<derivation> ::= <clause> ....... <clause id> | <inference><inference>*
<inference> ::= <space><clause> ....... <clause id>
<space><clause> ....... <clause id>
<space><blank><resolvent_factor> ....... R<id>
[<clause id>:<literal id>, <clause id>:<literal id>]
<space> ::= <blank>*
<blank> ::= " "
<clause> ::= <literal> <more literals>*
<literal> ::= <sign><atom>
<more literals> ::= <or> <literal>
<sign> ::= ~ | []
<atom> ::= <proposition> | <predicate><arguments>
<or> ::= |
<proposition> ::= <identifier>
<predicate> ::= <identifier>
<arguments> ::= (<term><more terms>*)
<term> ::= <constant> | <function> | <variable>
<more terms> ::= ,<term>
<constant> ::= <identifier>()
<function> ::= <identifier><arguments>
<variable> ::= <identifier>
<identifier> ::= <legal character><legal character>*
legal character>::= A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|a|b|c|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r|s|t|u|v|x|y|z|0|1|2|3|4|5|6|7|8|9|_
<clause id> ::= B<id> | U<id> | R<id>
<id> ::= <digit><digit>*
<digit> ::= 0|1|2|3|4|5|6|7|8|9
<literal id> :: = L<id>
<resolvent_factor> ::= <clause> | "[]"
Base Clauses and Unit Clauses used in proof:
============================================
Base Clauses:
-------------
B0: ~equal(f(x0),x0) | big_f(h(x0,x1),f(x0)) | equal(h(x0,x1),x1)
B1: ~equal(x0,g(x1)) | big_f(x0,f(x1)) | equal(f(x1),x1)
B6: ~big_f(h(x0,x1),f(x0)) | ~equal(f(x0),x0) | ~equal(h(x0,x1),x1)
B7: equal(x0,x0)
B8: ~equal(x0,x1) | equal(x1,x0)
B9: ~big_f(x0,x1) | equal(x0,a())
B10: ~big_f(x0,x1) | equal(x1,b())
B15: ~equal(x0,x1) | ~equal(x1,x2) | equal(x0,x2)
B16: ~big_f(x0,x2) | ~equal(x0,x1) | big_f(x1,x2)
B18: ~equal(x0,a()) | ~equal(x1,b()) | big_f(x0,x1)
Unit Clauses:
--------------
U0: equal(x0,x0)
U71: equal(f(b()),b())
U72: ~big_f(h(b(),a()),f(b()))
U73: equal(b(),f(b()))
U90: big_f(a(),f(b()))
U138: ~equal(h(b(),a()),a())
U660: equal(h(b(),a()),a())
--------------- Start of Proof ---------------
Derivation of unit clause U0:
equal(x0,x0) ....... U0
Derivation of unit clause U71:
~equal(x0,g(x1)) | big_f(x0,f(x1)) | equal(f(x1),x1) ....... B1
~big_f(x0,x1) | equal(x1,b()) ....... B10
~equal(x0, g(x1)) | equal(f(x1), x1) | equal(f(x1), b()) ....... R1 [B1:L1, B10:L0]
~equal(x0, g(b())) | equal(f(b()), b()) ....... R2 [R1:L1, R1:L2]
equal(x0,x0) ....... U0
equal(f(b()), b()) ....... R3 [R2:L0, U0:L0]
Derivation of unit clause U72:
~big_f(h(x0,x1),f(x0)) | ~equal(f(x0),x0) | ~equal(h(x0,x1),x1) ....... B6
~big_f(x0,x1) | equal(x0,a()) ....... B9
~big_f(h(x0, a()), f(x0)) | ~equal(f(x0), x0) | ~big_f(h(x0, a()), x1) ....... R1 [B6:L2, B9:L1]
~equal(f(x0), x0) | ~big_f(h(x0, a()), f(x0)) ....... R2 [R1:L0, R1:L2]
equal(f(b()),b()) ....... U71
~big_f(h(b(), a()), f(b())) ....... R3 [R2:L0, U71:L0]
Derivation of unit clause U73:
equal(x0,x0) ....... B7
~equal(x0,x1) | ~equal(x1,x2) | equal(x0,x2) ....... B15
~equal(x0, x1) | equal(x0, x1) ....... R1 [B7:L0, B15:L0]
~equal(x0,x1) | equal(x1,x0) ....... B8
~equal(x0, x1) | equal(x1, x0) ....... R2 [R1:L1, B8:L0]
equal(f(b()),b()) ....... U71
equal(b(), f(b())) ....... R3 [R2:L0, U71:L0]
Derivation of unit clause U90:
equal(x0,x0) ....... B7
~equal(x0,a()) | ~equal(x1,b()) | big_f(x0,x1) ....... B18
~equal(x0, b()) | big_f(a(), x0) ....... R1 [B7:L0, B18:L0]
~equal(x0,x1) | equal(x1,x0) ....... B8
big_f(a(), x0) | ~equal(b(), x0) ....... R2 [R1:L0, B8:L1]
equal(b(),f(b())) ....... U73
big_f(a(), f(b())) ....... R3 [R2:L1, U73:L0]
Derivation of unit clause U138:
~equal(x0,x1) | equal(x1,x0) ....... B8
~big_f(x0,x2) | ~equal(x0,x1) | big_f(x1,x2) ....... B16
~equal(x0, x1) | ~big_f(x1, x2) | big_f(x0, x2) ....... R1 [B8:L1, B16:L1]
big_f(a(),f(b())) ....... U90
~equal(x0, a()) | big_f(x0, f(b())) ....... R2 [R1:L1, U90:L0]
~big_f(h(b(),a()),f(b())) ....... U72
~equal(h(b(), a()), a()) ....... R3 [R2:L1, U72:L0]
Derivation of unit clause U660:
~equal(f(x0),x0) | big_f(h(x0,x1),f(x0)) | equal(h(x0,x1),x1) ....... B0
~equal(x0,x1) | equal(x1,x0) ....... B8
~equal(f(x0), x0) | big_f(h(x0, x1), f(x0)) | equal(x1, h(x0, x1)) ....... R1 [B0:L2, B8:L0]
equal(f(b()),b()) ....... U71
big_f(h(b(), x0), f(b())) | equal(x0, h(b(), x0)) ....... R2 [R1:L0, U71:L0]
~equal(x0,x1) | equal(x1,x0) ....... B8
big_f(h(b(), x0), f(b())) | equal(h(b(), x0), x0) ....... R3 [R2:L1, B8:L0]
~big_f(h(b(),a()),f(b())) ....... U72
equal(h(b(), a()), a()) ....... R4 [R3:L0, U72:L0]
Derivation of the empty clause:
equal(h(b(),a()),a()) ....... U660
~equal(h(b(),a()),a()) ....... U138
[] ....... R1 [U660:L0, U138:L0]
--------------- End of Proof ---------------
Here is a list of all inferences:
The first proof uses all but "ef", although it uses some in fairly trivial ways. Note that clause normalization is inherently performed after all inferences but rewriting. The second is the required proof for SYN075-1, and contains an example for "ef".
# Problem is unsatisfiable, constructing proof object
# TSTP exit status: Unsatisfiable
# Proof object starts here.
1 : [++equal(f(X1,X2), f(X2,X1))] : initial
2 : [++equal(f(X1,f(X2,X3)), f(f(X1,X2),X3))] : initial
3 : [++equal(g(X1,X2), g(X2,X1))] : initial
4 : [--equal(f(f(X1,X2),f(X3,g(X4,X5))), f(f(g(X4,X5),X3),f(X2,X1))),--equal(k(X1,X1), k(a,b))] : initial
5 : [++equal(b, c),--equal(X1, X2),--equal(X3, X4),--equal(c, d)] : initial
6 : [++equal(a, b),++equal(a, c)] : initial
7 : [++equal(i(X1), i(X2))] : initial
8 : [++equal(c, d),--equal(h(i(a)), h(i(e)))] : initial
13 : [--equal(k(a,b), k(X1,X1))] : ar(4,1,3,2)
23 : [++equal(c, b),++epred1_0,--equal(d, c),--equal(X3, X4)] : split(5)
24 : [++epred2_0,--equal(X1, X2)] : split(5)
25 : [--epred2_0,--epred1_0] : split(5)
26 : [++epred2_0] : er(24)
27 : [--$true,--epred1_0] : rw(25,26)
28 : [++equal(c, b),++epred1_0,--equal(d, c)] : er(23)
29 : [++equal(c, b),--equal(d, c)] : sr(28,27)
30 : [++equal(d, c)] : sr(8,7)
31 : [++equal(c, b),--equal(c, c)] : rw(29,30)
32 : [++equal(c, b)] : cn(31)
34 : [++equal(b, a)] : pm(6,32)
35 : [--equal(k(b,b), k(X1,X1))] : rw(13,34)
120 : [] : er(35)
121 : [] : 120 : "proof"
# Proof object ends here.
# Problem is unsatisfiable, constructing proof object
# TSTP exit status: Unsatisfiable
# Proof object starts here.
1 : [++equal(X1, a),--big_f(X1,X2)] : initial
3 : [++big_f(X1,X2),--equal(X1, a),--equal(X2, b)] : initial
4 : [++equal(f(X2), X2),--big_f(X1,f(X2)),--equal(X1, g(X2))] : initial
6 : [++big_f(X1,f(X2)),++equal(f(X2), X2),--equal(X1, g(X2))] : initial
9 : [++big_f(h(X1,X2),f(X1)),++equal(h(X1,X2), X2),--equal(f(X1), X1)] : initial
10 : [--equal(f(X1), X1),--equal(h(X1,X2), X2),--big_f(h(X1,X2),f(X1))] : initial
18 : [++equal(f(X2), X2),--equal(g(X2), X1)] : pm(4,6)
19 : [++equal(f(X1), X1)] : er(18)
24 : [--equal(X1, X1),--equal(h(X1,X2), X2),--big_f(h(X1,X2),f(X1))] : rw(10,19)
25 : [--equal(X1, X1),--equal(h(X1,X2), X2),--big_f(h(X1,X2),X1)] : rw(24,19)
26 : [--equal(h(X1,X2), X2),--big_f(h(X1,X2),X1)] : cn(25)
27 : [++equal(h(X1,X2), X2),++big_f(h(X1,X2),X1),--equal(f(X1), X1)] : rw(9,19)
28 : [++equal(h(X1,X2), X2),++big_f(h(X1,X2),X1),--equal(X1, X1)] : rw(27,19)
29 : [++equal(h(X1,X2), X2),++big_f(h(X1,X2),X1)] : cn(28)
30 : [++equal(a, h(X1,X2)),++equal(h(X1,X2), X2)] : pm(1,29)
36 : [++equal(h(X1,X2), X2),--equal(a, X2)] : ef(30)
46 : [--big_f(X2,X1),--equal(h(X1,X2), X2),--equal(a, X2)] : pm(26,36)
56 : [--big_f(X2,X1),--equal(a, X2)] : pm(46,36)
63 : [--equal(a, X1),--equal(b, X2)] : pm(56,3)
94 : [--equal(b, X1)] : er(63)
103 : [] : er(94)
104 : [] : 103 : "proof"
# Proof object ends here.
START OF PROOF 12 [] equal(X,X). 13 [] equal(X,a) | -big_f(X,Y). 15 [] -equal(Y,b) | -equal(X,a) | big_f(X,Y). 17 [] big_f(h(X,Y),f(X)) | equal(h(X,Y),Y) | -equal(f(X),X). 20 [] -equal(X,g(Y)) | big_f(X,f(Y)) | equal(f(Y),Y). 22 [] -big_f(X,f(Y)) | -equal(X,g(Y)) | equal(f(Y),Y). 27 [] -big_f(h(X,Y),f(X)) | -equal(h(X,Y),Y) | -equal(f(X),X). 30 [hyper:20,12] big_f(g(X),f(X)) | equal(f(X),X). 32 [hyper:22,12,binarycut:30] equal(f(X),X). 35 [hyper:15,12,12] big_f(a,b). 38 [hyper:17,32,demod:32] big_f(h(X,Y),X) | equal(h(X,Y),Y). 82 [hyper:13,38,factor] equal(h(X,a),a). 100 [hyper:27,82,demod:32,82,cut:12,slowcut:35] contradiction END OF PROOF
Gandalf v. c-2.6 beta starting to prove: /tmp/GandalfTemp4115
prove-all-passes started
detected problem class: peq
strategies selected:
(hyper 30 #f 12 5)
(binary-unit 12 #f)
(binary-unit-uniteq 12 #f)
(binary-posweight-kb-big-order 60 #f 12 5)
(binary-posweight-lex-big-order 30 #f 12 5)
(binary 30 #t)
(binary-posweight-kb-big-order 156 #f)
(binary-posweight-lex-big-order 102 #f)
(binary-posweight-firstpref-order 60 #f)
(binary-order 30 #f)
(binary-posweight-kb-small-order 48 #f)
(binary-posweight-lex-small-order 30 #f)
SOS clause
-equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
was split for some strategies as:
-equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
-equal(multiply(multiply(inverse(b2),b2),a2),a2).
-equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
Starting a split proof attempt with 3 components.
Split component 1 started.
START OF PROOFPART
Making new sos for split:
Original clause to be split:
-equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
Split part used next: -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
END OF PROOFPART
**** EMPTY CLAUSE DERIVED ****
timer checkpoints: c(3,40,2,6,0,2,13,50,5,16,0,5,9528,4,711,9663,5,906,9663,1,906,9663,50,908,9663,40,908,9666,0,908,10991,3,1113,12378,4,1211,14866,5,1393,14866,1,1393,14866,50,1394,14866,40,1394,14869,0,1394,17337,3,1656,17892,4,1697,19772,5,1795,19784,1,1795,19784,50,1796,19784,40,1796,19787,0,1796,19794,50,1798,19797,0,1798,28123,3,2840,32590,4,3312,37306,5,3747,37308,1,3747,37308,50,3750,37308,40,3750,37311,0,3750,37318,50,3752,37321,0,3752,44100,3,4227,51250,4,4433,55491,5,4653,55493,1,4653,55493,50,4656,55493,40,4656,55496,0,4656,55497,50,4656,55497,40,4656,55500,0,4656,81692,3,7398,89382,4,8908,98454,5,9857,98462,1,9857,98462,50,9860,98462,40,9860,98465,0,9860,118207,3,12472,118207,4,12472,126466,5,13261,126489,1,13263,126489,50,13266,126489,40,13266,126492,0,13266,136384,3,14336,141920,4,14775,148496,5,15470,148507,1,15470,148507,50,15473,148507,40,15473,148510,0,15473,155256,3,15983,161622,4,16226,162526,5,16474,162526,1,16474,162526,50,16476,162526,40,16476,162529,0,16476,174482,3,17313,178673,4,17695,188717,5,18077,188719,1,18077,188719,50,18079,188719,40,18079,188722,0,18079,194033,3,18627,200190,4,18838,206431,5,19080,206431,1,19080,206431,50,19083,206431,40,19083,206431,40,19083,206434,0,19083,206440,50,19085,206443,0,19085)
START OF PROOF
206442 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
206443 [] -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
206444 [para:206442.1.1,206442.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V))).
206445 [para:206444.1.1,206442.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)),Y).
206453 [para:206445.1.1,206445.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y),U).
206466 [para:206453.1.1,206442.1.1.1.1.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(inverse(Y)),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))).
206473 [para:206466.1.2,206444.1.2.1.1,demod:206445,206442] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))).
206481 [para:206466.1.2,206466.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)))).
206482 [para:206481.1.1,206442.1.1.1.1.1.2.1.1,demod:206442] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)),multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z))).
206506 [para:206442.1.1,206482.1.1.1.1.2,demod:206442] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
206537 [para:206506.1.1,206442.1.1.1.1.1.2.1.2.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U))))))))),multiply(X,multiply(Z,U)))),Y).
206575 [para:206506.1.1,206453.1.1.1.1.2.1.2.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))),Y),U).
207691 [para:206453.1.1,206537.1.1.1.1.1.2.1.2.1.1,demod:206575] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))),multiply(X,Z))),Y).
207713 [para:206445.1.1,207691.1.1.1.1.1.2.1.2.1.2.1.1.1,demod:206445] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))))),multiply(X,Z))),Y).
207760 [para:207713.1.1,206473.1.2.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))).
207856 [para:207760.1.2,206473.1.2] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))).
207857 [para:207760.1.1,206473.1.2.1.1.1.1.1,demod:207856] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(X),X)))).
208106 [para:207857.1.1,206473.1.2.1.1.1.1.1,demod:207856,slowcut:206443] contradiction
END OF PROOF
Proof found by the following strategy:
using hyperresolution
not using sos strategy
using positive unit paramodulation strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
clause length limited to 5
clause depth limited to 13
seconds given: 12
Split component 2 started.
START OF PROOFPART
Making new sos for split:
Original clause to be split:
-equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
Split part used next: -equal(multiply(multiply(inverse(b2),b2),a2),a2).
END OF PROOFPART
using hyperresolution
not using sos strategy
using positive unit paramodulation strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
clause length limited to 5
clause depth limited to 12
seconds given: 12
proof attempt stopped: sos exhausted
using hyperresolution
not using sos strategy
using positive unit paramodulation strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
clause length limited to 5
clause depth limited to 13
seconds given: 12
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
not using sos strategy
using unit strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 4
proof attempt stopped: time limit
using binary resolution
not using sos strategy
using unit paramodulation strategy
using unit strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 4
proof attempt stopped: time limit
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 12
seconds given: 26
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 13
seconds given: 26
proof attempt stopped: time limit
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 12
seconds given: 12
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 13
seconds given: 12
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 12
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 68
proof attempt stopped: time limit
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 44
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using first arg depth ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 26
proof attempt stopped: time limit
using binary resolution
using term-depth-order strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 12
proof attempt stopped: time limit
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring smaller arities for lex ordering
using clause demodulation
seconds given: 20
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring smaller arities for lex ordering
using clause demodulation
seconds given: 130
**** EMPTY CLAUSE DERIVED ****
timer checkpoints: c(3,40,2,6,0,2,13,50,5,16,0,5,9528,4,711,9663,5,906,9663,1,906,9663,50,908,9663,40,908,9666,0,908,10991,3,1113,12378,4,1211,14866,5,1393,14866,1,1393,14866,50,1394,14866,40,1394,14869,0,1394,17337,3,1656,17892,4,1697,19772,5,1795,19784,1,1795,19784,50,1796,19784,40,1796,19787,0,1796,19794,50,1798,19797,0,1798,28123,3,2840,32590,4,3312,37306,5,3747,37308,1,3747,37308,50,3750,37308,40,3750,37311,0,3750,37318,50,3752,37321,0,3752,44100,3,4227,51250,4,4433,55491,5,4653,55493,1,4653,55493,50,4656,55493,40,4656,55496,0,4656,55497,50,4656,55497,40,4656,55500,0,4656,81692,3,7398,89382,4,8908,98454,5,9857,98462,1,9857,98462,50,9860,98462,40,9860,98465,0,9860,118207,3,12472,118207,4,12472,126466,5,13261,126489,1,13263,126489,50,13266,126489,40,13266,126492,0,13266,136384,3,14336,141920,4,14775,148496,5,15470,148507,1,15470,148507,50,15473,148507,40,15473,148510,0,15473,155256,3,15983,161622,4,16226,162526,5,16474,162526,1,16474,162526,50,16476,162526,40,16476,162529,0,16476,174482,3,17313,178673,4,17695,188717,5,18077,188719,1,18077,188719,50,18079,188719,40,18079,188722,0,18079,194033,3,18627,200190,4,18838,206431,5,19080,206431,1,19080,206431,50,19083,206431,40,19083,206431,40,19083,206434,0,19083,206440,50,19085,206443,0,19085,208105,50,19282,208105,30,19282,208105,40,19282,208108,0,19282,208114,50,19284,208117,0,19284,217556,4,20130,218132,5,20385,218134,1,20386,218134,50,20386,218134,40,20386,218137,0,20386,220622,3,20602,221096,5,20861,221100,1,20861,221100,50,20862,221100,40,20862,221103,0,20862,223588,3,21097,224339,4,21169,225743,5,21263,225752,1,21263,225752,50,21263,225752,40,21263,225755,0,21263,225761,50,21265,225764,0,21497,234777,3,22756,239295,4,23428,242373,5,23998,242376,1,23998,242376,50,23998,242376,40,23998,242379,0,23999,242385,50,24001,242388,0,24001,245322,3,24559,247872,4,24849,250412,5,25102,250422,1,25102,250422,50,25103,250422,40,25103,250425,0,25103,250425,50,25103,250425,40,25103,250428,0,25103,270586,3,28515,277106,4,30352,281446,5,31904,281446,1,31904,281446,50,31904,281446,40,31904,281449,0,31904,302407,3,34111,308900,4,35270,315476,5,36305,315476,1,36305,315476,50,36306,315476,40,36306,315479,0,36306,325270,3,37607,328904,4,38271,331251,5,38908,331259,1,38908,331259,50,38908,331259,40,38908,331262,0,38908,340711,3,39530,341624,4,39820,344416,5,40109,344426,1,40109,344426,50,40110,344426,40,40110,344429,0,40110,354859,3,41131,359394,4,41614,362901,5,42208,362908,1,42209,362908,50,42210,362908,40,42210,362911,0,42210)
START OF PROOF
13810 [?] ?
13838 [?] ?
14020 [para:13810.1.1,13838.1.1.1.1] equal(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X),X)))))),inverse(multiply(inverse(Y),Y))).
14873 [?] ?
18935 [?] ?
19248 [para:14873.1.1,18935.1.2.1.1,demod:14873] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
70137 [?] ?
71493 [?] ?
97873 [para:70137.1.1,71493.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))),Y).
105933 [?] ?
106140 [?] ?
106412 [para:106140.1.2,105933.1.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
152443 [?] ?
155821 [?] ?
155996 [para:152443.1.1,155821.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
362910 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
362911 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2).
362912 [para:19248.1.1,362911.1.1.1] -equal(multiply(multiply(inverse(X),X),a2),a2).
362913 [para:19248.1.1,19248.1.1] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
362929 [para:362913.1.1,14020.1.1.1.1.1.1.1] equal(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X),X)))))),inverse(multiply(inverse(Y),Y))).
362933 [para:362913.1.1,97873.1.1.1.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))),Y).
362935 [para:362929.1.1,362929.1.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
362943 [para:362935.1.1,362913.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
363069 [para:106412.1.1,362933.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))).
363136 [para:363069.1.2,362912.1.1.1.1] -equal(multiply(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)),a2),a2).
364157 [para:362913.1.1,155996.1.1.1] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
364188 [para:155996.1.1,362943.1.1.1] equal(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
364207 [para:155996.1.1,363069.1.2] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
364284 [para:155996.1.2,363136.1.1.1.2] -equal(multiply(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))),a2),a2).
364302 [para:364157.1.2,362933.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))))),Y).
364364 [para:364157.1.1,364157.1.1.1.1] equal(inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
364365 [para:364157.1.1,364157.1.2.1] equal(inverse(multiply(inverse(X),X)),multiply(multiply(inverse(Y),Y),multiply(inverse(Z),Z))).
364436 [para:364207.1.1,362913.1.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
365858 [para:364364.1.2,362933.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(U),U))))))),Y).
369913 [para:364188.1.1,362910.1.1.1.2,demod:364302,362933] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
369939 [para:364365.1.2,362910.1.1.1.2,demod:365858,369913] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
369956 [para:364436.1.1,362910.1.1.1.2,demod:369913,369939,slowcut:364284] contradiction
END OF PROOF
Proof found by the following strategy:
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring smaller arities for lex ordering
using clause demodulation
seconds given: 130
Split component 3 started.
START OF PROOFPART
Making new sos for split:
Original clause to be split:
-equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
Split part used next: -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
END OF PROOFPART
using hyperresolution
not using sos strategy
using positive unit paramodulation strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
clause length limited to 5
clause depth limited to 12
seconds given: 12
proof attempt stopped: sos exhausted
using hyperresolution
not using sos strategy
using positive unit paramodulation strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
clause length limited to 5
clause depth limited to 13
seconds given: 12
proof attempt stopped: sos exhausted
using binary resolution
not using sos strategy
using unit strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 4
proof attempt stopped: time limit
using binary resolution
not using sos strategy
using unit paramodulation strategy
using unit strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 4
proof attempt stopped: time limit
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 12
seconds given: 26
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 13
seconds given: 26
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 12
seconds given: 12
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
clause length limited to 5
clause depth limited to 13
seconds given: 12
proof attempt stopped: time limit
using binary resolution
using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 12
proof attempt stopped: sos exhausted
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using kb ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 68
proof attempt stopped: time limit
old unit clauses discarded
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 44
********* EMPTY CLAUSE DERIVED *********
********* EMPTY CLAUSE DERIVED *********
timer checkpoints: c(3,40,2,6,0,2,13,50,5,16,0,5,9528,4,711,9663,5,906,9663,1,906,9663,50,908,9663,40,908,9666,0,908,10991,3,1113,12378,4,1211,14866,5,1393,14866,1,1393,14866,50,1394,14866,40,1394,14869,0,1394,17337,3,1656,17892,4,1697,19772,5,1795,19784,1,1795,19784,50,1796,19784,40,1796,19787,0,1796,19794,50,1798,19797,0,1798,28123,3,2840,32590,4,3312,37306,5,3747,37308,1,3747,37308,50,3750,37308,40,3750,37311,0,3750,37318,50,3752,37321,0,3752,44100,3,4227,51250,4,4433,55491,5,4653,55493,1,4653,55493,50,4656,55493,40,4656,55496,0,4656,55497,50,4656,55497,40,4656,55500,0,4656,81692,3,7398,89382,4,8908,98454,5,9857,98462,1,9857,98462,50,9860,98462,40,9860,98465,0,9860,118207,3,12472,118207,4,12472,126466,5,13261,126489,1,13263,126489,50,13266,126489,40,13266,126492,0,13266,136384,3,14336,141920,4,14775,148496,5,15470,148507,1,15470,148507,50,15473,148507,40,15473,148510,0,15473,155256,3,15983,161622,4,16226,162526,5,16474,162526,1,16474,162526,50,16476,162526,40,16476,162529,0,16476,174482,3,17313,178673,4,17695,188717,5,18077,188719,1,18077,188719,50,18079,188719,40,18079,188722,0,18079,194033,3,18627,200190,4,18838,206431,5,19080,206431,1,19080,206431,50,19083,206431,40,19083,206431,40,19083,206434,0,19083,206440,50,19085,206443,0,19085,208105,50,19282,208105,30,19282,208105,40,19282,208108,0,19282,208114,50,19284,208117,0,19284,217556,4,20130,218132,5,20385,218134,1,20386,218134,50,20386,218134,40,20386,218137,0,20386,220622,3,20602,221096,5,20861,221100,1,20861,221100,50,20862,221100,40,20862,221103,0,20862,223588,3,21097,224339,4,21169,225743,5,21263,225752,1,21263,225752,50,21263,225752,40,21263,225755,0,21263,225761,50,21265,225764,0,21497,234777,3,22756,239295,4,23428,242373,5,23998,242376,1,23998,242376,50,23998,242376,40,23998,242379,0,23999,242385,50,24001,242388,0,24001,245322,3,24559,247872,4,24849,250412,5,25102,250422,1,25102,250422,50,25103,250422,40,25103,250425,0,25103,250425,50,25103,250425,40,25103,250428,0,25103,270586,3,28515,277106,4,30352,281446,5,31904,281446,1,31904,281446,50,31904,281446,40,31904,281449,0,31904,302407,3,34111,308900,4,35270,315476,5,36305,315476,1,36305,315476,50,36306,315476,40,36306,315479,0,36306,325270,3,37607,328904,4,38271,331251,5,38908,331259,1,38908,331259,50,38908,331259,40,38908,331262,0,38908,340711,3,39530,341624,4,39820,344416,5,40109,344426,1,40109,344426,50,40110,344426,40,40110,344429,0,40110,354859,3,41131,359394,4,41614,362901,5,42208,362908,1,42209,362908,50,42210,362908,40,42210,362911,0,42210,369955,50,42901,369955,30,42901,369955,40,42901,369958,0,42901,369964,50,42903,369967,0,42903,376063,4,43738,376063,50,43747,376063,40,43747,376066,0,43747,378749,3,43973,380403,4,44095,381450,5,44148,381455,1,44148,381455,50,44148,381455,40,44148,381458,0,44148,382597,3,44449,382597,4,44449,384091,5,44549,384096,1,44549,384096,50,44549,384096,40,44549,384099,0,44549,384105,50,44552,384108,0,44552,397619,3,45818,401730,4,46428,409688,5,47162,409688,1,47162,409688,50,47163,409688,40,47163,409691,0,47164,409697,50,47165,409700,0,47166,415054,3,47936,415770,4,48023,419977,5,48267,419983,1,48267,419983,50,48267,419983,40,48267,419986,0,48267,419986,50,48267,419986,40,48267,419989,0,48267,462267,3,52446,471420,4,53760,484487,5,55068,484541,1,55075,484541,50,55076,484541,40,55076,484544,0,55076,517070,3,57282)
START OF PROOF
484543 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
484544 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
484545 [para:484543.1.1,484543.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V))).
484547 [para:484545.1.1,484543.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)),Y).
484548 [para:484545.1.2,484543.1.1.1] equal(inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))),Y).
484561 [para:484547.1.1,484543.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(U),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)),U).
484568 [para:484547.1.1,484547.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y),U).
484751 [para:484561.1.1,484543.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(Y),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))).
484920 [para:484751.1.2,484543.1.1.1.1.1,demod:484547] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),Y).
484944 [para:484751.1.2,484547.1.1.1.1,demod:484547] equal(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))),Y).
485076 [para:484751.1.2,484751.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))).
485088 [para:485076.1.1,484543.1.1.1.1.1.2.1.1,demod:484543] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
485089 [para:485076.1.1,484543.1.1.1.1.1.2.1.2.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U))))))))),multiply(X,multiply(Z,U)))),Y).
485157 [para:485076.1.1,484568.1.1.1.1.2.1.2.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))),Y),U).
485181 [para:485076.1.1,485076.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,U))),inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,Z))),multiply(inverse(multiply(Y,W)),U)))).
485365 [para:485076.1.1,485088.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
488220 [para:484568.1.1,485089.1.1.1.1.1.2.1.2.1.1,demod:485157] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))),multiply(X,Z))),Y).
488358 [para:484547.1.1,488220.1.1.1.1.1.2.1.2.1.2.1.1.1,demod:484547] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))))),multiply(X,Z))),Y).
488582 [para:488358.1.1,484944.1.1.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y))))),multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))))).
488865 [para:488582.1.1,484920.1.1.1.1.1.1.1.1,demod:484944] equal(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),inverse(multiply(X,inverse(multiply(inverse(X),X))))).
488885 [para:488582.1.1,484944.1.1] equal(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U))))),Y).
488886 [para:488582.1.1,484944.1.1.1.1.1.1.1,demod:488885] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(X),X)))).
489280 [para:488886.1.1,484920.1.1.1.1.1.1.1.1,demod:488885] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
489295 [para:488886.1.1,484944.1.1.1.1.1.1.1,demod:488885] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
489514 [para:488886.1.2,488886.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(Z),Z)))).
489628 [para:489295.1.1,484920.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
489641 [para:489295.1.1,484944.1.1.1.1.1] equal(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),inverse(multiply(inverse(inverse(Y)),inverse(Y)))))),Y).
489914 [para:489280.1.1,489295.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
489916 [para:489280.1.1,489280.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
490115 [para:489514.1.1,489295.1.1] equal(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
492053 [para:490115.1.1,488582.1.2,demod:489641] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
492373 [para:492053.1.2,484920.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
492697 [para:492053.1.1,488886.1.2.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,multiply(inverse(Z),Z))).
492711 [para:492053.1.1,489514.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,inverse(multiply(inverse(Z),Z)))).
492719 [para:492053.1.2,489914.1.1.2] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
492769 [para:492053.1.2,492053.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
493404 [para:492769.1.1,484920.1.1.1.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
493698 [para:492769.1.1,492053.1.2.1] equal(inverse(multiply(inverse(X),X)),multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z)))).
497276 [para:492053.1.1,492697.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(Z),Z))).
520429 [para:492053.1.1,493404.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))),Y).
520604 [para:492719.1.2,493404.1.1.1.2.1.2.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(U),U)))))))),Y).
522048 [para:493698.1.2,484543.1.1.1.2,demod:520604] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
522073 [para:493698.1.2,484547.1.1.2,demod:520429,522048] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))),X).
522108 [para:493698.1.2,484548.1.1.1.1.2,demod:520429,522048,522073] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(Y),Y))))),X).
522917 [para:522048.1.1,484548.1.1.1.1.1,demod:522108] equal(inverse(inverse(multiply(X,multiply(inverse(X),Y)))),Y).
522956 [para:522048.1.1,484561.1.1,demod:492373] equal(multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(Z),inverse(multiply(multiply(X,Y),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))))))),Z).
522985 [para:522048.1.1,484751.1.2.1.1.2.1.1.1.1.1.2,demod:522956,489628,522048] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),Z))))),Y).
523024 [para:522048.1.1,484920.1.1.1.2.1.2,demod:522048,522985] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
523324 [para:522048.1.1,493404.1.1.1.2] equal(inverse(multiply(multiply(inverse(X),X),Y)),inverse(Y)).
523465 [para:489280.1.1,522917.1.1.1.1.2.1,demod:523324] equal(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),Y))),Y).
523488 [para:489916.1.2,522917.1.1.1.1.2.1,demod:523324,523024] equal(inverse(inverse(X)),X).
523496 [para:492769.1.1,522917.1.1.1.1.2.1,demod:523465] equal(multiply(multiply(inverse(X),X),Y),Y).
523674 [para:488865.1.1,523488.1.1.1,demod:522108] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
523680 [para:523488.1.1,492697.1.2.2.1,demod:523674] equal(X,multiply(X,multiply(Y,inverse(Y)))).
523681 [para:523488.1.1,497276.1.1.2.1,demod:523680] equal(X,multiply(X,multiply(inverse(Y),Y))).
523682 [para:523488.1.1,492711.1.2.2.1.1,demod:523681] equal(X,multiply(X,inverse(multiply(Y,inverse(Y))))).
523704 [para:523488.1.1,522917.1.1.1.1.2.1,demod:523488] equal(multiply(inverse(X),multiply(X,Y)),Y).
523714 [para:523496.1.1,484547.1.1.1.1,demod:523496,523674,523488] equal(multiply(multiply(X,inverse(Y)),Y),X).
523741 [para:523496.1.1,485088.1.1.1.1,demod:523496] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
523759 [para:523680.1.2,484543.1.1.1,demod:523682,523488] equal(multiply(X,inverse(multiply(inverse(Y),X))),Y).
523760 [para:523680.1.2,484545.1.1.1,demod:523714,523741,523759,523682,523488] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
523768 [para:523680.1.2,485076.1.1.1,demod:523741,523488] equal(multiply(X,Y),inverse(multiply(inverse(Y),inverse(X)))).
523774 [para:523680.1.2,485365.1.1.1.1.1.1,demod:523741,523680,523704] equal(multiply(inverse(X),multiply(inverse(Y),Z)),multiply(inverse(multiply(Y,X)),Z)).
523781 [para:523680.1.2,485181.1.1.1,demod:523774,523741,523488] equal(multiply(X,multiply(Y,Z)),inverse(multiply(inverse(Z),multiply(inverse(Y),inverse(X))))).
523916 [para:523760.1.1,485088.1.1.1.1,demod:523741,523488] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
523946 [para:523768.1.1,484544.1.2,demod:523774,523916,cut:523781] contradiction
END OF PROOF
Proof found by the following strategy:
using binary resolution
using first neg lit preferred strategy
not using sos strategy
using unit paramodulation strategy
using unit strategy
using dynamic demodulation
using ordered paramodulation
using lex ordering for equality
preferring bigger arities for lex ordering
using clause demodulation
seconds given: 44
old unit clauses discarded
Split attempt finished with SUCCESS.
***GANDALF_FOUND_A_REFUTATION***
Global statistics over all passes:
given clauses: 2753
derived clauses: 1426622
kept clauses: 280468
kept size sum: 0
kept mid-nuclei: 2
kept new demods: 29146
forw unit-subs: 742803
forw double-subs: 360
forw overdouble-subs: 0
backward subs: 656
fast unit cutoff: 19
full unit cutoff: 0
dbl unit cutoff: 0
real runtime : 583.0
process. runtime: 582.64
specific non-discr-tree subsumption statistics:
tried: 0
length fails: 0
strength fails: 0
predlist fails: 0
aux str. fails: 0
by-lit fails: 0
full subs tried: 0
full subs fail: 0
; program args: ("/home/tptp/Systems/Gandalf---c-2.6B/gandalf" "/tmp/GandalfTemp4115")
MODEL STARTS sk2()=0 environment(0)=t environment(1)=f an_organisation()=0 appear(0,0)=0 appear(1,0)=1 appear(0,1)=1 appear(1,1)=0 in_environment(0,0)=t in_environment(1,0)=f in_environment(0,1)=f in_environment(1,1)=f first_movers()=1 equal(0,0)=t equal(1,0)=f equal(0,1)=f equal(1,1)=t e()=1 number_of_organizations(0,0)=0 number_of_organizations(1,0)=1 number_of_organizations(0,1)=0 number_of_organizations(1,1)=0 zero()=0 greater(0,0)=f greater(1,0)=t greater(0,1)=f greater(1,1)=t sk1(0,0)=0 sk1(1,0)=0 sk1(0,1)=0 sk1(1,1)=0 subpopulation(0,0,0)=f subpopulation(1,0,0)=f subpopulation(0,1,0)=f subpopulation(1,1,0)=f subpopulation(0,0,1)=f subpopulation(1,0,1)=f subpopulation(0,1,1)=f subpopulation(1,1,1)=f cardinality_at_time(0,0)=0 cardinality_at_time(1,0)=0 cardinality_at_time(0,1)=0 cardinality_at_time(1,1)=0 efficient_producers()=0 greater_or_equal(0,0)=t greater_or_equal(1,0)=t greater_or_equal(0,1)=f greater_or_equal(1,1)=t MODEL ENDS
---------------- PROOF ---------------- 1 [] animal(A)| -wolf(A). 2 [] animal(A)| -fox(A). 3 [] animal(A)| -bird(A). 5 [] animal(A)| -snail(A). 6 [] plant(A)| -grain(A). 7 [] eats(A,B)|eats(A,C)| -animal(A)| -plant(B)| -animal(C)| -plant(D)| -much_smaller(C,A)| -eats(C,D). 9 [] much_smaller(A,B)| -snail(A)| -bird(B). 10 [] much_smaller(A,B)| -bird(A)| -fox(B). 11 [] much_smaller(A,B)| -fox(A)| -wolf(B). 13 [] -wolf(A)| -grain(B)| -eats(A,B). 15 [] -bird(A)| -snail(B)| -eats(A,B). 18 [] plant(snail_food_of(A))| -snail(A). 19 [] eats(A,snail_food_of(A))| -snail(A). 20 [] -animal(A)| -animal(B)| -grain(C)| -eats(A,B)| -eats(B,C). 23 [factor,7.4.6] eats(A,B)|eats(A,C)| -animal(A)| -plant(B)| -animal(C)| -much_smaller(C,A)| -eats(C,B). 28 [] wolf(a_wolf). 29 [] fox(a_fox). 30 [] bird(a_bird). 32 [] snail(a_snail). 33 [] grain(a_grain). 34 [hyper,28,1] animal(a_wolf). 35 [hyper,29,11,28] much_smaller(a_fox,a_wolf). 36 [hyper,29,2] animal(a_fox). 37 [hyper,30,10,29] much_smaller(a_bird,a_fox). 38 [hyper,30,3] animal(a_bird). 44 [hyper,32,19] eats(a_snail,snail_food_of(a_snail)). 45 [hyper,32,18] plant(snail_food_of(a_snail)). 46 [hyper,32,9,30] much_smaller(a_snail,a_bird). 47 [hyper,32,5] animal(a_snail). 48 [hyper,33,6] plant(a_grain). 50 [hyper,44,7,38,48,47,45,46] eats(a_bird,a_grain)|eats(a_bird,a_snail). 55 [hyper,50,15,30,32] eats(a_bird,a_grain). 56 [hyper,55,23,36,48,38,37] eats(a_fox,a_grain)|eats(a_fox,a_bird). 62 [hyper,56,20,36,38,33,55] eats(a_fox,a_grain). 63 [hyper,62,23,34,48,36,35] eats(a_wolf,a_grain)|eats(a_wolf,a_fox). 67 [hyper,63,13,28,33] eats(a_wolf,a_fox). 69 [hyper,67,20,34,36,33,62] $F. ------------ end of proof -------------
NOTE: In order to save space in the representation of the model, sometimes, some entries in some of the definition tables are missing. This is not a bug! More detailedly, it might happen that for a model with a domain of size n, for some argument position, only a subset {'1,'2,..,'k} of all domain elements is shown, with k < n. What this means is that the entries for other domain elements 'j (with k < j <= n) occurring at that argument position look the same as entries with 'k at that position. Problem NLP041-1.p is an example where a model is represented in such a way.
an_organisation = '1
appear('1,'1) = '2
appear('1,'2) = '2
appear('2,'1) = '1
appear('2,'2) = '1
cardinality_at_time('1,'1) = '2
cardinality_at_time('1,'2) = '2
cardinality_at_time('2,'1) = '2
cardinality_at_time('2,'2) = '2
e = '1
efficient_producers = '2
environment('1) : FALSE
environment('2) : TRUE
first_movers = '2
greater('1,'1) : TRUE
greater('1,'2) : TRUE
greater('2,'1) : FALSE
greater('2,'2) : TRUE
greater_or_equal('1,'1) : TRUE
greater_or_equal('1,'2) : TRUE
greater_or_equal('2,'1) : FALSE
greater_or_equal('2,'2) : TRUE
in_environment('1,'1) : TRUE
in_environment('1,'2) : TRUE
in_environment('2,'1) : TRUE
in_environment('2,'2) : TRUE
number_of_organizations('1,'1) = '2
number_of_organizations('1,'2) = '1
number_of_organizations('2,'1) = '2
number_of_organizations('2,'2) = '2
sk1('1,'1) = '2
sk1('1,'2) = '2
sk1('2,'1) = '2
sk1('2,'2) = '2
sk2 = '2
subpopulation('1,'1,'1) : TRUE
subpopulation('1,'1,'2) : TRUE
subpopulation('1,'2,'1) : TRUE
subpopulation('1,'2,'2) : TRUE
subpopulation('2,'1,'1) : TRUE
subpopulation('2,'1,'2) : TRUE
subpopulation('2,'2,'1) : TRUE
subpopulation('2,'2,'2) : TRUE
zero = '1
abstraction('1,'1) : FALSE
abstraction('1,'2) : FALSE
abstraction('1,'3) : FALSE
abstraction('1,'4) : TRUE
act('1,'1) : FALSE
act('1,'2) : FALSE
act('1,'3) : TRUE
act('1,'4) : FALSE
actual_world('1) : TRUE
agent('1,'1,'1) : TRUE
agent('1,'1,'2) : TRUE
agent('1,'1,'3) : TRUE
agent('1,'1,'4) : TRUE
agent('1,'2,'1) : TRUE
agent('1,'2,'2) : TRUE
agent('1,'2,'3) : TRUE
agent('1,'2,'4) : TRUE
agent('1,'3,'1) : TRUE
agent('1,'3,'2) : FALSE
agent('1,'3,'3) : FALSE
agent('1,'3,'4) : FALSE
agent('1,'4,'1) : TRUE
agent('1,'4,'2) : TRUE
agent('1,'4,'3) : TRUE
agent('1,'4,'4) : FALSE
animate('1,'1) : TRUE
animate('1,'2) : FALSE
animate('1,'3) : FALSE
animate('1,'4) : FALSE
beverage('1,'1) : FALSE
beverage('1,'2) : TRUE
beverage('1,'3) : FALSE
beverage('1,'4) : FALSE
entity('1,'1) : TRUE
entity('1,'2) : TRUE
entity('1,'3) : FALSE
entity('1,'4) : FALSE
event('1,'1) : FALSE
event('1,'2) : FALSE
event('1,'3) : TRUE
event('1,'4) : FALSE
eventuality('1,'1) : FALSE
eventuality('1,'2) : FALSE
eventuality('1,'3) : TRUE
eventuality('1,'4) : FALSE
existent('1,'1) : TRUE
existent('1,'2) : TRUE
existent('1,'3) : FALSE
existent('1,'4) : FALSE
female('1,'1) : TRUE
female('1,'2) : FALSE
female('1,'3) : FALSE
female('1,'4) : FALSE
food('1,'1) : FALSE
food('1,'2) : TRUE
food('1,'3) : FALSE
food('1,'4) : FALSE
forename('1,'1) : FALSE
forename('1,'2) : FALSE
forename('1,'3) : FALSE
forename('1,'4) : TRUE
general('1,'1) : FALSE
general('1,'2) : FALSE
general('1,'3) : FALSE
general('1,'4) : TRUE
human('1,'1) : TRUE
human('1,'2) : FALSE
human('1,'3) : FALSE
human('1,'4) : FALSE
human_person('1,'1) : TRUE
human_person('1,'2) : FALSE
human_person('1,'3) : FALSE
human_person('1,'4) : FALSE
impartial('1,'1) : TRUE
impartial('1,'2) : TRUE
impartial('1,'3) : FALSE
impartial('1,'4) : FALSE
living('1,'1) : TRUE
living('1,'2) : FALSE
living('1,'3) : FALSE
living('1,'4) : FALSE
mia_forename('1,'1) : FALSE
mia_forename('1,'2) : FALSE
mia_forename('1,'3) : FALSE
mia_forename('1,'4) : TRUE
nonexistent('1,'1) : FALSE
nonexistent('1,'2) : FALSE
nonexistent('1,'3) : TRUE
nonexistent('1,'4) : TRUE
nonhuman('1,'1) : FALSE
nonhuman('1,'2) : TRUE
nonhuman('1,'3) : TRUE
nonhuman('1,'4) : TRUE
nonliving('1,'1) : FALSE
nonliving('1,'2) : TRUE
nonliving('1,'3) : TRUE
nonliving('1,'4) : TRUE
nonreflexive('1,'1) : FALSE
nonreflexive('1,'2) : FALSE
nonreflexive('1,'3) : TRUE
nonreflexive('1,'4) : TRUE
object('1,'1) : FALSE
object('1,'2) : TRUE
object('1,'3) : FALSE
object('1,'4) : FALSE
of('1,'1,'1) : FALSE
of('1,'1,'2) : TRUE
of('1,'1,'3) : TRUE
of('1,'1,'4) : TRUE
of('1,'2,'1) : FALSE
of('1,'2,'2) : TRUE
of('1,'2,'3) : TRUE
of('1,'2,'4) : TRUE
of('1,'3,'1) : FALSE
of('1,'3,'2) : TRUE
of('1,'3,'3) : TRUE
of('1,'3,'4) : TRUE
of('1,'4,'1) : TRUE
of('1,'4,'2) : TRUE
of('1,'4,'3) : TRUE
of('1,'4,'4) : TRUE
order('1,'1) : FALSE
order('1,'2) : FALSE
order('1,'3) : TRUE
order('1,'4) : FALSE
organism('1,'1) : TRUE
organism('1,'2) : FALSE
organism('1,'3) : FALSE
organism('1,'4) : FALSE
past('1,'1) : FALSE
past('1,'2) : FALSE
past('1,'3) : TRUE
past('1,'4) : FALSE
patient('1,'1,'1) : TRUE
patient('1,'1,'2) : TRUE
patient('1,'1,'3) : TRUE
patient('1,'1,'4) : TRUE
patient('1,'2,'1) : TRUE
patient('1,'2,'2) : TRUE
patient('1,'2,'3) : TRUE
patient('1,'2,'4) : TRUE
patient('1,'3,'1) : FALSE
patient('1,'3,'2) : TRUE
patient('1,'3,'3) : TRUE
patient('1,'3,'4) : TRUE
patient('1,'4,'1) : FALSE
patient('1,'4,'2) : FALSE
patient('1,'4,'3) : FALSE
patient('1,'4,'4) : TRUE
relation('1,'1) : FALSE
relation('1,'2) : FALSE
relation('1,'3) : FALSE
relation('1,'4) : TRUE
relname('1,'1) : FALSE
relname('1,'2) : FALSE
relname('1,'3) : FALSE
relname('1,'4) : TRUE
shake_beverage('1,'1) : FALSE
shake_beverage('1,'2) : TRUE
shake_beverage('1,'3) : FALSE
shake_beverage('1,'4) : FALSE
singleton('1,'1) : TRUE
singleton('1,'2) : TRUE
singleton('1,'3) : TRUE
singleton('1,'4) : TRUE
skc5 = '1
skc6 = '3
skc7 = '2
skc8 = '4
skc9 = '1
specific('1,'1) : TRUE
specific('1,'2) : TRUE
specific('1,'3) : TRUE
specific('1,'4) : FALSE
substance_matter('1,'1) : FALSE
substance_matter('1,'2) : TRUE
substance_matter('1,'3) : FALSE
substance_matter('1,'4) : FALSE
thing('1,'1) : TRUE
thing('1,'2) : TRUE
thing('1,'3) : TRUE
thing('1,'4) : TRUE
unisex('1,'1) : FALSE
unisex('1,'2) : TRUE
unisex('1,'3) : TRUE
unisex('1,'4) : TRUE
woman('1,'1) : TRUE
woman('1,'2) : FALSE
woman('1,'3) : FALSE
woman('1,'4) : FALSE
Axioms:
1: ~E.x:y ~big_fxz big_fyz
2: ~E.x:y ~big_fzx big_fzy
3: ~E.x:y ~E.y:z E.x:z
4 >~E.x:a ~E.y:b big_fxy
5: ~E.x:y E.hxz:hyz
6 >~E.x:y E.hzx:hzy
7: ~E.x:y E.fx:fy
8: ~E.x:y E.gx:gy
9 >~big_fxy E.x:a
10: ~big_fxy E.y:b
11: ~E.x:y E.y:x
12 >E.x:x
Negated conclusion:
13S ~big_fxfy E.x:gy big_fhyzfy ~big_fhyzfy
14S ~E.x:gy big_fxfy big_fhyzfy E.hyz:z
15S ~E.x:gy big_fxfy ~E.hyz:z ~big_fhyzfy
16S>~E.fx:x ~E.hxy:y ~big_fhxyfx
17S>~E.fx:x big_fhxyfx E.hxy:y
18S>~big_fxfy ~E.x:gy E.fy:y
19S>~E.x:gy big_fxfy E.fy:y
---------------
Phase 0 clauses used in proof:
20S>(19b*18a) ~E.x:gy E.fy:y
Phases 1 and 2 clauses used in proof:
21S>(20a,12a) E.fx:x
22S>(20b,17a) ~E.x:gy big_fhyzfy E.hyz:z
23S>(22b,9a) ~E.x:gy E.hyz:z E.hyz:a
24S>(23a,12a) E.hxy:y E.hxy:a
25S>(24ab) E.hxa:a
26S>(21a,4a) ~E.x:b big_ffax
27S>[26b,21a] ~E.x:b big_fax
28S>[27a,12a] big_fab
29S>(16b,6b) ~E.fx:x ~big_fhxhxyfx ~E.hxy:y
30S>[29a,21a] ~E.x:x ~big_fhxhxyfx ~E.hxy:y
31S>[30b,21a] ~E.x:x ~big_fhxhxyx ~E.hxy:y
32S>[31a,12a] ~big_fhxhxyx ~E.hxy:y
33S>(32b,6b) ~big_fhxhxhxyx ~E.hxy:y
34: 33|{a/y} ~big_fhxhxhxax ~E.hxa:a
35S>(34b,25a) ~big_fhxhxhxax
36S>[35a,25a] ~big_fhxhxax
37S>[36a,25a] ~big_fhxax
38S>[37a,25a] ~big_fax
39S>(38a,28a) []
<clause> : <number>"." <clause body> <auxilliary info> "["<background list>"]"
% nonempty clause
: <number>'. #' <auxilliary info> '['<background list>']'
% empty clause
<clause body> : <literals>
% all literals are selected
: <literals>1 | <literals>2
% <literals>1 are selected
% <literals>2 are nonselected
<background list> : <flags><ancestors>
<ancestors> : % empty (must be an input clause)
: <number> ("," <number>)*
<flags> : (<flag> )+
<flag> : "in" % input clause
: "pp" % clause obtained by preprocessing
: "br" % generated by binary resolution
: "hr" % generated by hyperresolution
: "fs" % generated by forward superposition
: "bs" % generated by backward superposition
: "er" % generated by equality resolution
: "ef" % generated by equality factoring
: "fd" % simplified by forward demodulation
: "bd" % simplified by backward demodulation
: "ers" % simplified by equality resolution
: "fsr" % simplified by forward subsumption resolution
: "sp" % splitting was used
: "rea" % "reanimated" passive clause (selected in Discount algorithm)
: "nm" % the clause is a part of a name introduction in
% splitting, or obtained by preprocessing from such
% a clause
: "ns" % negative selection was used (does not mean that
% all the selected literals are negative)
<literals> : <literal> [" \/ " <literals>]
<literal> : <standard literal>
: <equational literal>
: <splitting literal>
<standard literal> : ["~"]<atom> % "~" is for negation
<atom> : <predicate symbol> % propositional variable
: <predicate symbol><arguments>
<equational literal> : <term> = <term> % unoriented positive equality
: <term> != <term> % unoriented negative equality
: <term> == <term> % oriented positive equality
: <term> !== <term> % oriented negative equality
<splitting literal> : "["<predicate symbol>"]"
<term> : <variable>
: <constant>
: <function symbol><arguments>
<variable> : "X"<number>
<arguments> : "("<term> (","<term>)* ")"
vproof(<JobId>,[<clause body> <clause number> <ancestors> <flags>]).<JobId> is an atom, uniquely identifying the job that produced the proof. <ancestors> is a list of ancestor numbers. <flags> is a list of flags, every flag is an atom. <clause body> is a list of literals.
<literal> : "++"<atom> % unselected positive literal
: "+++"<atom> % selected positive literal
: "--"<atom> % unselected negative literal
: "---"<atom> % selected negative literal
<atom> : <term>
: "("<term>" = "<term>")" % unoriented equality
: "("<term>" => "<term>")" % oriented equality
<term> : <function symbol>["("<term>(","<term>)*")"]
: <variable>
<function symbol> is a Prolog alphanumeric identifier.
<variable> is a quoted Prolog atom "'X"%======================== Proof: ========================= % 1. member(z,z) /3/3/0/ 0pe [in ] % 2. member(z,diagonalise(element_relation)) /4/4/0/ 0pe [in ] % 120. X0=null_class \/ intersection(X0,regular(X0))=null_class /9/9/0/ 2pe [in ] % 121. X0=null_class \/ member(regular(X0),X0) /7/7/0/ 1pe [in ] % 144. union(X0,singleton(X0))=successor(X0) /7/7/0/ 1pe [in ] % 161. complement(intersection(complement(X0),complement(X1)))=union(X0,X1) /10/10/0/ 1pe [in ] % 162. member(X0,complement(X1)) \/ ~member(X0,universal_class) \/ member(X0,X1) /10/10/0/ 0pe [in ] % 163. ~member(X0,complement(X1)) \/ ~member(X0,X1) /7/7/0/ 0pe [in ] % 164. ~member(X0,X2) \/ ~member(X0,X1) \/ member(X0,intersection(X1,X2)) /11/11/0/ 0pe [in ] % 165. ~member(X0,intersection(X1,X2)) \/ member(X0,X2) /8/8/0/ 0pe [in ] % 166. ~member(X0,intersection(X1,X2)) \/ member(X0,X1) /8/8/0/ 0pe [in ] % 175. unordered_pair(X0,X0)=singleton(X0) /6/6/0/ 1pe [in ] % 178. ~member(X0,universal_class) \/ member(X0,unordered_pair(X0,X1)) /8/8/0/ 0pe [in ] % 179. X0=X1 \/ ~member(X0,unordered_pair(X1,X2)) \/ X0=X2 /11/11/0/ 2pe [in ] % 183. subclass(X0,universal_class) /3/3/0/ 0pe [in ] % 186. ~member(X2,X0) \/ ~subclass(X0,X1) \/ member(X2,X1) /9/9/0/ 0pe [in ] % 190. member(z,z) /3/3/0/ 0pe [pp 1] % 191. member(z,diagonalise(element_relation)) /4/4/0/ 0pe [pp 2] % 237. intersection(X0,regular(X0))==null_class | X0=null_class /9/9/5/ 2pe [pp 120] % 238. member(regular(X0),X0) | X0=null_class /7/7/3/ 1pe [pp 121] % 261. union(X0,singleton(X0))==successor(X0) /7/7/3/ 1pe [pp 144] % 278. complement(intersection(complement(X0),complement(X1)))==union(X0,X1) /10/10/4/ 1pe [pp 161]% 279. ~member(X0,universal_class) | member(X0,complement(X1)) \/ member(X0,X1) /10/10/7/ 0pe [pp 162] % 280. ~member(X0,complement(X1)) | ~member(X0,X1) /7/7/3/ 0pe [pp 163] % 281. ~member(X0,X1) | ~member(X0,X2) \/ member(X0,intersection(X1,X2)) /11/11/8/ 0pe [pp ns 164] % 282. ~member(X0,intersection(X1,X2)) | member(X0,X2) /8/8/3/ 0pe [pp 165] % 283. ~member(X0,intersection(X1,X2)) | member(X0,X1) /8/8/3/ 0pe [pp 166] % 292. unordered_pair(X0,X0)==singleton(X0) /6/6/3/ 1pe [pp 175] % 295. ~member(X0,universal_class) | member(X0,unordered_pair(X0,X1)) /8/8/5/ 0pe [pp 178] % 296. ~member(X0,unordered_pair(X1,X2)) | X0=X1 \/ X0=X2 /11/11/6/ 2pe [pp 179] % 299. subclass(X0,universal_class) /3/3/0/ 0pe [pp 183] % 302. ~subclass(X0,X1) | ~member(X2,X0) \/ member(X2,X1) /9/9/6/ 0pe [pp 186] % 303. member(z,z) /3/3/0/ 0pe [pp 190] % 304. member(z,diagonalise(element_relation)) /4/4/0/ 0pe [pp 191] % 350. intersection(X0,regular(X0))==null_class | X0=null_class /9/9/5/ 2pe [pp 237] % 351. member(regular(X0),X0) | X0=null_class /7/7/3/ 1pe [pp 238] % 374. union(X0,singleton(X0))==successor(X0) /7/7/3/ 1pe [pp 261] % 391. complement(intersection(complement(X0),complement(X1)))==union(X0,X1) /10/10/4/ 1pe [pp 278]% 392. ~member(X0,universal_class) | member(X0,complement(X1)) \/ member(X0,X1) /10/10/7/ 0pe [pp 279] % 393. ~member(X0,complement(X1)) | ~member(X0,X1) /7/7/3/ 0pe [pp 280] % 394. ~member(X0,X1) | ~member(X0,X2) \/ member(X0,intersection(X2,X1)) /11/11/8/ 0pe [pp ns 281] % 395. ~member(X0,intersection(X1,X2)) | member(X0,X2) /8/8/3/ 0pe [pp 282] % 396. ~member(X0,intersection(X1,X2)) | member(X0,X1) /8/8/3/ 0pe [pp 283] % 405. unordered_pair(X0,X0)==singleton(X0) /6/6/3/ 1pe [pp 292] % 408. ~member(X0,universal_class) | member(X0,unordered_pair(X0,X1)) /8/8/5/ 0pe [pp 295] % 409. ~member(X0,unordered_pair(X1,X2)) | X0=X1 \/ X0=X2 /11/11/6/ 2pe [pp 296] % 412. subclass(X0,universal_class) /3/3/0/ 0pe [pp 299] % 415. ~subclass(X0,X1) | ~member(X2,X0) \/ member(X2,X1) /9/9/6/ 0pe [pp 302] % 424. member(z,z) /3/3/0/ 0pe [pp 303] % 425. member(z,diagonalise(element_relation)) /4/4/0/ 0pe [pp 304] % 457. intersection(X0,regular(X0))==null_class | X0=null_class /9/9/5/ 2pe [pp 350] % 458. member(regular(X0),X0) | X0=null_class /7/7/3/ 1pe [pp 351] % 474. union(X0,singleton(X0))==successor(X0) /7/7/3/ 1pe [pp 374] % 491. complement(intersection(complement(X0),complement(X1)))==union(X0,X1) /10/10/4/ 1pe [pp 391]% 492. ~member(X0,universal_class) | member(X0,complement(X1)) \/ member(X0,X1) /10/10/7/ 0pe [pp 392] % 493. ~member(X0,complement(X1)) | ~member(X0,X1) /7/7/3/ 0pe [pp 393] % 494. ~member(X0,X1) | ~member(X0,X2) \/ member(X0,intersection(X1,X2)) /11/11/8/ 0pe [pp ns 394] % 495. ~member(X0,intersection(X1,X2)) | member(X0,X2) /8/8/3/ 0pe [pp 395] % 496. ~member(X0,intersection(X1,X2)) | member(X0,X1) /8/8/3/ 0pe [pp 396] % 505. unordered_pair(X0,X0)==singleton(X0) /6/6/3/ 1pe [pp 405] % 508. ~member(X0,universal_class) | member(X0,unordered_pair(X0,X1)) /8/8/5/ 0pe [pp 408] % 509. ~member(X0,unordered_pair(X1,X2)) | X0=X1 \/ X0=X2 /11/11/6/ 2pe [pp 409] % 512. subclass(X0,universal_class) /3/3/0/ 0pe [pp 412] % 515. ~subclass(X0,X1) | ~member(X2,X0) \/ member(X2,X1) /9/9/6/ 0pe [pp 415] % 526. member(z,z) /3/3/0/ 0pe [pp 424] % 527. member(z,diagonalise(element_relation)) /4/4/0/ 0pe [pp 425] % 556. intersection(X0,regular(X0))==null_class | X0=null_class /9/9/5/ 2pe [pp 457] % 557. member(regular(X0),X0) | X0=null_class /7/7/3/ 1pe [pp 458] % 573. union(X0,singleton(X0))==successor(X0) /7/7/3/ 1pe [pp 474] % 590. complement(intersection(complement(X0),complement(X1)))==union(X0,X1) /10/10/4/ 1pe [pp 491]% 591. ~member(X0,universal_class) | member(X0,complement(X1)) \/ member(X0,X1) /10/10/7/ 0pe [pp 492] % 592. ~member(X0,complement(X1)) | ~member(X0,X1) /7/7/3/ 0pe [pp 493] % 593. ~member(X0,X1) | ~member(X0,X2) \/ member(X0,intersection(X2,X1)) /11/11/8/ 0pe [pp ns 494] % 594. ~member(X0,intersection(X1,X2)) | member(X0,X2) /8/8/3/ 0pe [pp 495] % 595. ~member(X0,intersection(X1,X2)) | member(X0,X1) /8/8/3/ 0pe [pp 496] % 604. unordered_pair(X0,X0)==singleton(X0) /6/6/3/ 1pe [pp 505] % 607. ~member(X0,universal_class) | member(X0,unordered_pair(X0,X1)) /8/8/5/ 0pe [pp 508] % 608. ~member(X0,unordered_pair(X1,X2)) | X0=X1 \/ X0=X2 /11/11/6/ 2pe [pp 509] % 611. subclass(X0,universal_class) /3/3/0/ 0pe [pp 512] % 614. ~subclass(X0,X1) | ~member(X2,X0) \/ member(X2,X1) /9/9/6/ 0pe [pp 515] % * 620. member(z,z) /3/3/0/ 0pe vip [pp 526] % * 621. member(z,diagonalise(element_relation)) /4/4/0/ 0pe vip [pp 527] % * 650. intersection(X0,regular(X0))==null_class | X0=null_class /9/9/5/ 2pe vip [pp 556] % * 651. member(regular(X0),X0) | X0=null_class /7/7/3/ 1pe vip [pp 557] % * 667. union(X0,singleton(X0))==successor(X0) /7/7/3/ 1pe [pp 573] % * 685. complement(intersection(complement(X0),complement(X1)))==union(X0,X1) /10/10/4/ 1pe [pp 590] % * 687. ~member(X0,universal_class) | member(X0,complement(X1)) \/ member(X0,X1) /10/10/7/ 0pe [pp 591] % * 688. ~member(X0,complement(X1)) | ~member(X0,X1) /7/7/3/ 0pe vip [pp 592] % * 689. ~member(X0,X1) | ~member(X0,X2) \/ member(X0,intersection(X1,X2)) /11/11/8/ 0pe [pp ns 593] % * 690. ~member(X0,intersection(X1,X2)) | member(X0,X2) /8/8/3/ 0pe vip [pp 594] % * 691. ~member(X0,intersection(X1,X2)) | member(X0,X1) /8/8/3/ 0pe vip [pp 595] % * 700. unordered_pair(X0,X0)==singleton(X0) /6/6/3/ 1pe [pp 604] % * 703. ~member(X0,universal_class) | member(X0,unordered_pair(X0,X1)) /8/8/5/ 0pe [pp 607] % * 704. ~member(X0,unordered_pair(X1,X2)) | X0=X1 \/ X0=X2 /11/11/6/ 2pe [pp 608] % * 707. subclass(X0,universal_class) /3/3/0/ 0pe vip [pp 611] % * 710. ~subclass(X0,X1) | ~member(X2,X0) \/ member(X2,X1) /9/9/6/ 0pe [pp 614] % * 753. ~member(regular(complement(X0)),X0) | complement(X0)==null_class /9/9/4/ 1pe [br 651,688] % * 757. ~member(z,X0) | member(z,intersection(z,X0)) /8/8/5/ 0pe [br 620,689] % * 758. ~member(z,X0) | member(z,intersection(diagonalise(element_relation),X0)) /9/9/6/ 0pe [br 621,689] % * 761. member(regular(intersection(X0,X1)),X1) | intersection(X0,X1)==null_class /11/11/5/ 1pe [br 651,690] % * 768. member(regular(intersection(X0,X1)),X0) | intersection(X0,X1)==null_class /11/11/5/ 1pe [br 651,691] % * 798. ~member(X0,singleton(X1)) | X0=X1 /7/7/3/ 1pe vip [fs 700,704] % * 822. ~member(X0,X1) | member(X0,universal_class) /6/6/3/ 0pe [br 707,710] % * 999. member(z,universal_class) /3/3/0/ 0pe vip [br 620,822] % * 1000. member(regular(X0),universal_class) | X0=null_class /7/7/3/ 1pe vip [br 651,822] % * 1005. member(z,unordered_pair(z,X0)) /5/5/0/ 0pe vip [br 703,999] % * 1007. member(z,complement(X0)) | member(z,X0) /7/7/3/ 0pe vip [br 687,999] % * 1083. member(z,singleton(z)) /4/4/0/ 0pe vip [fs 700,1005] % * 1085. ~member(z,X0) | member(z,intersection(singleton(z),X0)) /9/9/6/ 0pe [br 689,1083] % * 1568. regular(singleton(X0))==X0 | singleton(X0)==null_class /9/9/6/ 2pe vip [br 651,798] % * 1669. member(z,intersection(complement(X0),complement(X1))) | member(z,union(X0,X1)) /12/12/5/ 0pe [fs 685,1007] % * 2598. complement(universal_class)==null_class /4/4/2/ 1pe vip [br 1000,753] % * 2619. ~member(X0,null_class) /3/3/0/ 0pe vip [bs fsr 822,688,2598] % * 2730. member(z,intersection(diagonalise(element_relation),singleton(z))) /7/7/0/ 0pe vip [br 1083,758] % * 2771. ~member(z,X0) | member(z,intersection(intersection(diagonalise(element_relation),singleton(z)),X0)) /12/12/9/ 0pe [br 689,2730] % * 2824. intersection(X0,null_class)==null_class /5/5/2/ 1pe vip [br 2619,761] % * 2971. intersection(null_class,X0)==null_class /5/5/2/ 1pe vip [br 2619,768] % * 20420. member(z,intersection(singleton(z),z)) /6/6/0/ 0pe vip [br 620,1085] % * 23048. intersection(singleton(X0),X0)==null_class | singleton(X0)==null_class /10/10/6/ 2pe [bs 650,1568] % * 110195. member(z,union(X0,X1)) | member(z,complement(X0)) /9/9/4/ 0pe [br 691,1669] % * 110426. member(z,complement(X0)) | member(z,successor(X0)) /8/8/4/ 0pe [fs 667,110195] % * 110427. ~member(z,X0) | member(z,successor(X0)) /7/7/4/ 0pe [br 688,110426] % * 110491. member(z,successor(z)) /4/4/0/ 0pe vip [br 620,110427] % * 110884. ~member(z,X0) | member(z,intersection(successor(z),X0)) /9/9/6/ 0pe [br 689,110491] % * 120575. member(z,intersection(successor(z),intersection(singleton(z),z))) /9/9/0/ 0pe [br 20420,110884] % * 144335. member(z,intersection(intersection(diagonalise(element_relation),singleton(z)),universal_class)) /9/9/0/ 0pe vip [br 999,2771] % 144354. member(z,intersection(z,intersection(intersection(diagonalise(element_relation),singleton(z)),universal_class))) /11/11/0/ 0pe [br 757,144335] % 144460. singleton(z)==null_class /4/4/2/ 1pe vip [bs fd fsr 2619,2824,120575,23048] % 144462. # /1/0/0/ 0pe vip [fd bd fsr 2619,2824,2971,2824,144354,144460] %================== End of proof. ========================
vproof('9520011456592226',[[+++member(z,z)],1,[],[in]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],2,[],[in]]).
vproof('9520011456592226',[[+++('X0' = null_class),+++(intersection('X0',regular('X0')) = null_class)],120,[],[in]]).
vproof('9520011456592226',[[+++('X0' = null_class),+++member(regular('X0'),'X0')],121,[],[in]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) = successor('X0'))],144,[],[in]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) = union('X0','X1'))],161,[],[in]]).
vproof('9520011456592226',[[+++member('X0',complement('X1')),---member('X0',universal_class),+++member('X0','X1')],162,[],[in]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),---member('X0','X1')],163,[],[in]]).
vproof('9520011456592226',[[---member('X0','X2'),---member('X0','X1'),+++member('X0',intersection('X1','X2'))],164,[],[in]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),+++member('X0','X2')],165,[],[in]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),+++member('X0','X1')],166,[],[in]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') = singleton('X0'))],175,[],[in]]).
vproof('9520011456592226',[[---member('X0',universal_class),+++member('X0',unordered_pair('X0','X1'))],178,[],[in]]).
vproof('9520011456592226',[[+++('X0' = 'X1'),---member('X0',unordered_pair('X1','X2')),+++('X0' = 'X2')],179,[],[in]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],183,[],[in]]).
vproof('9520011456592226',[[---member('X2','X0'),---subclass('X0','X1'),+++member('X2','X1')],186,[],[in]]).
vproof('9520011456592226',[[+++member(z,z)],190,[1],[pp]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],191,[2],[pp]]).
vproof('9520011456592226',[[+++(intersection('X0',regular('X0')) => null_class),++('X0' = null_class)],237,[120],[pp]]).
vproof('9520011456592226',[[+++member(regular('X0'),'X0'),++('X0' = null_class)],238,[121],[pp]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) => successor('X0'))],261,[144],[pp]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) => union('X0','X1'))],278,[161],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',complement('X1')),++member('X0','X1')],279,[162],[pp]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),--member('X0','X1')],280,[163],[pp]]).
vproof('9520011456592226',[[---member('X0','X1'),--member('X0','X2'),++member('X0',intersection('X1','X2'))],281,[164],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X2')],282,[165],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X1')],283,[166],[pp]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') => singleton('X0'))],292,[175],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',unordered_pair('X0','X1'))],295,[178],[pp]]).
vproof('9520011456592226',[[---member('X0',unordered_pair('X1','X2')),++('X0' = 'X1'),++('X0' = 'X2')],296,[179],[pp]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],299,[183],[pp]]).
vproof('9520011456592226',[[---subclass('X0','X1'),--member('X2','X0'),++member('X2','X1')],302,[186],[pp]]).
vproof('9520011456592226',[[+++member(z,z)],303,[190],[pp]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],304,[191],[pp]]).
vproof('9520011456592226',[[+++(intersection('X0',regular('X0')) => null_class),++('X0' = null_class)],350,[237],[pp]]).
vproof('9520011456592226',[[+++member(regular('X0'),'X0'),++('X0' = null_class)],351,[238],[pp]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) => successor('X0'))],374,[261],[pp]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) => union('X0','X1'))],391,[278],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',complement('X1')),++member('X0','X1')],392,[279],[pp]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),--member('X0','X1')],393,[280],[pp]]).
vproof('9520011456592226',[[---member('X0','X1'),--member('X0','X2'),++member('X0',intersection('X2','X1'))],394,[281],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X2')],395,[282],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X1')],396,[283],[pp]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') => singleton('X0'))],405,[292],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',unordered_pair('X0','X1'))],408,[295],[pp]]).
vproof('9520011456592226',[[---member('X0',unordered_pair('X1','X2')),++('X0' = 'X1'),++('X0' = 'X2')],409,[296],[pp]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],412,[299],[pp]]).
vproof('9520011456592226',[[---subclass('X0','X1'),--member('X2','X0'),++member('X2','X1')],415,[302],[pp]]).
vproof('9520011456592226',[[+++member(z,z)],424,[303],[pp]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],425,[304],[pp]]).
vproof('9520011456592226',[[+++(intersection('X0',regular('X0')) => null_class),++('X0' = null_class)],457,[350],[pp]]).
vproof('9520011456592226',[[+++member(regular('X0'),'X0'),++('X0' = null_class)],458,[351],[pp]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) => successor('X0'))],474,[374],[pp]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) => union('X0','X1'))],491,[391],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',complement('X1')),++member('X0','X1')],492,[392],[pp]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),--member('X0','X1')],493,[393],[pp]]).
vproof('9520011456592226',[[---member('X0','X1'),--member('X0','X2'),++member('X0',intersection('X1','X2'))],494,[394],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X2')],495,[395],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X1')],496,[396],[pp]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') => singleton('X0'))],505,[405],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',unordered_pair('X0','X1'))],508,[408],[pp]]).
vproof('9520011456592226',[[---member('X0',unordered_pair('X1','X2')),++('X0' = 'X1'),++('X0' = 'X2')],509,[409],[pp]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],512,[412],[pp]]).
vproof('9520011456592226',[[---subclass('X0','X1'),--member('X2','X0'),++member('X2','X1')],515,[415],[pp]]).
vproof('9520011456592226',[[+++member(z,z)],526,[424],[pp]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],527,[425],[pp]]).
vproof('9520011456592226',[[+++(intersection('X0',regular('X0')) => null_class),++('X0' = null_class)],556,[457],[pp]]).
vproof('9520011456592226',[[+++member(regular('X0'),'X0'),++('X0' = null_class)],557,[458],[pp]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) => successor('X0'))],573,[474],[pp]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) => union('X0','X1'))],590,[491],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',complement('X1')),++member('X0','X1')],591,[492],[pp]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),--member('X0','X1')],592,[493],[pp]]).
vproof('9520011456592226',[[---member('X0','X1'),--member('X0','X2'),++member('X0',intersection('X2','X1'))],593,[494],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X2')],594,[495],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X1')],595,[496],[pp]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') => singleton('X0'))],604,[505],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',unordered_pair('X0','X1'))],607,[508],[pp]]).
vproof('9520011456592226',[[---member('X0',unordered_pair('X1','X2')),++('X0' = 'X1'),++('X0' = 'X2')],608,[509],[pp]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],611,[512],[pp]]).
vproof('9520011456592226',[[---subclass('X0','X1'),--member('X2','X0'),++member('X2','X1')],614,[515],[pp]]).
vproof('9520011456592226',[[+++member(z,z)],620,[526],[pp]]).
vproof('9520011456592226',[[+++member(z,diagonalise(element_relation))],621,[527],[pp]]).
vproof('9520011456592226',[[+++(intersection('X0',regular('X0')) => null_class),++('X0' = null_class)],650,[556],[pp]]).
vproof('9520011456592226',[[+++member(regular('X0'),'X0'),++('X0' = null_class)],651,[557],[pp]]).
vproof('9520011456592226',[[+++(union('X0',singleton('X0')) => successor('X0'))],667,[573],[pp]]).
vproof('9520011456592226',[[+++(complement(intersection(complement('X0'),complement('X1'))) => union('X0','X1'))],685,[590],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',complement('X1')),++member('X0','X1')],687,[591],[pp]]).
vproof('9520011456592226',[[---member('X0',complement('X1')),--member('X0','X1')],688,[592],[pp]]).
vproof('9520011456592226',[[---member('X0','X1'),--member('X0','X2'),++member('X0',intersection('X1','X2'))],689,[593],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X2')],690,[594],[pp]]).
vproof('9520011456592226',[[---member('X0',intersection('X1','X2')),++member('X0','X1')],691,[595],[pp]]).
vproof('9520011456592226',[[+++(unordered_pair('X0','X0') => singleton('X0'))],700,[604],[pp]]).
vproof('9520011456592226',[[---member('X0',universal_class),++member('X0',unordered_pair('X0','X1'))],703,[607],[pp]]).
vproof('9520011456592226',[[---member('X0',unordered_pair('X1','X2')),++('X0' = 'X1'),++('X0' = 'X2')],704,[608],[pp]]).
vproof('9520011456592226',[[+++subclass('X0',universal_class)],707,[611],[pp]]).
vproof('9520011456592226',[[---subclass('X0','X1'),--member('X2','X0'),++member('X2','X1')],710,[614],[pp]]).
vproof('9520011456592226',[[---member(regular(complement('X0')),'X0'),++(complement('X0') => null_class)],753,[651,688],[br]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,intersection(z,'X0'))],757,[620,689],[br]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,intersection(diagonalise(element_relation),'X0'))],758,[621,689],[br]]).
vproof('9520011456592226',[[+++member(regular(intersection('X0','X1')),'X1'),++(intersection('X0','X1') => null_class)],761,[651,690],[br]]).
vproof('9520011456592226',[[+++member(regular(intersection('X0','X1')),'X0'),++(intersection('X0','X1') => null_class)],768,[651,691],[br]]).
vproof('9520011456592226',[[---member('X0',singleton('X1')),++('X0' = 'X1')],798,[700,704],[fs]]).
vproof('9520011456592226',[[---member('X0','X1'),++member('X0',universal_class)],822,[707,710],[br]]).
vproof('9520011456592226',[[+++member(z,universal_class)],999,[620,822],[br]]).
vproof('9520011456592226',[[+++member(regular('X0'),universal_class),++('X0' = null_class)],1000,[651,822],[br]]).
vproof('9520011456592226',[[+++member(z,unordered_pair(z,'X0'))],1005,[703,999],[br]]).
vproof('9520011456592226',[[+++member(z,complement('X0')),++member(z,'X0')],1007,[687,999],[br]]).
vproof('9520011456592226',[[+++member(z,singleton(z))],1083,[700,1005],[fs]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,intersection(singleton(z),'X0'))],1085,[689,1083],[br]]).
vproof('9520011456592226',[[+++(regular(singleton('X0')) => 'X0'),++(singleton('X0') => null_class)],1568,[651,798],[br]]).
vproof('9520011456592226',[[+++member(z,intersection(complement('X0'),complement('X1'))),++member(z,union('X0','X1'))],1669,[685,1007],[fs]]).
vproof('9520011456592226',[[+++(complement(universal_class) => null_class)],2598,[1000,753],[br]]).
vproof('9520011456592226',[[---member('X0',null_class)],2619,[822,688,2598],[bs,fsr]]).
vproof('9520011456592226',[[+++member(z,intersection(diagonalise(element_relation),singleton(z)))],2730,[1083,758],[br]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,intersection(intersection(diagonalise(element_relation),singleton(z)),'X0'))],2771,[689,2730],[br]]).
vproof('9520011456592226',[[+++(intersection('X0',null_class) => null_class)],2824,[2619,761],[br]]).
vproof('9520011456592226',[[+++(intersection(null_class,'X0') => null_class)],2971,[2619,768],[br]]).
vproof('9520011456592226',[[+++member(z,intersection(singleton(z),z))],20420,[620,1085],[br]]).
vproof('9520011456592226',[[+++(intersection(singleton('X0'),'X0') => null_class),++(singleton('X0') => null_class)],23048,[650,1568],[bs]]).
vproof('9520011456592226',[[+++member(z,union('X0','X1')),++member(z,complement('X0'))],107744,[691,1669],[br]]).
vproof('9520011456592226',[[+++member(z,complement('X0')),++member(z,successor('X0'))],108260,[667,107744],[fs]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,successor('X0'))],108261,[688,108260],[br]]).
vproof('9520011456592226',[[+++member(z,successor(z))],108325,[620,108261],[br]]).
vproof('9520011456592226',[[---member(z,'X0'),++member(z,intersection(successor(z),'X0'))],108718,[689,108325],[br]]).
vproof('9520011456592226',[[+++member(z,intersection(successor(z),intersection(singleton(z),z)))],118516,[20420,108718],[br]]).
vproof('9520011456592226',[[+++member(z,intersection(intersection(diagonalise(element_relation),singleton(z)),universal_class))],142519,[999,2771],[br]]).
vproof('9520011456592226',[[+++member(z,intersection(z,intersection(intersection(diagonalise(element_relation),singleton(z)),universal_class)))],142538,[757,142519],[br]]).
vproof('9520011456592226',[[+++(singleton(z) => null_class)],142584,[2619,2824,118516,23048],[bs,fd,fsr]]).
vproof('9520011456592226',[[],142585,[2619,2824,2971,2824,142538,142584],[fd,bd,fsr]]).
*********** [<number>] *************** <clause/formula body>
******* [<premise number>,..,<premise number>-><conclusion number>] ********** <premise> . . . <premise> ------------------------------- <conclusion>Premises and conclusions can be formulas or clauses.
*********** [11->20] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
The conclusion [20] is one of the clauses obtained by clausification
of the premise [11]. The constant sk5 was introduced by skolemisation.
Example 2. Three steps from the sample solution for SYN551+1
*********** [20->25] *********** sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0)) ----------------------------- ~g(f(X0))=X0 \/ p__2 *********** [20->31] *********** sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0)) ----------------------------- ~f(g(X0))=X0 \/ p__3 *********** [20->42] *********** sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0)) ----------------------------- f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3These steps together form a splitting inference. In the first two we introduce names p__2 and p__3 for the components ~X3=g(f(X3)) and ~X0=f(g(X0)) of the clause [20]. The last one is obtained by folding the components.
Example 3. Two steps from the sample solution for COL003-20:
*********** [9->10] *********** ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixe d_pt)) ----------------------------- ~p__0(apply(strong_fixed_point,fixed_pt) *********** [9->12] *********** ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixe d_pt)) ----------------------------- p__0(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)))These steps form a negative equality splitting. Again, p__0 is a new predicate.
Refutation found. Thanks to Tanya! *********** [12] *********** ~X0=a \/ ~X1=b \/ big_f(X0,X1) *********** [12->20] *********** ~X0=a \/ ~X1=b \/ big_f(X0,X1) ----------------------------- big_f(a,b) *********** [20->21] *********** big_f(a,b) ----------------------------- big_f(a,b) *********** [10] *********** ~big_f(X0,X1) \/ X0=a *********** [10->22] *********** ~big_f(X0,X1) \/ X0=a ----------------------------- ~big_f(X0,X1) \/ X0=a *********** [22->23] *********** ~big_f(X0,X1) \/ X0=a ----------------------------- ~big_f(X0,X1) \/ X0=a *********** [13] *********** ~big_f(X1,f(X0)) \/ ~X1=g(X0) \/ f(X0)=X0 *********** [13->24] *********** ~big_f(X1,f(X0)) \/ ~X1=g(X0) \/ f(X0)=X0 ----------------------------- ~big_f(g(X0),f(X0)) \/ f(X0)=X0 *********** [15] *********** ~X1=g(X0) \/ big_f(X1,f(X0)) \/ f(X0)=X0 *********** [24,15->25] *********** ~big_f(g(X0),f(X0)) \/ f(X0)=X0 ~X1=g(X0) \/ big_f(X1,f(X0)) \/ f(X0)=X0 ----------------------------- f(X0)=X0 *********** [25->26] *********** f(X0)=X0 ----------------------------- f(X0)=X0 *********** [18] *********** ~f(X0)=X0 \/ big_f(h(X0,X2),f(X0)) \/ h(X0,X2)=X2 *********** [18->27] *********** ~f(X0)=X0 \/ big_f(h(X0,X2),f(X0)) \/ h(X0,X2)=X2 ----------------------------- ~f(X0)=X0 \/ h(X0,X1)=X1 \/ big_f(h(X0,X1),f(X0)) *********** [26,26,27->28] *********** f(X0)=X0 f(X0)=X0 ~f(X0)=X0 \/ h(X0,X1)=X1 \/ big_f(h(X0,X1),f(X0)) ----------------------------- big_f(h(X0,X1),X0) \/ h(X0,X1)=X1 *********** [23,28->29] *********** ~big_f(X0,X1) \/ X0=a big_f(h(X0,X1),X0) \/ h(X0,X1)=X1 ----------------------------- h(X0,X1)=a \/ h(X0,X1)=X1 *********** [29->30] *********** h(X0,X1)=a \/ h(X0,X1)=X1 ----------------------------- h(X0,a)=a *********** [19] *********** ~f(X0)=X0 \/ ~h(X0,X2)=X2 \/ ~big_f(h(X0,X2),f(X0)) *********** [19->31] *********** ~f(X0)=X0 \/ ~h(X0,X2)=X2 \/ ~big_f(h(X0,X2),f(X0)) ----------------------------- ~big_f(h(X0,X1),f(X0)) \/ ~h(X0,X1)=X1 \/ ~f(X0)=X0 *********** [26,26,31->32] *********** f(X0)=X0 f(X0)=X0 ~big_f(h(X0,X1),f(X0)) \/ ~h(X0,X1)=X1 \/ ~f(X0)=X0 ----------------------------- ~h(X0,X1)=X1 \/ ~big_f(h(X0,X1),X0) *********** [30,32,30->33] *********** h(X0,a)=a ~h(X0,X1)=X1 \/ ~big_f(h(X0,X1),X0) h(X0,a)=a ----------------------------- ~big_f(a,X0) *********** [21,33->34] *********** big_f(a,b) ~big_f(a,X0) ----------------------------- # ======= End of refutation =======
Proof by contradiction found. Thanks to Tanya!
=========== Refutation ==========
*********** [6] ***********
~((? X0)X0=f(g(X0)) &
(! X1 X2)
(X1=f(g(X1)) & X2=f(g(X2)) =>
X1=X2) <=>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(X4=g(f(X4)) & X5=g(f(X5)) =>
X4=X5))
*********** [6->7] ***********
~((? X0)X0=f(g(X0)) &
(! X1 X2)
(X1=f(g(X1)) & X2=f(g(X2)) =>
X1=X2) <=>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(X4=g(f(X4)) & X5=g(f(X5)) =>
X4=X5))
-----------------------------
(? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2) <~>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5)
*********** [7->8] ***********
(? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2) <~>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5)
-----------------------------
((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2) =>
~((? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5))) &
(~((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2)) =>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5))
*********** [8->9] ***********
((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2) =>
~((? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5))) &
(~((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2)) =>
(? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5))
-----------------------------
((! X0)
~X0=f(g(X0)) \/
(? X1 X2)
(X1=f(g(X1)) &
X2=f(g(X2)) &
~X1=X2) \/
(! X3)
~X3=g(f(X3)) \/
(? X4 X5)
(X4=g(f(X4)) &
X5=g(f(X5)) &
~X4=X5)) &
(((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2)) \/
((? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5)))
*********** [9->10] ***********
((! X0)
~X0=f(g(X0)) \/
(? X1 X2)
(X1=f(g(X1)) &
X2=f(g(X2)) &
~X1=X2) \/
(! X3)
~X3=g(f(X3)) \/
(? X4 X5)
(X4=g(f(X4)) &
X5=g(f(X5)) &
~X4=X5)) &
(((? X0)X0=f(g(X0)) &
(! X1 X2)
(~X1=f(g(X1)) \/
~X2=f(g(X2)) \/
X1=X2)) \/
((? X3)X3=g(f(X3)) &
(! X4 X5)
(~X4=g(f(X4)) \/
~X5=g(f(X5)) \/
X4=X5)))
-----------------------------
((! X0)
~X0=f(g(X0)) \/
(? X1)
((? X2)
(X2=f(g(X2)) &
~X2=X1) &
X1=f(g(X1))) \/
(! X3)
~X3=g(f(X3)) \/
(? X4)
((? X5)
(X5=g(f(X5)) &
~X5=X4) &
X4=g(f(X4)))) &
(((? X6)X6=f(g(X6)) &
(! X7)
((! X8)
(~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
((? X9)X9=g(f(X9)) &
(! X10)
((! X11)
(~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
*********** [10->11] ***********
((! X0)
~X0=f(g(X0)) \/
(? X1)
((? X2)
(X2=f(g(X2)) &
~X2=X1) &
X1=f(g(X1))) \/
(! X3)
~X3=g(f(X3)) \/
(? X4)
((? X5)
(X5=g(f(X5)) &
~X5=X4) &
X4=g(f(X4)))) &
(((? X6)X6=f(g(X6)) &
(! X7)
((! X8)
(~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
((? X9)X9=g(f(X9)) &
(! X10)
((! X11)
(~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
*********** [11->20] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
*********** [20->25] ***********
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
-----------------------------
~g(f(X0))=X0 \/ p__2
*********** [25->26] ***********
~g(f(X0))=X0 \/ p__2
-----------------------------
~g(f(X0))=X0 \/ p__2
*********** [11->21] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk5=g(f(sk5)) \/ sk4=f(g(sk4))
*********** [21->27] ***********
sk5=g(f(sk5)) \/ sk4=f(g(sk4))
-----------------------------
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
*********** [27->28] ***********
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
-----------------------------
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
*********** [28,26->29] ***********
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
~g(f(X0))=X0 \/ p__2
-----------------------------
g(f(sk5))=sk5 \/ p__2
*********** [26,29->30] ***********
~g(f(X0))=X0 \/ p__2
g(f(sk5))=sk5 \/ p__2
-----------------------------
p__2
*********** [20->31] ***********
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
-----------------------------
~f(g(X0))=X0 \/ p__3
*********** [31->32] ***********
~f(g(X0))=X0 \/ p__3
-----------------------------
~f(g(X0))=X0 \/ p__3
*********** [28,32->33] ***********
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
~f(g(X0))=X0 \/ p__3
-----------------------------
g(f(sk5))=sk5 \/ p__3
*********** [32,33->34] ***********
~f(g(X0))=X0 \/ p__3
g(f(sk5))=sk5 \/ p__3
-----------------------------
p__3
*********** [11->16] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
~sk3=sk2 \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
*********** [16->35] ***********
~sk3=sk2 \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
-----------------------------
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
*********** [35->36] ***********
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
*********** [11->22] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
~X10=g(f(X10)) \/ X11=X10 \/ ~X11=g(f(X11)) \/ sk4=f(g(sk4))
*********** [22->37] ***********
~X10=g(f(X10)) \/ X11=X10 \/ ~X11=g(f(X11)) \/ sk4=f(g(sk4))
-----------------------------
f(g(sk4))=sk4 \/ ~p__0
*********** [37->38] ***********
f(g(sk4))=sk4 \/ ~p__0
-----------------------------
f(g(sk4))=sk4 \/ ~p__0
*********** [38,26->39] ***********
f(g(sk4))=sk4 \/ ~p__0
~g(f(X0))=X0 \/ p__2
-----------------------------
p__2 \/ ~p__0
*********** [11->24] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
~X10=g(f(X10)) \/ X11=X10 \/ ~X11=g(f(X11)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
*********** [24->40] ***********
~X10=g(f(X10)) \/ X11=X10 \/ ~X11=g(f(X11)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
-----------------------------
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
*********** [40->41] ***********
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
-----------------------------
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
*********** [20->42] ***********
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
-----------------------------
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [42->43] ***********
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [39,32,41,43->44] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__5
*********** [41,38->45] ***********
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk4))=sk4 \/ ~p__0
-----------------------------
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
*********** [44,45->46] ***********
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__5
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
-----------------------------
f(sk2)=sk4 \/ ~p__0 \/ ~p__5
*********** [44,46->47] ***********
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__5
f(sk2)=sk4 \/ ~p__0 \/ ~p__5
-----------------------------
g(sk4)=sk2 \/ ~p__0 \/ ~p__5
*********** [11->18] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
*********** [18->48] ***********
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
-----------------------------
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [48->49] ***********
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [39,32,41,49->50] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__5
*********** [50,45->51] ***********
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__5
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
-----------------------------
f(sk3)=sk4 \/ ~p__0 \/ ~p__5
*********** [47,50,51->52] ***********
g(sk4)=sk2 \/ ~p__0 \/ ~p__5
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__5
f(sk3)=sk4 \/ ~p__0 \/ ~p__5
-----------------------------
sk2=sk3 \/ ~p__0 \/ ~p__5
*********** [11->19] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
~sk3=sk2 \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
*********** [19->53] ***********
~sk3=sk2 \/ ~X3=g(f(X3)) \/ sk0=f(g(sk0)) \/ ~X0=f(g(X0))
-----------------------------
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
*********** [53->54] ***********
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
-----------------------------
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
*********** [30,34,54,52->55] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__0 \/ ~p__5
-----------------------------
f(g(sk0))=sk0 \/ ~p__0 \/ ~p__5
*********** [45,55->56] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
f(g(sk0))=sk0 \/ ~p__0 \/ ~p__5
-----------------------------
sk0=sk4 \/ ~p__0 \/ ~p__5
*********** [52,30,34,36,56->57] ***********
sk2=sk3 \/ ~p__0 \/ ~p__5
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__0 \/ ~p__5
-----------------------------
~sk1=sk4 \/ ~p__0 \/ ~p__5
*********** [11->13] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
~sk3=sk2 \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
*********** [13->58] ***********
~sk3=sk2 \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
-----------------------------
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
*********** [58->59] ***********
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
-----------------------------
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
*********** [30,34,59,52->60] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__0 \/ ~p__5
-----------------------------
f(g(sk1))=sk1 \/ ~p__0 \/ ~p__5
*********** [45,60->61] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
f(g(sk1))=sk1 \/ ~p__0 \/ ~p__5
-----------------------------
sk1=sk4 \/ ~p__0 \/ ~p__5
*********** [57,61->62] ***********
~sk1=sk4 \/ ~p__0 \/ ~p__5
sk1=sk4 \/ ~p__0 \/ ~p__5
-----------------------------
~p__5 \/ ~p__0
*********** [39,32,41,43->63] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
~f(g(X0))=X0 \/ sk0=X0 \/ p__5
*********** [62,38,63->64] ***********
~p__5 \/ ~p__0
f(g(sk4))=sk4 \/ ~p__0
~f(g(X0))=X0 \/ sk0=X0 \/ p__5
-----------------------------
sk0=sk4 \/ ~p__0
*********** [30,34,36,64->65] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__0
-----------------------------
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__0
*********** [11->14] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
*********** [14->66] ***********
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
-----------------------------
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [66->67] ***********
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [39,32,41,67->68] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__7
*********** [68,45->69] ***********
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__7
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
-----------------------------
f(sk2)=sk4 \/ ~p__0 \/ ~p__7
*********** [68,69->70] ***********
g(f(sk2))=sk2 \/ ~p__0 \/ ~p__7
f(sk2)=sk4 \/ ~p__0 \/ ~p__7
-----------------------------
g(sk4)=sk2 \/ ~p__0 \/ ~p__7
*********** [11->12] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
*********** [12->71] ***********
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ sk1=f(g(sk1)) \/ ~X0=f(g(X0))
-----------------------------
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [71->72] ***********
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [39,32,41,72->73] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__7
*********** [73,45->74] ***********
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__7
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
-----------------------------
f(sk3)=sk4 \/ ~p__0 \/ ~p__7
*********** [70,73,74->75] ***********
g(sk4)=sk2 \/ ~p__0 \/ ~p__7
g(f(sk3))=sk3 \/ ~p__0 \/ ~p__7
f(sk3)=sk4 \/ ~p__0 \/ ~p__7
-----------------------------
sk2=sk3 \/ ~p__0 \/ ~p__7
*********** [30,34,54,75->76] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__0 \/ ~p__7
-----------------------------
f(g(sk0))=sk0 \/ ~p__0 \/ ~p__7
*********** [45,76->77] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
f(g(sk0))=sk0 \/ ~p__0 \/ ~p__7
-----------------------------
sk0=sk4 \/ ~p__0 \/ ~p__7
*********** [75,30,34,36,77->78] ***********
sk2=sk3 \/ ~p__0 \/ ~p__7
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__0 \/ ~p__7
-----------------------------
~sk1=sk4 \/ ~p__0 \/ ~p__7
*********** [30,34,59,75->79] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__0 \/ ~p__7
-----------------------------
f(g(sk1))=sk1 \/ ~p__0 \/ ~p__7
*********** [45,79->80] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__0
f(g(sk1))=sk1 \/ ~p__0 \/ ~p__7
-----------------------------
sk1=sk4 \/ ~p__0 \/ ~p__7
*********** [78,80->81] ***********
~sk1=sk4 \/ ~p__0 \/ ~p__7
sk1=sk4 \/ ~p__0 \/ ~p__7
-----------------------------
~p__7 \/ ~p__0
*********** [39,32,41,67->82] ***********
p__2 \/ ~p__0
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__0
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
*********** [81,38,82->83] ***********
~p__7 \/ ~p__0
f(g(sk4))=sk4 \/ ~p__0
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
-----------------------------
sk1=sk4 \/ ~p__0
*********** [65,83->84] ***********
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__0
sk1=sk4 \/ ~p__0
-----------------------------
~sk2=sk3 \/ ~p__0
*********** [11->15] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
*********** [15->85] ***********
sk3=g(f(sk3)) \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
-----------------------------
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [85->86] ***********
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
*********** [30,34,86,64->87] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__0
-----------------------------
~sk1=sk4 \/ g(f(sk3))=sk3 \/ ~p__0
*********** [87,83->88] ***********
~sk1=sk4 \/ g(f(sk3))=sk3 \/ ~p__0
sk1=sk4 \/ ~p__0
-----------------------------
g(f(sk3))=sk3 \/ ~p__0
*********** [83,81,82,88->89] ***********
sk1=sk4 \/ ~p__0
~p__7 \/ ~p__0
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
g(f(sk3))=sk3 \/ ~p__0
-----------------------------
f(sk3)=sk4 \/ ~p__0
*********** [88,89->90] ***********
g(f(sk3))=sk3 \/ ~p__0
f(sk3)=sk4 \/ ~p__0
-----------------------------
g(sk4)=sk3 \/ ~p__0
*********** [11->17] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
*********** [17->91] ***********
sk2=g(f(sk2)) \/ ~X3=g(f(X3)) \/ ~sk1=sk0 \/ ~X0=f(g(X0))
-----------------------------
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [91->92] ***********
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
*********** [30,34,92,64->93] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__0
-----------------------------
~sk1=sk4 \/ g(f(sk2))=sk2 \/ ~p__0
*********** [93,83->94] ***********
~sk1=sk4 \/ g(f(sk2))=sk2 \/ ~p__0
sk1=sk4 \/ ~p__0
-----------------------------
g(f(sk2))=sk2 \/ ~p__0
*********** [83,81,82,94->95] ***********
sk1=sk4 \/ ~p__0
~p__7 \/ ~p__0
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
g(f(sk2))=sk2 \/ ~p__0
-----------------------------
f(sk2)=sk4 \/ ~p__0
*********** [90,94,95->96] ***********
g(sk4)=sk3 \/ ~p__0
g(f(sk2))=sk2 \/ ~p__0
f(sk2)=sk4 \/ ~p__0
-----------------------------
sk2=sk3 \/ ~p__0
*********** [84,96->97] ***********
~sk2=sk3 \/ ~p__0
sk2=sk3 \/ ~p__0
-----------------------------
~p__0
*********** [11->23] ***********
(~X0=f(g(X0)) \/
((sk1=f(g(sk1)) &
~sk1=sk0) &
sk0=f(g(sk0))) \/
~X3=g(f(X3)) \/
((sk3=g(f(sk3)) &
~sk3=sk2) &
sk2=g(f(sk2)))) &
((sk4=f(g(sk4)) &
((~X8=f(g(X8)) \/
X8=X7) \/
~X7=f(g(X7)))) \/
(sk5=g(f(sk5)) &
((~X11=g(f(X11)) \/
X11=X10) \/
~X10=g(f(X10)))))
-----------------------------
sk5=g(f(sk5)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
*********** [23->98] ***********
sk5=g(f(sk5)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
-----------------------------
g(f(sk5))=sk5 \/ p__1
*********** [98->99] ***********
g(f(sk5))=sk5 \/ p__1
-----------------------------
g(f(sk5))=sk5 \/ p__1
*********** [23->100] ***********
sk5=g(f(sk5)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
-----------------------------
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
*********** [100->101] ***********
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
-----------------------------
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
*********** [99,101,28->102] ***********
g(f(sk5))=sk5 \/ p__1
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
-----------------------------
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
*********** [32,101,67->103] ***********
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__7
*********** [30,102,103->104] ***********
p__2
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__7
-----------------------------
f(sk2)=sk4 \/ ~p__1 \/ ~p__7
*********** [24->105] ***********
~X10=g(f(X10)) \/ X11=X10 \/ ~X11=g(f(X11)) \/ ~X7=f(g(X7)) \/ X8=X7 \/ ~X8=f(g(X8))
-----------------------------
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
*********** [105->106] ***********
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
-----------------------------
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
*********** [106,28->107] ***********
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
-----------------------------
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
*********** [26,106,67->108] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__6
*********** [34,107,108->109] ***********
p__3
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
g(sk4)=sk2 \/ p__0 \/ ~p__1 \/ ~p__6
*********** [26,106,72->110] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__6
*********** [97,34,107,110->111] ***********
~p__0
p__3
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
g(sk4)=sk3 \/ ~p__1 \/ ~p__6
*********** [97,109,111->112] ***********
~p__0
g(sk4)=sk2 \/ p__0 \/ ~p__1 \/ ~p__6
g(sk4)=sk3 \/ ~p__1 \/ ~p__6
-----------------------------
sk2=sk3 \/ ~p__1 \/ ~p__6
*********** [26,106,67->113] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
*********** [30,113,103->114] ***********
p__2
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__7
-----------------------------
g(sk1)=sk2 \/ ~p__1 \/ p__6 \/ ~p__7
*********** [32,101,72->115] ***********
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__2 \/ ~p__7
*********** [112,114,30,113,115->116] ***********
sk2=sk3 \/ ~p__1 \/ ~p__6
g(sk1)=sk2 \/ ~p__1 \/ p__6 \/ ~p__7
p__2
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__2 \/ ~p__7
-----------------------------
sk2=sk3 \/ ~p__1 \/ ~p__7
*********** [104,116->117] ***********
f(sk2)=sk4 \/ ~p__1 \/ ~p__7
sk2=sk3 \/ ~p__1 \/ ~p__7
-----------------------------
f(sk3)=sk4 \/ ~p__1 \/ ~p__7
*********** [106,99->118] ***********
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk5))=sk5 \/ p__1
-----------------------------
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
*********** [26,106,43->119] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__4
*********** [34,118,119->120] ***********
p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__4
-----------------------------
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__4
*********** [30,34,54,120->121] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__4
-----------------------------
~sk3=sk5 \/ f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__4
*********** [26,106,49->122] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__4
*********** [34,118,122->123] ***********
p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__4
-----------------------------
sk3=sk5 \/ p__0 \/ p__1 \/ ~p__4
*********** [121,123->124] ***********
~sk3=sk5 \/ f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__4
sk3=sk5 \/ p__0 \/ p__1 \/ ~p__4
-----------------------------
f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__4
*********** [34,107,119->125] ***********
p__3
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__4
-----------------------------
g(sk4)=sk2 \/ p__0 \/ ~p__1 \/ ~p__4
*********** [125,34,107,122->126] ***********
g(sk4)=sk2 \/ p__0 \/ ~p__1 \/ ~p__4
p__3
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__4
-----------------------------
sk2=sk3 \/ p__0 \/ ~p__1 \/ ~p__4
*********** [30,34,124,54,126->127] ***********
p__2
p__3
f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__4
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ p__0 \/ ~p__1 \/ ~p__4
-----------------------------
f(g(sk0))=sk0 \/ p__0 \/ ~p__4
*********** [64,102,127->128] ***********
sk0=sk4 \/ ~p__0
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
f(g(sk0))=sk0 \/ p__0 \/ ~p__4
-----------------------------
sk0=sk4 \/ ~p__1 \/ ~p__4
*********** [34,102,108->129] ***********
p__3
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
f(sk2)=sk4 \/ p__0 \/ ~p__1 \/ ~p__6
*********** [97,129,112->130] ***********
~p__0
f(sk2)=sk4 \/ p__0 \/ ~p__1 \/ ~p__6
sk2=sk3 \/ ~p__1 \/ ~p__6
-----------------------------
f(sk3)=sk4 \/ ~p__1 \/ ~p__6
*********** [26,106,43->131] ***********
~g(f(X0))=X0 \/ p__2
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
*********** [97,34,131,110->132] ***********
~p__0
p__3
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
g(sk0)=sk3 \/ p__4 \/ ~p__6
*********** [34,131,108->133] ***********
p__3
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
g(sk0)=sk2 \/ p__0 \/ p__4 \/ ~p__6
*********** [97,133,132->134] ***********
~p__0
g(sk0)=sk2 \/ p__0 \/ p__4 \/ ~p__6
g(sk0)=sk3 \/ p__4 \/ ~p__6
-----------------------------
sk2=sk3 \/ p__4 \/ ~p__6
*********** [132,30,34,54,134->135] ***********
g(sk0)=sk3 \/ p__4 \/ ~p__6
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ p__4 \/ ~p__6
-----------------------------
f(sk3)=sk0 \/ p__4 \/ ~p__6
*********** [128,130,135->136] ***********
sk0=sk4 \/ ~p__1 \/ ~p__4
f(sk3)=sk4 \/ ~p__1 \/ ~p__6
f(sk3)=sk0 \/ p__4 \/ ~p__6
-----------------------------
sk0=sk4 \/ ~p__1 \/ ~p__6
*********** [112,30,34,36,136->137] ***********
sk2=sk3 \/ ~p__1 \/ ~p__6
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1 \/ ~p__6
-----------------------------
~sk1=sk4 \/ ~p__1 \/ ~p__6
*********** [34,118,108->138] ***********
p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__6
*********** [30,34,59,138->139] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__6
-----------------------------
~sk3=sk5 \/ f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__6
*********** [97,34,118,110->140] ***********
~p__0
p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__6
-----------------------------
sk3=sk5 \/ p__1 \/ ~p__6
*********** [97,139,140->141] ***********
~p__0
~sk3=sk5 \/ f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__6
sk3=sk5 \/ p__1 \/ ~p__6
-----------------------------
f(g(sk1))=sk1 \/ p__1 \/ ~p__6
*********** [30,34,141,59,112->142] ***********
p__2
p__3
f(g(sk1))=sk1 \/ p__1 \/ ~p__6
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__1 \/ ~p__6
-----------------------------
f(g(sk1))=sk1 \/ ~p__6
*********** [102,142->143] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
f(g(sk1))=sk1 \/ ~p__6
-----------------------------
sk1=sk4 \/ ~p__1 \/ ~p__6
*********** [137,143->144] ***********
~sk1=sk4 \/ ~p__1 \/ ~p__6
sk1=sk4 \/ ~p__1 \/ ~p__6
-----------------------------
~p__6 \/ ~p__1
*********** [30,34,54,138->145] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__6
-----------------------------
~sk3=sk5 \/ f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__6
*********** [99,131->146] ***********
g(f(sk5))=sk5 \/ p__1
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
-----------------------------
g(sk0)=sk5 \/ p__1 \/ p__4
*********** [146,118,127->147] ***********
g(sk0)=sk5 \/ p__1 \/ p__4
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
f(g(sk0))=sk0 \/ p__0 \/ ~p__4
-----------------------------
g(sk0)=sk5 \/ p__0 \/ p__1
*********** [145,147->148] ***********
~sk3=sk5 \/ f(g(sk0))=sk0 \/ p__0 \/ p__1 \/ ~p__6
g(sk0)=sk5 \/ p__0 \/ p__1
-----------------------------
~sk3=sk5 \/ f(sk5)=sk0 \/ p__0 \/ p__1 \/ ~p__6
*********** [97,148,140->149] ***********
~p__0
~sk3=sk5 \/ f(sk5)=sk0 \/ p__0 \/ p__1 \/ ~p__6
sk3=sk5 \/ p__1 \/ ~p__6
-----------------------------
f(sk5)=sk0 \/ p__1 \/ ~p__6
*********** [99,113->150] ***********
g(f(sk5))=sk5 \/ p__1
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
-----------------------------
g(sk1)=sk5 \/ p__1 \/ p__6
*********** [97,150,118,142->151] ***********
~p__0
g(sk1)=sk5 \/ p__1 \/ p__6
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
f(g(sk1))=sk1 \/ ~p__6
-----------------------------
g(sk1)=sk5 \/ p__1
*********** [144,142,151->152] ***********
~p__6 \/ ~p__1
f(g(sk1))=sk1 \/ ~p__6
g(sk1)=sk5 \/ p__1
-----------------------------
f(sk5)=sk1 \/ ~p__6
*********** [144,149,152->153] ***********
~p__6 \/ ~p__1
f(sk5)=sk0 \/ p__1 \/ ~p__6
f(sk5)=sk1 \/ ~p__6
-----------------------------
sk0=sk1 \/ ~p__6
*********** [30,34,36,153->154] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ ~p__6
-----------------------------
~sk2=sk3 \/ ~p__6
*********** [97,144,138,154->155] ***********
~p__0
~p__6 \/ ~p__1
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__6
~sk2=sk3 \/ ~p__6
-----------------------------
~sk3=sk5 \/ ~p__6
*********** [144,140,155->156] ***********
~p__6 \/ ~p__1
sk3=sk5 \/ p__1 \/ ~p__6
~sk3=sk5 \/ ~p__6
-----------------------------
~p__6
*********** [114,116->157] ***********
g(sk1)=sk2 \/ ~p__1 \/ p__6 \/ ~p__7
sk2=sk3 \/ ~p__1 \/ ~p__7
-----------------------------
g(sk1)=sk3 \/ ~p__1 \/ p__6 \/ ~p__7
*********** [156,82,101,157->158] ***********
~p__6
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
g(sk1)=sk3 \/ ~p__1 \/ p__6 \/ ~p__7
-----------------------------
~f(sk3)=sk1 \/ ~p__1 \/ ~p__7
*********** [117,158->159] ***********
f(sk3)=sk4 \/ ~p__1 \/ ~p__7
~f(sk3)=sk1 \/ ~p__1 \/ ~p__7
-----------------------------
~sk1=sk4 \/ ~p__1 \/ ~p__7
*********** [30,34,59,116->160] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__1 \/ ~p__7
-----------------------------
f(g(sk1))=sk1 \/ ~p__1 \/ ~p__7
*********** [117,156,157,160->161] ***********
f(sk3)=sk4 \/ ~p__1 \/ ~p__7
~p__6
g(sk1)=sk3 \/ ~p__1 \/ p__6 \/ ~p__7
f(g(sk1))=sk1 \/ ~p__1 \/ ~p__7
-----------------------------
sk1=sk4 \/ ~p__1 \/ ~p__7
*********** [159,161->162] ***********
~sk1=sk4 \/ ~p__1 \/ ~p__7
sk1=sk4 \/ ~p__1 \/ ~p__7
-----------------------------
~p__7 \/ ~p__1
*********** [28,82->163] ***********
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
-----------------------------
g(f(sk5))=sk5 \/ sk1=sk4 \/ p__7
*********** [82,163->164] ***********
~f(g(X0))=X0 \/ sk1=X0 \/ p__7
g(f(sk5))=sk5 \/ sk1=sk4 \/ p__7
-----------------------------
f(sk5)=sk1 \/ sk1=sk4 \/ p__7
*********** [162,102,163->165] ***********
~p__7 \/ ~p__1
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
g(f(sk5))=sk5 \/ sk1=sk4 \/ p__7
-----------------------------
f(sk5)=sk4 \/ sk1=sk4 \/ ~p__1
*********** [162,164,165->166] ***********
~p__7 \/ ~p__1
f(sk5)=sk1 \/ sk1=sk4 \/ p__7
f(sk5)=sk4 \/ sk1=sk4 \/ ~p__1
-----------------------------
sk1=sk4 \/ ~p__1
*********** [32,101,43->167] ***********
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__5
*********** [30,102,167->168] ***********
p__2
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__5
-----------------------------
f(sk2)=sk4 \/ ~p__1 \/ ~p__5
*********** [62,30,107,167->169] ***********
~p__5 \/ ~p__0
p__2
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__5
-----------------------------
g(sk4)=sk2 \/ ~p__1 \/ ~p__5
*********** [32,101,49->170] ***********
~f(g(X0))=X0 \/ p__3
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
-----------------------------
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__2 \/ ~p__5
*********** [169,62,30,107,170->171] ***********
g(sk4)=sk2 \/ ~p__1 \/ ~p__5
~p__5 \/ ~p__0
p__2
~g(f(X0))=X0 \/ g(sk4)=X0 \/ p__0 \/ ~p__1
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__2 \/ ~p__5
-----------------------------
sk2=sk3 \/ ~p__1 \/ ~p__5
*********** [168,171->172] ***********
f(sk2)=sk4 \/ ~p__1 \/ ~p__5
sk2=sk3 \/ ~p__1 \/ ~p__5
-----------------------------
f(sk3)=sk4 \/ ~p__1 \/ ~p__5
*********** [34,119,113->173] ***********
p__3
g(f(sk2))=sk2 \/ p__0 \/ ~p__3 \/ ~p__4
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
-----------------------------
g(sk1)=sk2 \/ p__0 \/ ~p__4 \/ p__6
*********** [173,34,122,113->174] ***********
g(sk1)=sk2 \/ p__0 \/ ~p__4 \/ p__6
p__3
g(f(sk3))=sk3 \/ p__0 \/ ~p__3 \/ ~p__4
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
-----------------------------
sk2=sk3 \/ p__0 \/ ~p__4 \/ p__6
*********** [30,34,36,128->175] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1 \/ ~p__4
-----------------------------
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__1 \/ ~p__4
*********** [30,34,59,120->176] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk5 \/ p__0 \/ p__1 \/ ~p__4
-----------------------------
~sk3=sk5 \/ f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__4
*********** [176,123->177] ***********
~sk3=sk5 \/ f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__4
sk3=sk5 \/ p__0 \/ p__1 \/ ~p__4
-----------------------------
f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__4
*********** [30,34,177,59,126->178] ***********
p__2
p__3
f(g(sk1))=sk1 \/ p__0 \/ p__1 \/ ~p__4
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ p__0 \/ ~p__1 \/ ~p__4
-----------------------------
f(g(sk1))=sk1 \/ p__0 \/ ~p__4
*********** [97,102,178->179] ***********
~p__0
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
f(g(sk1))=sk1 \/ p__0 \/ ~p__4
-----------------------------
sk1=sk4 \/ ~p__1 \/ ~p__4
*********** [175,179->180] ***********
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__1 \/ ~p__4
sk1=sk4 \/ ~p__1 \/ ~p__4
-----------------------------
~sk2=sk3 \/ ~p__1 \/ ~p__4
*********** [127,147->181] ***********
f(g(sk0))=sk0 \/ p__0 \/ ~p__4
g(sk0)=sk5 \/ p__0 \/ p__1
-----------------------------
f(sk5)=sk0 \/ p__0 \/ p__1 \/ ~p__4
*********** [97,151,178->182] ***********
~p__0
g(sk1)=sk5 \/ p__1
f(g(sk1))=sk1 \/ p__0 \/ ~p__4
-----------------------------
f(sk5)=sk1 \/ p__1 \/ ~p__4
*********** [97,181,182->183] ***********
~p__0
f(sk5)=sk0 \/ p__0 \/ p__1 \/ ~p__4
f(sk5)=sk1 \/ p__1 \/ ~p__4
-----------------------------
sk0=sk1 \/ p__1 \/ ~p__4
*********** [30,34,180,36,183->184] ***********
p__2
p__3
~sk2=sk3 \/ ~p__1 \/ ~p__4
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ p__1 \/ ~p__4
-----------------------------
~sk2=sk3 \/ ~p__4
*********** [97,156,174,184->185] ***********
~p__0
~p__6
sk2=sk3 \/ p__0 \/ ~p__4 \/ p__6
~sk2=sk3 \/ ~p__4
-----------------------------
~p__4
*********** [30,131,167->186] ***********
p__2
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__2 \/ ~p__5
-----------------------------
g(sk0)=sk2 \/ ~p__1 \/ p__4 \/ ~p__5
*********** [186,30,131,170->187] ***********
g(sk0)=sk2 \/ ~p__1 \/ p__4 \/ ~p__5
p__2
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__2 \/ ~p__5
-----------------------------
sk2=sk3 \/ ~p__1 \/ p__4 \/ ~p__5
*********** [186,187->188] ***********
g(sk0)=sk2 \/ ~p__1 \/ p__4 \/ ~p__5
sk2=sk3 \/ ~p__1 \/ p__4 \/ ~p__5
-----------------------------
g(sk0)=sk3 \/ ~p__1 \/ p__4 \/ ~p__5
*********** [185,63,101,188->189] ***********
~p__4
~f(g(X0))=X0 \/ sk0=X0 \/ p__5
~f(g(X0))=X0 \/ ~f(g(X1))=X1 \/ X0=X1 \/ ~p__1
g(sk0)=sk3 \/ ~p__1 \/ p__4 \/ ~p__5
-----------------------------
~f(sk3)=sk0 \/ ~p__1 \/ ~p__5
*********** [172,189->190] ***********
f(sk3)=sk4 \/ ~p__1 \/ ~p__5
~f(sk3)=sk0 \/ ~p__1 \/ ~p__5
-----------------------------
~sk0=sk4 \/ ~p__1 \/ ~p__5
*********** [30,34,54,171->191] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk3 \/ ~p__1 \/ ~p__5
-----------------------------
f(g(sk0))=sk0 \/ ~p__1 \/ ~p__5
*********** [172,185,188,191->192] ***********
f(sk3)=sk4 \/ ~p__1 \/ ~p__5
~p__4
g(sk0)=sk3 \/ ~p__1 \/ p__4 \/ ~p__5
f(g(sk0))=sk0 \/ ~p__1 \/ ~p__5
-----------------------------
sk0=sk4 \/ ~p__1 \/ ~p__5
*********** [190,192->193] ***********
~sk0=sk4 \/ ~p__1 \/ ~p__5
sk0=sk4 \/ ~p__1 \/ ~p__5
-----------------------------
~p__5 \/ ~p__1
*********** [30,34,49,102->194] ***********
p__2
p__3
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
-----------------------------
g(f(sk3))=sk3 \/ sk0=sk4 \/ ~p__1
*********** [102,194->195] ***********
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
g(f(sk3))=sk3 \/ sk0=sk4 \/ ~p__1
-----------------------------
f(sk3)=sk4 \/ sk0=sk4 \/ ~p__1
*********** [30,34,72,63->196] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
~f(g(X0))=X0 \/ sk0=X0 \/ p__5
-----------------------------
g(f(sk3))=sk3 \/ sk0=sk1 \/ p__5
*********** [63,196->197] ***********
~f(g(X0))=X0 \/ sk0=X0 \/ p__5
g(f(sk3))=sk3 \/ sk0=sk1 \/ p__5
-----------------------------
f(sk3)=sk0 \/ sk0=sk1 \/ p__5
*********** [193,195,197->198] ***********
~p__5 \/ ~p__1
f(sk3)=sk4 \/ sk0=sk4 \/ ~p__1
f(sk3)=sk0 \/ sk0=sk1 \/ p__5
-----------------------------
sk0=sk1 \/ sk0=sk4 \/ ~p__1
*********** [198,166->199] ***********
sk0=sk1 \/ sk0=sk4 \/ ~p__1
sk1=sk4 \/ ~p__1
-----------------------------
sk0=sk4 \/ ~p__1
*********** [166,30,34,36,199->200] ***********
sk1=sk4 \/ ~p__1
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1
-----------------------------
~sk2=sk3 \/ ~p__1
*********** [97,106,194->201] ***********
~p__0
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ sk0=sk4 \/ ~p__1
-----------------------------
sk0=sk4 \/ ~p__1 \/ ~p__8
*********** [30,34,36,201->202] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__1 \/ ~p__8
*********** [30,34,72,102->203] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
~f(g(X0))=X0 \/ sk4=X0 \/ ~p__1
-----------------------------
g(f(sk3))=sk3 \/ sk1=sk4 \/ ~p__1
*********** [97,106,203->204] ***********
~p__0
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ sk1=sk4 \/ ~p__1
-----------------------------
sk1=sk4 \/ ~p__1 \/ ~p__8
*********** [202,204->205] ***********
~sk1=sk4 \/ ~sk2=sk3 \/ ~p__1 \/ ~p__8
sk1=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
~sk2=sk3 \/ ~p__1 \/ ~p__8
*********** [30,34,72,131->206] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
-----------------------------
g(f(sk3))=sk3 \/ g(sk0)=g(sk1) \/ p__4
*********** [97,185,106,206->207] ***********
~p__0
~p__4
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ g(sk0)=g(sk1) \/ p__4
-----------------------------
g(sk0)=g(sk1) \/ ~p__8
*********** [30,34,86,201->208] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
~sk1=sk4 \/ g(f(sk3))=sk3 \/ ~p__1 \/ ~p__8
*********** [208,204->209] ***********
~sk1=sk4 \/ g(f(sk3))=sk3 \/ ~p__1 \/ ~p__8
sk1=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__8
*********** [204,207,185,131,209->210] ***********
sk1=sk4 \/ ~p__1 \/ ~p__8
g(sk0)=g(sk1) \/ ~p__8
~p__4
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__8
-----------------------------
g(sk4)=sk3 \/ ~p__1 \/ ~p__8
*********** [30,34,92,201->211] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
~sk1=sk4 \/ g(f(sk2))=sk2 \/ ~p__1 \/ ~p__8
*********** [211,204->212] ***********
~sk1=sk4 \/ g(f(sk2))=sk2 \/ ~p__1 \/ ~p__8
sk1=sk4 \/ ~p__1 \/ ~p__8
-----------------------------
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__8
*********** [210,204,207,185,131,212->213] ***********
g(sk4)=sk3 \/ ~p__1 \/ ~p__8
sk1=sk4 \/ ~p__1 \/ ~p__8
g(sk0)=g(sk1) \/ ~p__8
~p__4
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk2))=sk2 \/ ~p__1 \/ ~p__8
-----------------------------
sk2=sk3 \/ ~p__1 \/ ~p__8
*********** [205,213->214] ***********
~sk2=sk3 \/ ~p__1 \/ ~p__8
sk2=sk3 \/ ~p__1 \/ ~p__8
-----------------------------
~p__8 \/ ~p__1
*********** [99,32->215] ***********
g(f(sk5))=sk5 \/ p__1
~f(g(X0))=X0 \/ p__3
-----------------------------
p__3 \/ p__1
*********** [30,215,72,118->216] ***********
p__2
p__3 \/ p__1
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
-----------------------------
g(f(sk3))=sk3 \/ g(sk1)=sk5 \/ p__0 \/ p__1
*********** [97,106,216->217] ***********
~p__0
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ g(sk1)=sk5 \/ p__0 \/ p__1
-----------------------------
~g(f(X0))=X0 \/ sk3=X0 \/ p__8
*********** [166,30,34,92,199->218] ***********
sk1=sk4 \/ ~p__1
p__2
p__3
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
sk0=sk4 \/ ~p__1
-----------------------------
g(f(sk2))=sk2 \/ ~p__1
*********** [214,217,218->219] ***********
~p__8 \/ ~p__1
~g(f(X0))=X0 \/ sk3=X0 \/ p__8
g(f(sk2))=sk2 \/ ~p__1
-----------------------------
sk2=sk3 \/ ~p__1
*********** [200,219->220] ***********
~sk2=sk3 \/ ~p__1
sk2=sk3 \/ ~p__1
-----------------------------
~p__1
*********** [30,215,67,118->221] ***********
p__2
p__3 \/ p__1
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
-----------------------------
g(f(sk2))=sk2 \/ g(sk1)=sk5 \/ p__0 \/ p__1
*********** [97,106,221->222] ***********
~p__0
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk2))=sk2 \/ g(sk1)=sk5 \/ p__0 \/ p__1
-----------------------------
~g(f(X0))=X0 \/ sk2=X0 \/ p__9
*********** [99,222->223] ***********
g(f(sk5))=sk5 \/ p__1
~g(f(X0))=X0 \/ sk2=X0 \/ p__9
-----------------------------
sk2=sk5 \/ p__1 \/ p__9
*********** [30,34,43,146->224] ***********
p__2
p__3
f(g(sk0))=sk0 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
g(sk0)=sk5 \/ p__1 \/ p__4
-----------------------------
g(f(sk2))=sk2 \/ f(sk5)=sk0 \/ p__1 \/ p__4
*********** [97,185,106,224->225] ***********
~p__0
~p__4
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk2))=sk2 \/ f(sk5)=sk0 \/ p__1 \/ p__4
-----------------------------
f(sk5)=sk0 \/ p__1 \/ ~p__9
*********** [30,34,67,151->226] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
g(sk1)=sk5 \/ p__1
-----------------------------
g(f(sk2))=sk2 \/ f(sk5)=sk1 \/ p__1
*********** [97,220,106,226->227] ***********
~p__0
~p__1
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk2))=sk2 \/ f(sk5)=sk1 \/ p__1
-----------------------------
f(sk5)=sk1 \/ ~p__9
*********** [220,225,227->228] ***********
~p__1
f(sk5)=sk0 \/ p__1 \/ ~p__9
f(sk5)=sk1 \/ ~p__9
-----------------------------
sk0=sk1 \/ ~p__9
*********** [30,34,92,228->229] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ ~p__9
-----------------------------
g(f(sk2))=sk2 \/ ~p__9
*********** [97,220,223,118,229->230] ***********
~p__0
~p__1
sk2=sk5 \/ p__1 \/ p__9
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk2))=sk2 \/ ~p__9
-----------------------------
sk2=sk5
*********** [30,34,36,230->231] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk2=sk5
-----------------------------
~sk0=sk1 \/ ~sk3=sk5
*********** [97,217,106,209->232] ***********
~p__0
~g(f(X0))=X0 \/ sk3=X0 \/ p__8
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ ~p__1 \/ ~p__8
-----------------------------
~g(f(X0))=X0 \/ sk3=X0 \/ ~p__1
*********** [30,34,49,147->233] ***********
p__2
p__3
f(g(sk0))=sk0 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
g(sk0)=sk5 \/ p__0 \/ p__1
-----------------------------
g(f(sk3))=sk3 \/ f(sk5)=sk0 \/ p__0 \/ p__1
*********** [97,232,106,233->234] ***********
~p__0
~g(f(X0))=X0 \/ sk3=X0 \/ ~p__1
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ f(sk5)=sk0 \/ p__0 \/ p__1
-----------------------------
f(sk5)=sk0 \/ ~p__8
*********** [30,34,72,151->235] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
g(sk1)=sk5 \/ p__1
-----------------------------
g(f(sk3))=sk3 \/ f(sk5)=sk1 \/ p__1
*********** [97,220,106,235->236] ***********
~p__0
~p__1
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk3))=sk3 \/ f(sk5)=sk1 \/ p__1
-----------------------------
f(sk5)=sk1 \/ ~p__8
*********** [234,236->237] ***********
f(sk5)=sk0 \/ ~p__8
f(sk5)=sk1 \/ ~p__8
-----------------------------
sk0=sk1 \/ ~p__8
*********** [237,231->238] ***********
sk0=sk1 \/ ~p__8
~sk0=sk1 \/ ~sk3=sk5
-----------------------------
~sk3=sk5 \/ ~p__8
*********** [207,97,106,234->239] ***********
g(sk0)=g(sk1) \/ ~p__8
~p__0
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(sk5)=sk0 \/ ~p__8
-----------------------------
~g(sk1)=sk5 \/ ~p__8 \/ ~p__12
*********** [207,214,99,234->240] ***********
g(sk0)=g(sk1) \/ ~p__8
~p__8 \/ ~p__1
g(f(sk5))=sk5 \/ p__1
f(sk5)=sk0 \/ ~p__8
-----------------------------
g(sk1)=sk5 \/ ~p__8
*********** [239,240->241] ***********
~g(sk1)=sk5 \/ ~p__8 \/ ~p__12
g(sk1)=sk5 \/ ~p__8
-----------------------------
~p__12 \/ ~p__8
*********** [28,131->242] ***********
f(g(sk4))=sk4 \/ g(f(sk5))=sk5
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
-----------------------------
g(f(sk5))=sk5 \/ g(sk0)=g(sk4) \/ p__4
*********** [97,185,106,242->243] ***********
~p__0
~p__4
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
g(f(sk5))=sk5 \/ g(sk0)=g(sk4) \/ p__4
-----------------------------
~g(f(X0))=X0 \/ sk5=X0 \/ p__12
*********** [30,34,86,237->244] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ ~p__8
-----------------------------
g(f(sk3))=sk3 \/ ~p__8
*********** [241,243,244->245] ***********
~p__12 \/ ~p__8
~g(f(X0))=X0 \/ sk5=X0 \/ p__12
g(f(sk3))=sk3 \/ ~p__8
-----------------------------
sk3=sk5 \/ ~p__8
*********** [238,245->246] ***********
~sk3=sk5 \/ ~p__8
sk3=sk5 \/ ~p__8
-----------------------------
~p__8
*********** [97,220,118,235->247] ***********
~p__0
~p__1
~g(f(X0))=X0 \/ sk5=X0 \/ p__0 \/ p__1
g(f(sk3))=sk3 \/ f(sk5)=sk1 \/ p__1
-----------------------------
f(sk5)=sk1 \/ sk3=sk5
*********** [246,217,247->248] ***********
~p__8
~g(f(X0))=X0 \/ sk3=X0 \/ p__8
f(sk5)=sk1 \/ sk3=sk5
-----------------------------
~g(sk1)=sk5 \/ sk3=sk5
*********** [220,151,248->249] ***********
~p__1
g(sk1)=sk5 \/ p__1
~g(sk1)=sk5 \/ sk3=sk5
-----------------------------
sk3=sk5
*********** [231,249->250] ***********
~sk0=sk1 \/ ~sk3=sk5
sk3=sk5
-----------------------------
~sk0=sk1
*********** [30,34,36,228->251] ***********
p__2
p__3
~sk0=sk1 \/ ~sk2=sk3 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ ~p__9
-----------------------------
~sk2=sk3 \/ ~p__9
*********** [251,230->252] ***********
~sk2=sk3 \/ ~p__9
sk2=sk5
-----------------------------
~sk3=sk5 \/ ~p__9
*********** [97,113,106,142->253] ***********
~p__0
~g(f(X0))=X0 \/ g(sk1)=X0 \/ p__6
~g(f(X0))=X0 \/ ~g(f(X1))=X1 \/ X0=X1 \/ p__0
f(g(sk1))=sk1 \/ ~p__6
-----------------------------
~g(f(X0))=X0 \/ g(sk1)=X0
*********** [253,229->254] ***********
~g(f(X0))=X0 \/ g(sk1)=X0
g(f(sk2))=sk2 \/ ~p__9
-----------------------------
g(sk1)=sk2 \/ ~p__9
*********** [254,230->255] ***********
g(sk1)=sk2 \/ ~p__9
sk2=sk5
-----------------------------
g(sk1)=sk5 \/ ~p__9
*********** [30,34,86,228->256] ***********
p__2
p__3
~sk0=sk1 \/ g(f(sk3))=sk3 \/ ~p__2 \/ ~p__3
sk0=sk1 \/ ~p__9
-----------------------------
g(f(sk3))=sk3 \/ ~p__9
*********** [255,253,256->257] ***********
g(sk1)=sk5 \/ ~p__9
~g(f(X0))=X0 \/ g(sk1)=X0
g(f(sk3))=sk3 \/ ~p__9
-----------------------------
sk3=sk5 \/ ~p__9
*********** [252,257->258] ***********
~sk3=sk5 \/ ~p__9
sk3=sk5 \/ ~p__9
-----------------------------
~p__9
*********** [151,30,34,59,223->259] ***********
g(sk1)=sk5 \/ p__1
p__2
p__3
~sk2=sk3 \/ f(g(sk1))=sk1 \/ ~p__2 \/ ~p__3
sk2=sk5 \/ p__1 \/ p__9
-----------------------------
~sk3=sk5 \/ f(sk5)=sk1 \/ p__1 \/ p__9
*********** [220,258,259,249->260] ***********
~p__1
~p__9
~sk3=sk5 \/ f(sk5)=sk1 \/ p__1 \/ p__9
sk3=sk5
-----------------------------
f(sk5)=sk1
*********** [30,34,54,230->261] ***********
p__2
p__3
~sk2=sk3 \/ f(g(sk0))=sk0 \/ ~p__2 \/ ~p__3
sk2=sk5
-----------------------------
~sk3=sk5 \/ f(g(sk0))=sk0
*********** [261,249->262] ***********
~sk3=sk5 \/ f(g(sk0))=sk0
sk3=sk5
-----------------------------
f(g(sk0))=sk0
*********** [30,34,67,131->263] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
-----------------------------
g(f(sk2))=sk2 \/ g(sk0)=g(sk1) \/ p__4
*********** [185,131,263->264] ***********
~p__4
~g(f(X0))=X0 \/ g(sk0)=X0 \/ p__4
g(f(sk2))=sk2 \/ g(sk0)=g(sk1) \/ p__4
-----------------------------
g(sk0)=g(sk1) \/ g(sk0)=sk2
*********** [264,230->265] ***********
g(sk0)=g(sk1) \/ g(sk0)=sk2
sk2=sk5
-----------------------------
g(sk0)=g(sk1) \/ g(sk0)=sk5
*********** [30,34,67,222->266] ***********
p__2
p__3
f(g(sk1))=sk1 \/ g(f(sk2))=sk2 \/ ~p__2 \/ ~p__3
~g(f(X0))=X0 \/ sk2=X0 \/ p__9
-----------------------------
g(f(sk2))=sk2 \/ g(sk1)=sk2 \/ p__9
*********** [255,266,230->267] ***********
g(sk1)=sk5 \/ ~p__9
g(f(sk2))=sk2 \/ g(sk1)=sk2 \/ p__9
sk2=sk5
-----------------------------
g(f(sk5))=sk5 \/ g(sk1)=sk5
*********** [267,260->268] ***********
g(f(sk5))=sk5 \/ g(sk1)=sk5
f(sk5)=sk1
-----------------------------
g(sk1)=sk5
*********** [265,268->269] ***********
g(sk0)=g(sk1) \/ g(sk0)=sk5
g(sk1)=sk5
-----------------------------
g(sk0)=sk5
*********** [260,262,269->270] ***********
f(sk5)=sk1
f(g(sk0))=sk0
g(sk0)=sk5
-----------------------------
sk0=sk1
*********** [250,270->271] ***********
~sk0=sk1
sk0=sk1
-----------------------------
#
======= End of refutation =======
Refutation found. Thanks to Tanya! =========== Refutation ========== *********** [9] *********** ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) *********** [9->10] *********** ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ----------------------------- ~p__0(apply(strong_fixed_point,fixed_pt)) *********** [10->11] *********** ~p__0(apply(strong_fixed_point,fixed_pt)) ----------------------------- ~p__0(apply(strong_fixed_point,fixed_pt)) *********** [9->12] *********** ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ----------------------------- p__0(apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) *********** [12->13] *********** p__0(apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) ----------------------------- p__0(apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) *********** [4] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) *********** [4->14] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) ----------------------------- apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) *********** [14->15] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) ----------------------------- apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) *********** [5] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) *********** [5->16] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) *********** [16->17] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) *********** [8] *********** strong_fixed_point=apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))) *********** [8->18] *********** strong_fixed_point=apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))) ----------------------------- apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b)))=strong_fixed_point *********** [17,17,18->19] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b)))=strong_fixed_point ----------------------------- apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))=strong_fixed_point *********** [15,15,19->20] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))=strong_fixed_point ----------------------------- apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),X0)))=apply(strong_fixed_point,X0) *********** [17,17->21] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,w),X0)=apply(apply(X0,X0),X0) *********** [15,21->22] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(w,w),X0)=apply(apply(X0,X0),X0) ----------------------------- apply(apply(apply(w,w),b),X0)=apply(b,apply(b,X0)) *********** [20,22->23] *********** apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),X0)))=apply(strong_fixed_point,X0) apply(apply(apply(w,w),b),X0)=apply(b,apply(b,X0)) ----------------------------- apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))=apply(strong_fixed_point,X0) *********** [15,17->24] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,apply(b,X0)),X1)=apply(X0,apply(X1,X1)) *********** [15,24->25] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(w,apply(b,X0)),X1)=apply(X0,apply(X1,X1)) ----------------------------- apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X1,X1),X2)) *********** [17,21,25->26] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,w),X0)=apply(apply(X0,X0),X0) apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X1,X1),X2)) ----------------------------- apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1)=apply(X0,apply(apply(w,w),X1)) *********** [15,17->27] *********** apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,apply(apply(b,X0),X1)),X2)=apply(apply(X0,apply(X1,X2)),X2) *********** [17,17,17->28] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) ----------------------------- apply(apply(w,apply(w,X0)),X1)=apply(apply(w,apply(X0,X1)),X1) *********** [27,28->29] *********** apply(apply(w,apply(apply(b,X0),X1)),X2)=apply(apply(X0,apply(X1,X2)),X2) apply(apply(w,apply(w,X0)),X1)=apply(apply(w,apply(X0,X1)),X1) ----------------------------- apply(apply(w,apply(apply(b,w),X0)),X1)=apply(apply(w,apply(w,X0)),X1) *********** [17,29->30] *********** apply(apply(w,X0),X1)=apply(apply(X0,X1),X1) apply(apply(w,apply(apply(b,w),X0)),X1)=apply(apply(w,apply(w,X0)),X1) ----------------------------- apply(apply(w,apply(w,X0)),apply(apply(b,w),X0))=apply(apply(w,w),apply(apply(b,w),X0)) *********** [23,23,26,30->31] *********** apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))=apply(strong_fixed_point,X0) apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))=apply(strong_fixed_point,X0) apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1)=apply(X0,apply(apply(w,w),X1)) apply(apply(w,apply(w,X0)),apply(apply(b,w),X0))=apply(apply(w,w),apply(apply(b,w),X0)) ----------------------------- apply(X0,apply(strong_fixed_point,X0))=apply(strong_fixed_point,X0) *********** [11,13,31->32] *********** ~p__0(apply(strong_fixed_point,fixed_pt)) p__0(apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) apply(X0,apply(strong_fixed_point,X0))=apply(strong_fixed_point,X0) ----------------------------- # ======= End of refutation =======