%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX186+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 06:56:45 PM UTC 2026
% Result : Theorem 0.71s 1.11s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : bliksem %s
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % DateTime : Tue May 5 09:35:31 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11
% 0.71/1.11 { head( cons( X, Y ) ) = X }.
% 0.71/1.11 { tail( cons( X, Y ) ) = Y }.
% 0.71/1.11 { ! nil = cons( X, Y ) }.
% 0.71/1.11 { proj1S( s( X ) ) = X }.
% 0.71/1.11 { ! s( X ) = z }.
% 0.71/1.11 { drop( s( X ), nil ) = nil }.
% 0.71/1.11 { drop( s( X ), cons( Y, Z ) ) = drop( X, Z ) }.
% 0.71/1.11 { drop( z, X ) = X }.
% 0.71/1.11 { ! drop( X, Y ) = drop( X, Z ), Y = Z }.
% 0.71/1.11
% 0.71/1.11 percentage equality = 1.000000, percentage horn = 1.000000
% 0.71/1.11 This is a pure equality problem
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Options Used:
% 0.71/1.11
% 0.71/1.11 useres = 1
% 0.71/1.11 useparamod = 1
% 0.71/1.11 useeqrefl = 1
% 0.71/1.11 useeqfact = 1
% 0.71/1.11 usefactor = 1
% 0.71/1.11 usesimpsplitting = 0
% 0.71/1.11 usesimpdemod = 5
% 0.71/1.11 usesimpres = 3
% 0.71/1.11
% 0.71/1.11 resimpinuse = 1000
% 0.71/1.11 resimpclauses = 20000
% 0.71/1.11 substype = eqrewr
% 0.71/1.11 backwardsubs = 1
% 0.71/1.11 selectoldest = 5
% 0.71/1.11
% 0.71/1.11 litorderings [0] = split
% 0.71/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.11
% 0.71/1.11 termordering = kbo
% 0.71/1.11
% 0.71/1.11 litapriori = 0
% 0.71/1.11 termapriori = 1
% 0.71/1.11 litaposteriori = 0
% 0.71/1.11 termaposteriori = 0
% 0.71/1.11 demodaposteriori = 0
% 0.71/1.11 ordereqreflfact = 0
% 0.71/1.11
% 0.71/1.11 litselect = negord
% 0.71/1.11
% 0.71/1.11 maxweight = 15
% 0.71/1.11 maxdepth = 30000
% 0.71/1.11 maxlength = 115
% 0.71/1.11 maxnrvars = 195
% 0.71/1.11 excuselevel = 1
% 0.71/1.11 increasemaxweight = 1
% 0.71/1.11
% 0.71/1.11 maxselected = 10000000
% 0.71/1.11 maxnrclauses = 10000000
% 0.71/1.11
% 0.71/1.11 showgenerated = 0
% 0.71/1.11 showkept = 0
% 0.71/1.11 showselected = 0
% 0.71/1.11 showdeleted = 0
% 0.71/1.11 showresimp = 1
% 0.71/1.11 showstatus = 2000
% 0.71/1.11
% 0.71/1.11 prologoutput = 0
% 0.71/1.11 nrgoals = 5000000
% 0.71/1.11 totalproof = 1
% 0.71/1.11
% 0.71/1.11 Symbols occurring in the translation:
% 0.71/1.11
% 0.71/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.11 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.71/1.11 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.71/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 cons [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.11 head [38, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.11 tail [39, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.71/1.11 nil [40, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.71/1.11 s [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.71/1.11 proj1S [42, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.71/1.11 z [43, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.71/1.11 drop [45, 2] (w:1, o:50, a:1, s:1, b:0).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Starting Search:
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Bliksems!, er is een bewijs:
% 0.71/1.11 % SZS status Theorem
% 0.71/1.11 % SZS output start Refutation
% 0.71/1.11
% 0.71/1.11 (2) {G0,W5,D3,L1,V2,M1} I { ! cons( X, Y ) ==> nil }.
% 0.71/1.11 (5) {G0,W6,D4,L1,V1,M1} I { drop( s( X ), nil ) ==> nil }.
% 0.71/1.11 (6) {G0,W10,D4,L1,V3,M1} I { drop( s( X ), cons( Y, Z ) ) ==> drop( X, Z )
% 0.71/1.11 }.
% 0.71/1.11 (8) {G0,W10,D3,L2,V3,M2} I { ! drop( X, Y ) = drop( X, Z ), Y = Z }.
% 0.71/1.11 (18) {G1,W12,D4,L2,V4,M2} P(8,2) { ! Z = nil, ! drop( T, cons( X, Y ) ) =
% 0.71/1.11 drop( T, Z ) }.
% 0.71/1.11 (21) {G2,W9,D4,L1,V3,M1} Q(18) { ! drop( X, cons( Y, Z ) ) ==> drop( X, nil
% 0.71/1.11 ) }.
% 0.71/1.11 (25) {G3,W5,D3,L1,V2,M1} P(6,21);d(5) { ! drop( X, Z ) ==> nil }.
% 0.71/1.11 (29) {G4,W0,D0,L0,V0,M0} R(25,5) { }.
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 % SZS output end Refutation
% 0.71/1.11 found a proof!
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Unprocessed initial clauses:
% 0.71/1.11
% 0.71/1.11 (31) {G0,W6,D4,L1,V2,M1} { head( cons( X, Y ) ) = X }.
% 0.71/1.11 (32) {G0,W6,D4,L1,V2,M1} { tail( cons( X, Y ) ) = Y }.
% 0.71/1.11 (33) {G0,W5,D3,L1,V2,M1} { ! nil = cons( X, Y ) }.
% 0.71/1.11 (34) {G0,W5,D4,L1,V1,M1} { proj1S( s( X ) ) = X }.
% 0.71/1.11 (35) {G0,W4,D3,L1,V1,M1} { ! s( X ) = z }.
% 0.71/1.11 (36) {G0,W6,D4,L1,V1,M1} { drop( s( X ), nil ) = nil }.
% 0.71/1.11 (37) {G0,W10,D4,L1,V3,M1} { drop( s( X ), cons( Y, Z ) ) = drop( X, Z )
% 0.71/1.11 }.
% 0.71/1.11 (38) {G0,W5,D3,L1,V1,M1} { drop( z, X ) = X }.
% 0.71/1.11 (39) {G0,W10,D3,L2,V3,M2} { ! drop( X, Y ) = drop( X, Z ), Y = Z }.
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Total Proof:
% 0.71/1.11
% 0.71/1.11 eqswap: (42) {G0,W5,D3,L1,V2,M1} { ! cons( X, Y ) = nil }.
% 0.71/1.11 parent0[0]: (33) {G0,W5,D3,L1,V2,M1} { ! nil = cons( X, Y ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (2) {G0,W5,D3,L1,V2,M1} I { ! cons( X, Y ) ==> nil }.
% 0.71/1.11 parent0: (42) {G0,W5,D3,L1,V2,M1} { ! cons( X, Y ) = nil }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (5) {G0,W6,D4,L1,V1,M1} I { drop( s( X ), nil ) ==> nil }.
% 0.71/1.11 parent0: (36) {G0,W6,D4,L1,V1,M1} { drop( s( X ), nil ) = nil }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (6) {G0,W10,D4,L1,V3,M1} I { drop( s( X ), cons( Y, Z ) ) ==>
% 0.71/1.11 droTerminated
% 299.66/300.03 Bliksem ended
%------------------------------------------------------------------------------