3 @ X4 ) ) )
=> ( X5 @ ( c_starb @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X3: a,X4: a,X5: c > $o] :
( ( X5 @ ( X1 @ ( c_stara @ X3 @ X4 ) ) )
=> ( X5 @ ( c_starc @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) )
=> ! [X3: b,X4: b,X5: c > $o] :
( ( X5 @ ( X2 @ ( c_starb @ X3 @ X4 ) ) )
=> ( X5 @ ( c_starc @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: b > c] :
( ~ ( ~ ( ~ ( ! [X2: a,X3: c > $o] :
( ( X3 @ ( X1 @ ( eigen__0 @ X2 ) ) )
=> ( X3 @ ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: b] :
~ ! [X3: a] :
~ ! [X4: b > $o] :
( ( X4 @ ( eigen__0 @ X3 ) )
=> ( X4 @ X2 ) ) )
=> ~ ! [X2: a,X3: a,X4: b > $o] :
( ( X4 @ ( eigen__0 @ ( c_stara @ X2 @ X3 ) ) )
=> ( X4 @ ( c_starb @ ( eigen__0 @ X2 ) @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X2: a,X3: a,X4: c > $o] :
( ( X4 @ ( eigen__1 @ ( c_stara @ X2 @ X3 ) ) )
=> ( X4 @ ( c_starc @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) ) )
=> ! [X2: b,X3: b,X4: c > $o] :
( ( X4 @ ( X1 @ ( c_starb @ X2 @ X3 ) ) )
=> ( X4 @ ( c_starc @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( eigen__0 @ X1 ) ) )
=> ( X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b] :
~ ! [X2: a] :
~ ! [X3: b > $o] :
( ( X3 @ ( eigen__0 @ X2 ) )
=> ( X3 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: b > $o] :
( ( X3 @ ( eigen__0 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starb @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X1: a,X2: a,X3: c > $o] :
( ( X3 @ ( eigen__1 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starc @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) )
=> ! [X1: b,X2: b,X3: c > $o] :
( ( X3 @ ( eigen__2 @ ( c_starb @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starc @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ! [X1: a,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( eigen__0 @ X1 ) ) )
=> ( X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b] :
~ ! [X2: a] :
~ ! [X3: b > $o] :
( ( X3 @ ( eigen__0 @ X2 ) )
=> ( X3 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: b > $o] :
( ( X3 @ ( eigen__0 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starb @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X1: a,X2: a,X3: c > $o] :
( ( X3 @ ( eigen__1 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starc @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b,X2: b,X3: c > $o] :
( ( X3 @ ( eigen__2 @ ( c_starb @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starc @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ! [X1: a,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( eigen__0 @ X1 ) ) )
=> ( X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b] :
~ ! [X2: a] :
~ ! [X3: b > $o] :
( ( X3 @ ( eigen__0 @ X2 ) )
=> ( X3 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: b > $o] :
( ( X3 @ ( eigen__0 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starb @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: a,X2: a,X3: c > $o] :
( ( X3 @ ( eigen__1 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starc @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ! [X1: a,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( eigen__0 @ X1 ) ) )
=> ( X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b] :
~ ! [X2: a] :
~ ! [X3: b > $o] :
( ( X3 @ ( eigen__0 @ X2 ) )
=> ( X3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: a,X2: a,X3: b > $o] :
( ( X3 @ ( eigen__0 @ ( c_stara @ X1 @ X2 ) ) )
=> ( X3 @ ( c_starb @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( eigen__0 @ X1 ) ) )
=> ( X2 @ ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: b] :
~ ! [X2: a] :
~ ! [X3: b > $o] :
( ( X3 @ ( eigen__0 @ X2 ) )
=> ( X3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: b,X2: c > $o] :
( ( X2 @ ( eigen__2 @ ( c_starb @ eigen__3 @ X1 ) ) )
=> ( X2 @ ( c_starc @ ( eigen__2 @ eigen__3 ) @ ( eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: c > $o] :
( ( X1 @ ( eigen__2 @ ( c_starb @ eigen__3 @ eigen__4 ) ) )
=> ( X1 @ ( c_starc @ ( eigen__2 @ eigen__3 ) @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( eigen__5 @ ( eigen__2 @ ( c_starb @ eigen__3 @ eigen__4 ) ) )
=> ( eigen__5 @ ( c_starc @ ( eigen__2 @ eigen__3 ) @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
eigen__5 @ ( eigen__2 @ ( c_starb @ eigen__3 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( eigen__5 @ ( c_starc @ ( eigen__2 @ eigen__3 ) @ ( eigen__2 @ eigen__4 ) ) ),
introduced(assumption,[]) ).
thf(ax2226,axiom,
( ~ p5
| ~ p8 ),
file('<stdin>',ax2226) ).
thf(ax2183,axiom,
( ~ p31
| p47 ),
file('<stdin>',ax2183) ).
thf(ax2227,axiom,
( ~ p5
| ~ p7 ),
file('<stdin>',ax2227) ).
thf(ax2189,axiom,
( ~ p31
| p42 ),
file('<stdin>',ax2189) ).
thf(ax2229,axiom,
p5,
file('<stdin>',ax2229) ).
thf(ax2182,axiom,
( ~ p47
| p48 ),
file('<stdin>',ax2182) ).
thf(ax2202,axiom,
p31,
file('<stdin>',ax2202) ).
thf(ax1306,axiom,
( ~ p15
| p415 ),
file('<stdin>',ax1306) ).
thf(ax2188,axiom,
( ~ p42
| p43 ),
file('<stdin>',ax2188) ).
thf(ax1276,axiom,
( ~ p15
| p442 ),
file('<stdin>',ax1276) ).
thf(ax2181,axiom,
( ~ p48
| ~ p21
| p46 ),
file('<stdin>',ax2181) ).
thf(ax2212,axiom,
( p8
| p21 ),
file('<stdin>',ax2212) ).
thf(ax1848,axiom,
( ~ p6
| p209 ),
file('<stdin>',ax1848) ).
thf(ax1305,axiom,
( ~ p415
| p416 ),
file('<stdin>',ax1305) ).
thf(ax2220,axiom,
p15,
file('<stdin>',ax2220) ).
thf(ax2187,axiom,
( ~ p43
| ~ p20
| p41 ),
file('<stdin>',ax2187) ).
thf(ax2213,axiom,
( p7
| p20 ),
file('<stdin>',ax2213) ).
thf(ax1834,axiom,
( ~ p6
| p219 ),
file('<stdin>',ax1834) ).
thf(ax1275,axiom,
( ~ p442
| p443 ),
file('<stdin>',ax1275) ).
thf(ax2225,axiom,
( ~ p5
| ~ p9 ),
file('<stdin>',ax2225) ).
thf(pax46,axiom,
( p46
=> ( f__3
= ( f__0 @ f__8 ) ) ),
file('<stdin>',pax46) ).
thf(ax1304,axiom,
( ~ p416
| ~ p209
| p414 ),
file('<stdin>',ax1304) ).
thf(ax2228,axiom,
p6,
file('<stdin>',ax2228) ).
thf(pax41,axiom,
( p41
=> ( f__4
= ( f__0 @ f__7 ) ) ),
file('<stdin>',pax41) ).
thf(ax1274,axiom,
( ~ p443
| ~ p219
| p441 ),
file('<stdin>',ax1274) ).
thf(ax1846,axiom,
( ~ p3
| p211 ),
file('<stdin>',ax1846) ).
thf(ax1847,axiom,
( ~ p4
| p210 ),
file('<stdin>',ax1847) ).
thf(pax414,axiom,
( p414
=> ( ( f__1 @ f__8 )
= ( f__2 @ ( f__0 @ f__8 ) ) ) ),
file('<stdin>',pax414) ).
thf(pax441,axiom,
( p441
=> ( ( f__1 @ f__7 )
= ( f__2 @ ( f__0 @ f__7 ) ) ) ),
file('<stdin>',pax441) ).
thf(pax22,axiom,
( p22
=> ( ( f__0 @ f__9 )
= ( fc_starb @ f__3 @ f__4 ) ) ),
file('<stdin>',pax22) ).
thf(ax2211,axiom,
( p9
| p22 ),
file('<stdin>',ax2211) ).
thf(pax6,axiom,
( p6
=> ! [X30: a] :
( ( f__2 @ ( f__0 @ X30 ) )
= ( f__1 @ X30 ) ) ),
file('<stdin>',pax6) ).
thf(ax2224,axiom,
( ~ p2
| p1
| ~ p10 ),
file('<stdin>',ax2224) ).
thf(ax2233,axiom,
~ p1,
file('<stdin>',ax2233) ).
thf(ax1293,axiom,
( ~ p211
| p426 ),
file('<stdin>',ax1293) ).
thf(ax2231,axiom,
p3,
file('<stdin>',ax2231) ).
thf(ax1299,axiom,
( ~ p210
| p420 ),
file('<stdin>',ax1299) ).
thf(ax2230,axiom,
p4,
file('<stdin>',ax2230) ).
thf(nax10,axiom,
( p10
<= ( ( f__2 @ ( fc_starb @ f__3 @ f__4 ) )
= ( fc_starc @ ( f__2 @ f__3 ) @ ( f__2 @ f__4 ) ) ) ),
file('<stdin>',nax10) ).
thf(ax2232,axiom,
p2,
file('<stdin>',ax2232) ).
thf(pax426,axiom,
( p426
=> ( ( f__1 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starc @ ( f__1 @ f__8 ) @ ( f__1 @ f__7 ) ) ) ),
file('<stdin>',pax426) ).
thf(pax420,axiom,
( p420
=> ( ( f__0 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starb @ ( f__0 @ f__8 ) @ ( f__0 @ f__7 ) ) ) ),
file('<stdin>',pax420) ).
thf(c_0_42,plain,
( ~ p5
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax2226]) ).
thf(c_0_43,plain,
( ~ p31
| p47 ),
inference(fof_simplification,[status(thm)],[ax2183]) ).
thf(c_0_44,plain,
( ~ p5
| ~ p7 ),
inference(fof_simplification,[status(thm)],[ax2227]) ).
thf(c_0_45,plain,
( ~ p31
| p42 ),
inference(fof_simplification,[status(thm)],[ax2189]) ).
thf(c_0_46,plain,
( ~ p5
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_47,plain,
p5,
inference(split_conjunct,[status(thm)],[ax2229]) ).
thf(c_0_48,plain,
( ~ p47
| p48 ),
inference(fof_simplification,[status(thm)],[ax2182]) ).
thf(c_0_49,plain,
( p47
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,plain,
p31,
inference(split_conjunct,[status(thm)],[ax2202]) ).
thf(c_0_51,plain,
( ~ p15
| p415 ),
inference(fof_simplification,[status(thm)],[ax1306]) ).
thf(c_0_52,plain,
( ~ p5
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_53,plain,
( ~ p42
| p43 ),
inference(fof_simplification,[status(thm)],[ax2188]) ).
thf(c_0_54,plain,
( p42
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_55,plain,
( ~ p15
| p442 ),
inference(fof_simplification,[status(thm)],[ax1276]) ).
thf(c_0_56,plain,
( ~ p48
| ~ p21
| p46 ),
inference(fof_simplification,[status(thm)],[ax2181]) ).
thf(c_0_57,plain,
( p8
| p21 ),
inference(split_conjunct,[status(thm)],[ax2212]) ).
thf(c_0_58,plain,
~ p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_59,plain,
( p48
| ~ p47 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_60,plain,
p47,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
thf(c_0_61,plain,
( ~ p6
| p209 ),
inference(fof_simplification,[status(thm)],[ax1848]) ).
thf(c_0_62,plain,
( ~ p415
| p416 ),
inference(fof_simplification,[status(thm)],[ax1305]) ).
thf(c_0_63,plain,
( p415
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_64,plain,
p15,
inference(split_conjunct,[status(thm)],[ax2220]) ).
thf(c_0_65,plain,
( ~ p43
| ~ p20
| p41 ),
inference(fof_simplification,[status(thm)],[ax2187]) ).
thf(c_0_66,plain,
( p7
| p20 ),
inference(split_conjunct,[status(thm)],[ax2213]) ).
thf(c_0_67,plain,
~ p7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_47])]) ).
thf(c_0_68,plain,
( p43
| ~ p42 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_69,plain,
p42,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_50])]) ).
thf(c_0_70,plain,
( ~ p6
| p219 ),
inference(fof_simplification,[status(thm)],[ax1834]) ).
thf(c_0_71,plain,
( ~ p442
| p443 ),
inference(fof_simplification,[status(thm)],[ax1275]) ).
thf(c_0_72,plain,
( p442
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_73,plain,
( ~ p5
| ~ p9 ),
inference(fof_simplification,[status(thm)],[ax2225]) ).
thf(c_0_74,plain,
( ~ p46
| ( f__3
= ( f__0 @ f__8 ) ) ),
inference(fof_nnf,[status(thm)],[pax46]) ).
thf(c_0_75,plain,
( p46
| ~ p48
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_76,plain,
p21,
inference(sr,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_77,plain,
p48,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
thf(c_0_78,plain,
( ~ p416
| ~ p209
| p414 ),
inference(fof_simplification,[status(thm)],[ax1304]) ).
thf(c_0_79,plain,
( p209
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_80,plain,
p6,
inference(split_conjunct,[status(thm)],[ax2228]) ).
thf(c_0_81,plain,
( p416
| ~ p415 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_82,plain,
p415,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
thf(c_0_83,plain,
( ~ p41
| ( f__4
= ( f__0 @ f__7 ) ) ),
inference(fof_nnf,[status(thm)],[pax41]) ).
thf(c_0_84,plain,
( p41
| ~ p43
| ~ p20 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_85,plain,
p20,
inference(sr,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_86,plain,
p43,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
thf(c_0_87,plain,
( ~ p443
| ~ p219
| p441 ),
inference(fof_simplification,[status(thm)],[ax1274]) ).
thf(c_0_88,plain,
( p219
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_89,plain,
( p443
| ~ p442 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_90,plain,
p442,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_64])]) ).
thf(c_0_91,plain,
( ~ p5
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_92,plain,
( ~ p3
| p211 ),
inference(fof_simplification,[status(thm)],[ax1846]) ).
thf(c_0_93,plain,
( ~ p4
| p210 ),
inference(fof_simplification,[status(thm)],[ax1847]) ).
thf(c_0_94,plain,
( ~ p414
| ( ( f__1 @ f__8 )
= ( f__2 @ ( f__0 @ f__8 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax414]) ).
thf(c_0_95,plain,
( ( f__3
= ( f__0 @ f__8 ) )
| ~ p46 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_96,plain,
p46,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
thf(c_0_97,plain,
( p414
| ~ p416
| ~ p209 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_98,plain,
p209,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
thf(c_0_99,plain,
p416,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
thf(c_0_100,plain,
( ~ p441
| ( ( f__1 @ f__7 )
= ( f__2 @ ( f__0 @ f__7 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax441]) ).
thf(c_0_101,plain,
( ( f__4
= ( f__0 @ f__7 ) )
| ~ p41 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_102,plain,
p41,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
thf(c_0_103,plain,
( p441
| ~ p443
| ~ p219 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_104,plain,
p219,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_80])]) ).
thf(c_0_105,plain,
p443,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
thf(c_0_106,plain,
( ~ p22
| ( ( f__0 @ f__9 )
= ( fc_starb @ f__3 @ f__4 ) ) ),
inference(fof_nnf,[status(thm)],[pax22]) ).
thf(c_0_107,plain,
( p9
| p22 ),
inference(split_conjunct,[status(thm)],[ax2211]) ).
thf(c_0_108,plain,
~ p9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_47])]) ).
thf(c_0_109,plain,
! [X300: a] :
( ~ p6
| ( ( f__2 @ ( f__0 @ X300 ) )
= ( f__1 @ X300 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_110,plain,
( ~ p2
| p1
| ~ p10 ),
inference(fof_simplification,[status(thm)],[ax2224]) ).
thf(c_0_111,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax2233]) ).
thf(c_0_112,plain,
( ~ p211
| p426 ),
inference(fof_simplification,[status(thm)],[ax1293]) ).
thf(c_0_113,plain,
( p211
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
thf(c_0_114,plain,
p3,
inference(split_conjunct,[status(thm)],[ax2231]) ).
thf(c_0_115,plain,
( ~ p210
| p420 ),
inference(fof_simplification,[status(thm)],[ax1299]) ).
thf(c_0_116,plain,
( p210
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_117,plain,
p4,
inference(split_conjunct,[status(thm)],[ax2230]) ).
thf(c_0_118,plain,
( ( ( f__2 @ ( fc_starb @ f__3 @ f__4 ) )
!= ( fc_starc @ ( f__2 @ f__3 ) @ ( f__2 @ f__4 ) ) )
| p10 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax10])]) ).
thf(c_0_119,plain,
( ( ( f__1 @ f__8 )
= ( f__2 @ ( f__0 @ f__8 ) ) )
| ~ p414 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
thf(c_0_120,plain,
( ( f__0 @ f__8 )
= f__3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
thf(c_0_121,plain,
p414,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
thf(c_0_122,plain,
( ( ( f__1 @ f__7 )
= ( f__2 @ ( f__0 @ f__7 ) ) )
| ~ p441 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
thf(c_0_123,plain,
( ( f__0 @ f__7 )
= f__4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
thf(c_0_124,plain,
p441,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
thf(c_0_125,plain,
( ( ( f__0 @ f__9 )
= ( fc_starb @ f__3 @ f__4 ) )
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_126,plain,
p22,
inference(sr,[status(thm)],[c_0_107,c_0_108]) ).
thf(c_0_127,plain,
! [X6: a] :
( ( ( f__2 @ ( f__0 @ X6 ) )
= ( f__1 @ X6 ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_128,plain,
( p1
| ~ p2
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
thf(c_0_129,plain,
p2,
inference(split_conjunct,[status(thm)],[ax2232]) ).
thf(c_0_130,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_131,plain,
( ~ p426
| ( ( f__1 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starc @ ( f__1 @ f__8 ) @ ( f__1 @ f__7 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax426]) ).
thf(c_0_132,plain,
( p426
| ~ p211 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_133,plain,
p211,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
thf(c_0_134,plain,
( ~ p420
| ( ( f__0 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starb @ ( f__0 @ f__8 ) @ ( f__0 @ f__7 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax420]) ).
thf(c_0_135,plain,
( p420
| ~ p210 ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
thf(c_0_136,plain,
p210,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
thf(c_0_137,plain,
( p10
| ( ( f__2 @ ( fc_starb @ f__3 @ f__4 ) )
!= ( fc_starc @ ( f__2 @ f__3 ) @ ( f__2 @ f__4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
thf(c_0_138,plain,
( ( f__2 @ f__3 )
= ( f__1 @ f__8 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120]),c_0_121])]) ).
thf(c_0_139,plain,
( ( f__2 @ f__4 )
= ( f__1 @ f__7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_124])]) ).
thf(c_0_140,plain,
( ( fc_starb @ f__3 @ f__4 )
= ( f__0 @ f__9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
thf(c_0_141,plain,
! [X6: a] :
( ( f__2 @ ( f__0 @ X6 ) )
= ( f__1 @ X6 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_80])]) ).
thf(c_0_142,plain,
~ p10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]),c_0_130]) ).
thf(c_0_143,plain,
( ( ( f__1 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starc @ ( f__1 @ f__8 ) @ ( f__1 @ f__7 ) ) )
| ~ p426 ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
thf(c_0_144,plain,
p426,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
thf(c_0_145,plain,
( ( ( f__0 @ ( fc_stara @ f__8 @ f__7 ) )
= ( fc_starb @ ( f__0 @ f__8 ) @ ( f__0 @ f__7 ) ) )
| ~ p420 ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
thf(c_0_146,plain,
p420,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136])]) ).
thf(c_0_147,plain,
( fc_starc @ ( f__1 @ f__8 ) @ ( f__1 @ f__7 ) )
!= ( f__1 @ f__9 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_140]),c_0_141]),c_0_142]) ).
thf(c_0_148,plain,
( ( fc_starc @ ( f__1 @ f__8 ) @ ( f__1 @ f__7 ) )
= ( f__1 @ ( fc_stara @ f__8 @ f__7 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
thf(c_0_149,plain,
( ( f__0 @ ( fc_stara @ f__8 @ f__7 ) )
= ( f__0 @ f__9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_120]),c_0_123]),c_0_140]),c_0_146])]) ).
thf(c_0_150,plain,
( f__1 @ ( fc_stara @ f__8 @ f__7 ) )
!= ( f__1 @ f__9 ),
inference(rw,[status(thm)],[c_0_147,c_0_148]) ).
thf(c_0_151,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_149]),c_0_141]),c_0_150]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h15,h16,h14,h13,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,1,h15,h16]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,2,h14]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,3,h13]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h5,4,h12]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,5,h10,h11]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,6,h8,h9]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,7,h6,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,9,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,10,h2]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1]) ).
thf(0,theorem,
! [X1: a > b,X2: a > c,X3: b > c] :
( ~ ( ~ ( ~ ( ! [X4: a,X5: c > $o] :
( ( X5 @ ( X3 @ ( X1 @ X4 ) ) )
=> ( X5 @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
~ ! [X5: a] :
~ ! [X6: b > $o] :
( ( X6 @ ( X1 @ X5 ) )
=> ( X6 @ X4 ) ) )
=> ~ ! [X4: a,X5: a,X6: b > $o] :
( ( X6 @ ( X1 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starb @ ( X1 @ X4 ) @ ( X1 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a,X6: c > $o] :
( ( X6 @ ( X2 @ ( c_stara @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) ) ) )
=> ! [X4: b,X5: b,X6: c > $o] :
( ( X6 @ ( X3 @ ( c_starb @ X4 @ X5 ) ) )
=> ( X6 @ ( c_starc @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO334^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 16:06:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 77.66/77.58 % SZS status Theorem
% 77.66/77.58 % Mode: mode484
% 77.66/77.58 % Inferences: 1210
% 77.66/77.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------