%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue May 5 06:56:47 PM UTC 2026
% Result : Theorem 0.72s 1.12s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : bliksem %s
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % DateTime : Tue May 5 11:28:01 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.72/1.12 *** allocated 10000 integers for termspace/termends
% 0.72/1.12 *** allocated 10000 integers for clauses
% 0.72/1.12 *** allocated 10000 integers for justifications
% 0.72/1.12 Bliksem 1.12
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Automatic Strategy Selection
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Clauses:
% 0.72/1.12
% 0.72/1.12 { proj1S( s( X ) ) = X }.
% 0.72/1.12 { ! z = s( X ) }.
% 0.72/1.12 { x2( z, X ) = X }.
% 0.72/1.12 { x2( s( Y ), X ) = s( x2( Y, X ) ) }.
% 0.72/1.12 { x22( z, X ) = z }.
% 0.72/1.12 { x22( s( Y ), X ) = x2( X, x22( Y, X ) ) }.
% 0.72/1.12 { x22( X, X ) = X }.
% 0.72/1.12
% 0.72/1.12 percentage equality = 1.000000, percentage horn = 1.000000
% 0.72/1.12 This is a pure equality problem
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Options Used:
% 0.72/1.12
% 0.72/1.12 useres = 1
% 0.72/1.12 useparamod = 1
% 0.72/1.12 useeqrefl = 1
% 0.72/1.12 useeqfact = 1
% 0.72/1.12 usefactor = 1
% 0.72/1.12 usesimpsplitting = 0
% 0.72/1.12 usesimpdemod = 5
% 0.72/1.12 usesimpres = 3
% 0.72/1.12
% 0.72/1.12 resimpinuse = 1000
% 0.72/1.12 resimpclauses = 20000
% 0.72/1.12 substype = eqrewr
% 0.72/1.12 backwardsubs = 1
% 0.72/1.12 selectoldest = 5
% 0.72/1.12
% 0.72/1.12 litorderings [0] = split
% 0.72/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.12
% 0.72/1.12 termordering = kbo
% 0.72/1.12
% 0.72/1.12 litapriori = 0
% 0.72/1.12 termapriori = 1
% 0.72/1.12 litaposteriori = 0
% 0.72/1.12 termaposteriori = 0
% 0.72/1.12 demodaposteriori = 0
% 0.72/1.12 ordereqreflfact = 0
% 0.72/1.12
% 0.72/1.12 litselect = negord
% 0.72/1.12
% 0.72/1.12 maxweight = 15
% 0.72/1.12 maxdepth = 30000
% 0.72/1.12 maxlength = 115
% 0.72/1.12 maxnrvars = 195
% 0.72/1.12 excuselevel = 1
% 0.72/1.12 increasemaxweight = 1
% 0.72/1.12
% 0.72/1.12 maxselected = 10000000
% 0.72/1.12 maxnrclauses = 10000000
% 0.72/1.12
% 0.72/1.12 showgenerated = 0
% 0.72/1.12 showkept = 0
% 0.72/1.12 showselected = 0
% 0.72/1.12 showdeleted = 0
% 0.72/1.12 showresimp = 1
% 0.72/1.12 showstatus = 2000
% 0.72/1.12
% 0.72/1.12 prologoutput = 0
% 0.72/1.12 nrgoals = 5000000
% 0.72/1.12 totalproof = 1
% 0.72/1.12
% 0.72/1.12 Symbols occurring in the translation:
% 0.72/1.12
% 0.72/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.12 . [1, 2] (w:1, o:17, a:1, s:1, b:0),
% 0.72/1.12 ! [4, 1] (w:0, o:10, a:1, s:1, b:0),
% 0.72/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.12 s [36, 1] (w:1, o:15, a:1, s:1, b:0),
% 0.72/1.12 proj1S [37, 1] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.12 z [38, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.72/1.12 x2 [40, 2] (w:1, o:41, a:1, s:1, b:0),
% 0.72/1.12 x22 [42, 2] (w:1, o:42, a:1, s:1, b:0).
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Starting Search:
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Bliksems!, er is een bewijs:
% 0.72/1.12 % SZS status Theorem
% 0.72/1.12 % SZS output start Refutation
% 0.72/1.12
% 0.72/1.12 (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.12 (1) {G0,W4,D3,L1,V1,M1} I { ! s( X ) ==> z }.
% 0.72/1.12 (2) {G0,W5,D3,L1,V1,M1} I { x2( z, X ) ==> X }.
% 0.72/1.12 (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X ) ) }.
% 0.72/1.12 (4) {G0,W5,D3,L1,V1,M1} I { x22( z, X ) ==> z }.
% 0.72/1.12 (5) {G0,W10,D4,L1,V2,M1} I { x2( X, x22( Y, X ) ) ==> x22( s( Y ), X ) }.
% 0.72/1.12 (6) {G0,W5,D3,L1,V1,M1} I { x22( X, X ) ==> X }.
% 0.72/1.12 (9) {G1,W8,D4,L1,V1,M1} P(4,5) { x22( s( z ), X ) ==> x2( X, z ) }.
% 0.72/1.12 (11) {G2,W11,D5,L1,V1,M1} P(9,5) { x2( X, x2( X, z ) ) = x22( s( s( z ) ),
% 0.72/1.12 X ) }.
% 0.72/1.12 (30) {G3,W9,D6,L1,V0,M1} P(11,6);d(3);d(3);d(2);d(3);d(3);d(2) { s( s( s( s
% 0.72/1.12 ( z ) ) ) ) ==> s( s( z ) ) }.
% 0.72/1.12 (34) {G4,W7,D5,L1,V0,M1} P(30,0);d(0) { s( s( s( z ) ) ) ==> s( z ) }.
% 0.72/1.12 (37) {G5,W5,D4,L1,V0,M1} P(34,0);d(0) { s( s( z ) ) ==> z }.
% 0.72/1.12 (38) {G6,W0,D0,L0,V0,M0} S(37);r(1) { }.
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 % SZS output end Refutation
% 0.72/1.12 found a proof!
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Unprocessed initial clauses:
% 0.72/1.12
% 0.72/1.12 (40) {G0,W5,D4,L1,V1,M1} { proj1S( s( X ) ) = X }.
% 0.72/1.12 (41) {G0,W4,D3,L1,V1,M1} { ! z = s( X ) }.
% 0.72/1.12 (42) {G0,W5,D3,L1,V1,M1} { x2( z, X ) = X }.
% 0.72/1.12 (43) {G0,W9,D4,L1,V2,M1} { x2( s( Y ), X ) = s( x2( Y, X ) ) }.
% 0.72/1.12 (44) {G0,W5,D3,L1,V1,M1} { x22( z, X ) = z }.
% 0.72/1.12 (45) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) = x2( X, x22( Y, X ) ) }.
% 0.72/1.12 (46) {G0,W5,D3,L1,V1,M1} { x22( X, X ) = X }.
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Total Proof:
% 0.72/1.12
% 0.72/1.12 subsumption: (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.12 parent0: (40) {G0,W5,D4,L1,V1,M1} { proj1S( s( X ) ) = X }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (49) {G0,W4,D3,L1,V1,M1} { ! s( X ) = z }.
% 0.72/1.12 parent0[0]: (41) {G0,W4,D3,L1,V1,M1} { ! z = s( X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (1) {G0,W4,D3,L1,V1,M1} I { ! s( X ) ==> z }.
% 0.72/1.12 parent0: (49) {G0,W4,D3,L1,V1,M1} { ! s( X ) = z }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { x2( z, X ) ==> X }.
% 0.72/1.12 parent0: (42) {G0,W5,D3,L1,V1,M1} { x2( z, X ) = X }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X )
% 0.72/1.12 ) }.
% 0.72/1.12 parent0: (43) {G0,W9,D4,L1,V2,M1} { x2( s( Y ), X ) = s( x2( Y, X ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (4) {G0,W5,D3,L1,V1,M1} I { x22( z, X ) ==> z }.
% 0.72/1.12 parent0: (44) {G0,W5,D3,L1,V1,M1} { x22( z, X ) = z }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (67) {G0,W10,D4,L1,V2,M1} { x2( Y, x22( X, Y ) ) = x22( s( X ), Y
% 0.72/1.12 ) }.
% 0.72/1.12 parent0[0]: (45) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) = x2( X, x22( Y,
% 0.72/1.12 X ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := Y
% 0.72/1.12 Y := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (5) {G0,W10,D4,L1,V2,M1} I { x2( X, x22( Y, X ) ) ==> x22( s(
% 0.72/1.12 Y ), X ) }.
% 0.72/1.12 parent0: (67) {G0,W10,D4,L1,V2,M1} { x2( Y, x22( X, Y ) ) = x22( s( X ), Y
% 0.72/1.12 ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := Y
% 0.72/1.12 Y := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { x22( X, X ) ==> X }.
% 0.72/1.12 parent0: (46) {G0,W5,D3,L1,V1,M1} { x22( X, X ) = X }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (76) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) ==> x2( X, x22( Y, X
% 0.72/1.12 ) ) }.
% 0.72/1.12 parent0[0]: (5) {G0,W10,D4,L1,V2,M1} I { x2( X, x22( Y, X ) ) ==> x22( s( Y
% 0.72/1.12 ), X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (77) {G1,W8,D4,L1,V1,M1} { x22( s( z ), X ) ==> x2( X, z ) }.
% 0.72/1.12 parent0[0]: (4) {G0,W5,D3,L1,V1,M1} I { x22( z, X ) ==> z }.
% 0.72/1.12 parent1[0; 7]: (76) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) ==> x2( X, x22
% 0.72/1.12 ( Y, X ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 X := X
% 0.72/1.12 Y := z
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (9) {G1,W8,D4,L1,V1,M1} P(4,5) { x22( s( z ), X ) ==> x2( X, z
% 0.72/1.12 ) }.
% 0.72/1.12 parent0: (77) {G1,W8,D4,L1,V1,M1} { x22( s( z ), X ) ==> x2( X, z ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (80) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) ==> x2( X, x22( Y, X
% 0.72/1.12 ) ) }.
% 0.72/1.12 parent0[0]: (5) {G0,W10,D4,L1,V2,M1} I { x2( X, x22( Y, X ) ) ==> x22( s( Y
% 0.72/1.12 ), X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (82) {G1,W11,D5,L1,V1,M1} { x22( s( s( z ) ), X ) ==> x2( X, x2(
% 0.72/1.12 X, z ) ) }.
% 0.72/1.12 parent0[0]: (9) {G1,W8,D4,L1,V1,M1} P(4,5) { x22( s( z ), X ) ==> x2( X, z
% 0.72/1.12 ) }.
% 0.72/1.12 parent1[0; 8]: (80) {G0,W10,D4,L1,V2,M1} { x22( s( Y ), X ) ==> x2( X, x22
% 0.72/1.12 ( Y, X ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 X := X
% 0.72/1.12 Y := s( z )
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (84) {G1,W11,D5,L1,V1,M1} { x2( X, x2( X, z ) ) ==> x22( s( s( z )
% 0.72/1.12 ), X ) }.
% 0.72/1.12 parent0[0]: (82) {G1,W11,D5,L1,V1,M1} { x22( s( s( z ) ), X ) ==> x2( X,
% 0.72/1.12 x2( X, z ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (11) {G2,W11,D5,L1,V1,M1} P(9,5) { x2( X, x2( X, z ) ) = x22(
% 0.72/1.12 s( s( z ) ), X ) }.
% 0.72/1.12 parent0: (84) {G1,W11,D5,L1,V1,M1} { x2( X, x2( X, z ) ) ==> x22( s( s( z
% 0.72/1.12 ) ), X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (85) {G2,W11,D5,L1,V1,M1} { x22( s( s( z ) ), X ) = x2( X, x2( X,
% 0.72/1.12 z ) ) }.
% 0.72/1.12 parent0[0]: (11) {G2,W11,D5,L1,V1,M1} P(9,5) { x2( X, x2( X, z ) ) = x22( s
% 0.72/1.12 ( s( z ) ), X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (86) {G0,W5,D3,L1,V1,M1} { X ==> x22( X, X ) }.
% 0.72/1.12 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { x22( X, X ) ==> X }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (93) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) ), x2(
% 0.72/1.12 s( s( z ) ), z ) ) }.
% 0.72/1.12 parent0[0]: (85) {G2,W11,D5,L1,V1,M1} { x22( s( s( z ) ), X ) = x2( X, x2
% 0.72/1.12 ( X, z ) ) }.
% 0.72/1.12 parent1[0; 4]: (86) {G0,W5,D3,L1,V1,M1} { X ==> x22( X, X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := s( s( z ) )
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 X := s( s( z ) )
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (95) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) ), s(
% 0.72/1.12 x2( s( z ), z ) ) ) }.
% 0.72/1.12 parent0[0]: (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X ) )
% 0.72/1.12 }.
% 0.72/1.12 parent1[0; 8]: (93) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) )
% 0.72/1.12 , x2( s( s( z ) ), z ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := z
% 0.72/1.12 Y := s( z )
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (103) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) ), s(
% 0.72/1.12 s( x2( z, z ) ) ) ) }.
% 0.72/1.12 parent0[0]: (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X ) )
% 0.72/1.12 }.
% 0.72/1.12 parent1[0; 9]: (95) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) )
% 0.72/1.12 , s( x2( s( z ), z ) ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := z
% 0.72/1.12 Y := z
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (107) {G1,W11,D5,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z ) ), s(
% 0.72/1.13 s( z ) ) ) }.
% 0.72/1.13 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { x2( z, X ) ==> X }.
% 0.72/1.13 parent1[0; 10]: (103) {G1,W13,D6,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z )
% 0.72/1.13 ), s( s( x2( z, z ) ) ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := z
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (108) {G1,W11,D6,L1,V0,M1} { s( s( z ) ) ==> s( x2( s( z ), s( s
% 0.72/1.13 ( z ) ) ) ) }.
% 0.72/1.13 parent0[0]: (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X ) )
% 0.72/1.13 }.
% 0.72/1.13 parent1[0; 4]: (107) {G1,W11,D5,L1,V0,M1} { s( s( z ) ) ==> x2( s( s( z )
% 0.72/1.13 ), s( s( z ) ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := s( s( z ) )
% 0.72/1.13 Y := s( z )
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (110) {G1,W11,D7,L1,V0,M1} { s( s( z ) ) ==> s( s( x2( z, s( s( z
% 0.72/1.13 ) ) ) ) ) }.
% 0.72/1.13 parent0[0]: (3) {G0,W9,D4,L1,V2,M1} I { x2( s( Y ), X ) ==> s( x2( Y, X ) )
% 0.72/1.13 }.
% 0.72/1.13 parent1[0; 5]: (108) {G1,W11,D6,L1,V0,M1} { s( s( z ) ) ==> s( x2( s( z )
% 0.72/1.13 , s( s( z ) ) ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := s( s( z ) )
% 0.72/1.13 Y := z
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (111) {G1,W9,D6,L1,V0,M1} { s( s( z ) ) ==> s( s( s( s( z ) ) ) )
% 0.72/1.13 }.
% 0.72/1.13 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { x2( z, X ) ==> X }.
% 0.72/1.13 parent1[0; 6]: (110) {G1,W11,D7,L1,V0,M1} { s( s( z ) ) ==> s( s( x2( z, s
% 0.72/1.13 ( s( z ) ) ) ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := s( s( z ) )
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 eqswap: (112) {G1,W9,D6,L1,V0,M1} { s( s( s( s( z ) ) ) ) ==> s( s( z ) )
% 0.72/1.13 }.
% 0.72/1.13 parent0[0]: (111) {G1,W9,D6,L1,V0,M1} { s( s( z ) ) ==> s( s( s( s( z ) )
% 0.72/1.13 ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 subsumption: (30) {G3,W9,D6,L1,V0,M1} P(11,6);d(3);d(3);d(2);d(3);d(3);d(2)
% 0.72/1.13 { s( s( s( s( z ) ) ) ) ==> s( s( z ) ) }.
% 0.72/1.13 parent0: (112) {G1,W9,D6,L1,V0,M1} { s( s( s( s( z ) ) ) ) ==> s( s( z ) )
% 0.72/1.13 }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 permutation0:
% 0.72/1.13 0 ==> 0
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 eqswap: (114) {G0,W5,D4,L1,V1,M1} { X ==> proj1S( s( X ) ) }.
% 0.72/1.13 parent0[0]: (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := X
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (116) {G1,W9,D5,L1,V0,M1} { s( s( s( z ) ) ) ==> proj1S( s( s( z
% 0.72/1.13 ) ) ) }.
% 0.72/1.13 parent0[0]: (30) {G3,W9,D6,L1,V0,M1} P(11,6);d(3);d(3);d(2);d(3);d(3);d(2)
% 0.72/1.13 { s( s( s( s( z ) ) ) ) ==> s( s( z ) ) }.
% 0.72/1.13 parent1[0; 6]: (114) {G0,W5,D4,L1,V1,M1} { X ==> proj1S( s( X ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 X := s( s( s( z ) ) )
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (117) {G1,W7,D5,L1,V0,M1} { s( s( s( z ) ) ) ==> s( z ) }.
% 0.72/1.13 parent0[0]: (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.13 parent1[0; 5]: (116) {G1,W9,D5,L1,V0,M1} { s( s( s( z ) ) ) ==> proj1S( s
% 0.72/1.13 ( s( z ) ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := s( z )
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 subsumption: (34) {G4,W7,D5,L1,V0,M1} P(30,0);d(0) { s( s( s( z ) ) ) ==> s
% 0.72/1.13 ( z ) }.
% 0.72/1.13 parent0: (117) {G1,W7,D5,L1,V0,M1} { s( s( s( z ) ) ) ==> s( z ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 permutation0:
% 0.72/1.13 0 ==> 0
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 eqswap: (120) {G0,W5,D4,L1,V1,M1} { X ==> proj1S( s( X ) ) }.
% 0.72/1.13 parent0[0]: (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := X
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (122) {G1,W7,D4,L1,V0,M1} { s( s( z ) ) ==> proj1S( s( z ) ) }.
% 0.72/1.13 parent0[0]: (34) {G4,W7,D5,L1,V0,M1} P(30,0);d(0) { s( s( s( z ) ) ) ==> s
% 0.72/1.13 ( z ) }.
% 0.72/1.13 parent1[0; 5]: (120) {G0,W5,D4,L1,V1,M1} { X ==> proj1S( s( X ) ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 X := s( s( z ) )
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 paramod: (123) {G1,W5,D4,L1,V0,M1} { s( s( z ) ) ==> z }.
% 0.72/1.13 parent0[0]: (0) {G0,W5,D4,L1,V1,M1} I { proj1S( s( X ) ) ==> X }.
% 0.72/1.13 parent1[0; 4]: (122) {G1,W7,D4,L1,V0,M1} { s( s( z ) ) ==> proj1S( s( z )
% 0.72/1.13 ) }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := z
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 subsumption: (37) {G5,W5,D4,L1,V0,M1} P(34,0);d(0) { s( s( z ) ) ==> z }.
% 0.72/1.13 parent0: (123) {G1,W5,D4,L1,V0,M1} { s( s( z ) ) ==> z }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 permutation0:
% 0.72/1.13 0 ==> 0
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 resolution: (127) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.13 parent0[0]: (1) {G0,W4,D3,L1,V1,M1} I { ! s( X ) ==> z }.
% 0.72/1.13 parent1[0]: (37) {G5,W5,D4,L1,V0,M1} P(34,0);d(0) { s( s( z ) ) ==> z }.
% 0.72/1.13 substitution0:
% 0.72/1.13 X := s( z )
% 0.72/1.13 end
% 0.72/1.13 substitution1:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 subsumption: (38) {G6,W0,D0,L0,V0,M0} S(37);r(1) { }.
% 0.72/1.13 parent0: (127) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.13 substitution0:
% 0.72/1.13 end
% 0.72/1.13 permutation0:
% 0.72/1.13 end
% 0.72/1.13
% 0.72/1.13 Proof check complete!
% 0.72/1.13
% 0.72/1.13 Memory use:
% 0.72/1.13
% 0.72/1.13 space for terms: 521
% 0.72/1.13 space for clauses: 3966
% 0.72/1.13
% 0.72/1.13
% 0.72/1.13 clauses generated: 144
% 0.72/1.13 clauses kept: 39
% 0.72/1.13 clauses selected: 18
% 0.72/1.13 clauses deleted: 1
% 0.72/1.13 clauses inuse deleted: 0
% 0.72/1.13
% 0.72/1.13 subsentry: 347
% 0.72/1.13 literals s-matched: 155
% 0.72/1.13 literals matched: 155
% 0.72/1.13 full subsumption: 0
% 0.72/1.13
% 0.72/1.13 checksum: -821159558
% 0.72/1.13
% 0.72/1.13
% 0.72/1.13 Bliksem ended
%------------------------------------------------------------------------------