TSTP Solution File: SWV111+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV111+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:41:19 EDT 2022
% Result : Theorem 2.44s 2.63s
% Output : Refutation 2.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV111+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 00:35:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.44/2.63
% 2.44/2.63 SPASS V 3.9
% 2.44/2.63 SPASS beiseite: Proof found.
% 2.44/2.63 % SZS status Theorem
% 2.44/2.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.44/2.63 SPASS derived 7533 clauses, backtracked 283 clauses, performed 5 splits and kept 4001 clauses.
% 2.44/2.63 SPASS allocated 92513 KBytes.
% 2.44/2.63 SPASS spent 0:00:02.28 on the problem.
% 2.44/2.63 0:00:00.04 for the input.
% 2.44/2.63 0:00:00.09 for the FLOTTER CNF translation.
% 2.44/2.63 0:00:00.05 for inferences.
% 2.44/2.63 0:00:00.05 for the backtracking.
% 2.44/2.63 0:00:01.88 for the reduction.
% 2.44/2.63
% 2.44/2.63
% 2.44/2.63 Here is a proof with depth 2, length 128 :
% 2.44/2.63 % SZS output start Refutation
% 2.44/2.63 1[0:Inp] || -> SkC0*.
% 2.44/2.63 2[0:Inp] || -> SkC1*.
% 2.44/2.63 3[0:Inp] || -> SkC2*.
% 2.44/2.63 5[0:Inp] || -> leq(n0,skc19)*r.
% 2.44/2.63 9[0:Inp] || -> leq(n0,skc11)*r.
% 2.44/2.63 10[0:Inp] || -> leq(n0,skc10)*r.
% 2.44/2.63 11[0:Inp] || -> leq(n0,pv5)*r.
% 2.44/2.63 12[0:Inp] || -> leq(n0,pv57)*r.
% 2.44/2.63 28[0:Inp] || -> gt(n5,n0)*l.
% 2.44/2.63 50[0:Inp] || -> SkC3* leq(skc19,pv57).
% 2.44/2.63 51[0:Inp] || -> SkC3* leq(n0,skc18).
% 2.44/2.63 52[0:Inp] || -> equal(succ(n0),n1)**.
% 2.44/2.63 53[0:Inp] || gt(u,u)* -> .
% 2.44/2.63 54[0:Inp] || -> gt(succ(u),u)*l.
% 2.44/2.63 55[0:Inp] || -> equal(succ(tptp_minus_1),n0)**.
% 2.44/2.63 57[0:Inp] || -> leq(skc18,minus(n6,n1))*r.
% 2.44/2.63 61[0:Inp] || -> leq(pv5,minus(n999,n1))*r.
% 2.44/2.63 62[0:Inp] || -> leq(pv57,minus(n6,n1))*r.
% 2.44/2.63 63[0:Inp] || -> equal(succ(succ(n0)),n2)**.
% 2.44/2.63 80[0:Inp] || -> equal(pred(succ(u)),u)**.
% 2.44/2.63 81[0:Inp] || -> equal(succ(pred(u)),u)**.
% 2.44/2.63 82[0:Inp] || -> equal(succ(succ(succ(n0))),n3)**.
% 2.44/2.63 86[0:Inp] || -> equal(plus(n1,u),succ(u))**.
% 2.44/2.63 87[0:Inp] || -> equal(minus(u,n1),pred(u))**.
% 2.44/2.63 89[0:Inp] || -> equal(succ(succ(succ(succ(n0)))),n4)**.
% 2.44/2.63 91[0:Inp] || gt(u,v) -> lt(v,u)*.
% 2.44/2.63 94[0:Inp] || gt(u,v)* -> leq(v,u).
% 2.44/2.63 99[0:Inp] || -> equal(succ(succ(succ(succ(succ(n0))))),n5)**.
% 2.44/2.63 101[0:Inp] || gt(u,v)*+ -> leq(v,pred(u))*.
% 2.44/2.63 103[0:Inp] || leq(u,v)*+ -> gt(succ(v),u)*.
% 2.44/2.63 115[0:Inp] || -> equal(succ(succ(succ(succ(succ(succ(n0)))))),n6)**.
% 2.44/2.63 124[0:Inp] || leq(u,v)* -> gt(v,u) equal(u,v).
% 2.44/2.63 128[0:Inp] || equal(a_select3(id_ds1_filter,skc19,skc18),a_select3(id_ds1_filter,skc18,skc19))** -> SkC3.
% 2.44/2.63 129[0:Inp] || leq(u,n0)*+ leq(n0,u)* -> equal(u,n0).
% 2.44/2.63 130[0:Inp] || gt(u,v)* gt(v,w)* -> gt(u,w)*.
% 2.44/2.63 131[0:Inp] || leq(u,v)* leq(v,w)* -> leq(u,w)*.
% 2.44/2.63 135[0:Inp] || leq(u,n1)* leq(n0,u) -> equal(u,n1) equal(u,n0).
% 2.44/2.63 152[0:Inp] || leq(n0,u) leq(u,minus(pv57,n1)) leq(n0,v) leq(v,minus(n6,n1)) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 162[0:Inp] || leq(n0,pv5) leq(n0,pv57) leq(pv5,minus(n999,n1)) leq(pv57,minus(n6,n1))*r SkC0 SkC1 SkC2 SkC3 -> leq(skc11,minus(n6,n1)).
% 2.44/2.63 163[0:Inp] || leq(n0,pv5) leq(n0,pv57) leq(pv5,minus(n999,n1)) leq(pv57,minus(n6,n1))*r SkC0 SkC1 SkC2 SkC3 -> leq(skc10,minus(pv57,n1)).
% 2.44/2.63 166[0:Inp] || equal(a_select3(id_ds1_filter,skc11,skc10),a_select3(id_ds1_filter,skc10,skc11))** leq(n0,pv5) leq(n0,pv57) leq(pv5,minus(n999,n1)) leq(pv57,minus(n6,n1)) SkC0 SkC1 SkC2 SkC3 -> .
% 2.44/2.63 172[0:Inp] || lt(u,plus(n1,minus(n6,n1)))* equal(v,pv57) leq(n0,v) leq(v,minus(n6,n1)) leq(u,minus(n6,n1)) leq(n0,u) -> equal(a_select3(id_ds1_filter,v,u),a_select3(id_ds1_filter,u,v))*.
% 2.44/2.63 180[0:Rew:52.0,63.0] || -> equal(succ(n1),n2)**.
% 2.44/2.63 183[0:Rew:180.0,82.0,52.0,82.0] || -> equal(succ(n2),n3)**.
% 2.44/2.63 185[0:Rew:183.0,89.0,180.0,89.0,52.0,89.0] || -> equal(succ(n3),n4)**.
% 2.44/2.63 188[0:Rew:185.0,99.0,183.0,99.0,180.0,99.0,52.0,99.0] || -> equal(succ(n4),n5)**.
% 2.44/2.63 191[0:Rew:188.0,115.0,185.0,115.0,183.0,115.0,180.0,115.0,52.0,115.0] || -> equal(succ(n5),n6)**.
% 2.44/2.63 194[0:Rew:87.0,62.0] || -> leq(pv57,pred(n6))*r.
% 2.44/2.63 195[0:Rew:87.0,61.0] || -> leq(pv5,pred(n999))*r.
% 2.44/2.63 199[0:Rew:87.0,57.0] || -> leq(skc18,pred(n6))*r.
% 2.44/2.63 200[0:Rew:87.0,152.3,87.0,152.1] || leq(u,pred(n6)) leq(v,pred(pv57)) leq(n0,u) leq(n0,v) -> equal(a_select3(id_ds1_filter,v,u),a_select3(id_ds1_filter,u,v))*.
% 2.44/2.63 208[0:Rew:87.0,162.8,87.0,162.3,87.0,162.2] || leq(n0,pv5) leq(n0,pv57) leq(pv5,pred(n999)) leq(pv57,pred(n6))*r SkC0 SkC1 SkC2 SkC3 -> leq(skc11,pred(n6)).
% 2.44/2.63 209[0:MRR:208.0,208.1,208.2,208.3,208.4,208.5,208.6,11.0,12.0,195.0,194.0,1.0,2.0,3.0] || SkC3 -> leq(skc11,pred(n6))*r.
% 2.44/2.63 210[0:Rew:87.0,163.8,87.0,163.3,87.0,163.2] || leq(n0,pv5) leq(n0,pv57) leq(pv5,pred(n999)) leq(pv57,pred(n6))*r SkC0 SkC1 SkC2 SkC3 -> leq(skc10,pred(pv57)).
% 2.44/2.63 211[0:MRR:210.0,210.1,210.2,210.3,210.4,210.5,210.6,11.0,12.0,195.0,194.0,1.0,2.0,3.0] || SkC3 -> leq(skc10,pred(pv57))*r.
% 2.44/2.63 212[0:Rew:87.0,166.4,87.0,166.3] || equal(a_select3(id_ds1_filter,skc11,skc10),a_select3(id_ds1_filter,skc10,skc11))** leq(n0,pv5) leq(n0,pv57) leq(pv5,pred(n999)) leq(pv57,pred(n6)) SkC0 SkC1 SkC2 SkC3 -> .
% 2.44/2.63 213[0:MRR:212.1,212.2,212.3,212.4,212.5,212.6,212.7,11.0,12.0,195.0,194.0,1.0,2.0,3.0] || SkC3 equal(a_select3(id_ds1_filter,skc11,skc10),a_select3(id_ds1_filter,skc10,skc11))** -> .
% 2.44/2.63 214[0:Rew:87.0,172.4,87.0,172.3,81.0,172.0,87.0,172.0,86.0,172.0] || equal(u,pv57) lt(v,n6) leq(v,pred(n6)) leq(u,pred(n6)) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 240[0:Res:12.0,135.0] || leq(pv57,n1)*r -> equal(n1,pv57) equal(pv57,n0).
% 2.44/2.63 535[1:Spt:240.2] || -> equal(pv57,n0)**.
% 2.44/2.63 538[1:Rew:535.0,211.1] || SkC3 -> leq(skc10,pred(n0))*r.
% 2.44/2.63 593[1:Rew:535.0,214.0] || equal(u,n0) lt(v,n6) leq(v,pred(n6)) leq(u,pred(n6)) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 612[1:Rew:535.0,50.1] || -> SkC3* leq(skc19,n0).
% 2.44/2.63 846[2:Spt:51.0] || -> SkC3*.
% 2.44/2.63 849[2:MRR:538.0,846.0] || -> leq(skc10,pred(n0))*r.
% 2.44/2.63 861[0:SpR:55.0,80.0] || -> equal(pred(n0),tptp_minus_1)**.
% 2.44/2.63 867[0:SpR:191.0,80.0] || -> equal(pred(n6),n5)**.
% 2.44/2.63 872[2:Rew:861.0,849.0] || -> leq(skc10,tptp_minus_1)*l.
% 2.44/2.63 876[1:Rew:867.0,593.2] || equal(u,n0) lt(v,n6) leq(v,n5) leq(u,pred(n6)) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 888[0:Rew:867.0,199.0] || -> leq(skc18,n5)*l.
% 2.44/2.63 898[1:Rew:867.0,876.3] || equal(u,n0) lt(v,n6) leq(v,n5) leq(u,n5) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 1059[2:OCh:131.1,131.0,872.0,10.0] || -> leq(n0,tptp_minus_1)*r.
% 2.44/2.63 3288[0:NCh:130.2,130.0,94.0,28.0] || equal(n0,u)* -> leq(u,n5)*.
% 2.44/2.63 3348[1:MRR:898.3,3288.1] || equal(u,n0) lt(v,n6) leq(v,n5) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 3356[2:Res:1059.0,103.0] || -> gt(succ(tptp_minus_1),n0)*l.
% 2.44/2.63 3376[0:Res:888.0,103.0] || -> gt(succ(n5),skc18)*l.
% 2.44/2.63 3492[2:Rew:55.0,3356.0] || -> gt(n0,n0)*.
% 2.44/2.63 3493[2:MRR:3492.0,53.0] || -> .
% 2.44/2.63 3498[0:Rew:191.0,3376.0] || -> gt(n6,skc18)*r.
% 2.44/2.63 3517[2:Spt:3493.0,51.0,846.0] || SkC3* -> .
% 2.44/2.63 3518[2:Spt:3493.0,51.1] || -> leq(n0,skc18)*r.
% 2.44/2.63 3519[2:MRR:612.0,3517.0] || -> leq(skc19,n0)*l.
% 2.44/2.63 3520[2:MRR:128.1,3517.0] || equal(a_select3(id_ds1_filter,skc19,skc18),a_select3(id_ds1_filter,skc18,skc19))** -> .
% 2.44/2.63 3660[0:NCh:130.2,130.0,101.0,54.0] || equal(u,v)* -> leq(v,pred(succ(u)))*.
% 2.44/2.63 3760[0:Rew:80.0,3660.1] || equal(u,v)* -> leq(v,u).
% 2.44/2.63 3761[1:MRR:3348.4,3760.1] || equal(u,n0) lt(v,n6) leq(v,n5) leq(n0,v) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 5414[2:Res:3519.0,129.0] || leq(n0,skc19)*r -> equal(skc19,n0).
% 2.44/2.63 5518[2:MRR:5414.0,5.0] || -> equal(skc19,n0)**.
% 2.44/2.63 5521[2:Rew:5518.0,3520.0] || equal(a_select3(id_ds1_filter,skc18,n0),a_select3(id_ds1_filter,n0,skc18))** -> .
% 2.44/2.63 6776[2:SpL:3761.4,5521.0] || equal(n0,n0) lt(skc18,n6) leq(skc18,n5) leq(n0,skc18) equal(a_select3(id_ds1_filter,n0,skc18),a_select3(id_ds1_filter,n0,skc18))* -> .
% 2.44/2.63 6780[2:Obv:6776.4] || lt(skc18,n6)* leq(skc18,n5) leq(n0,skc18) -> .
% 2.44/2.63 6781[2:MRR:6780.1,6780.2,888.0,3518.0] || lt(skc18,n6)* -> .
% 2.44/2.63 6796[2:Res:91.1,6781.0] || gt(n6,skc18)*r -> .
% 2.44/2.63 6797[2:MRR:6796.0,3498.0] || -> .
% 2.44/2.63 6798[1:Spt:6797.0,240.2,535.0] || equal(pv57,n0)** -> .
% 2.44/2.63 6799[1:Spt:6797.0,240.0,240.1] || leq(pv57,n1)*r -> equal(n1,pv57).
% 2.44/2.63 6800[0:Rew:867.0,194.0] || -> leq(pv57,n5)*r.
% 2.44/2.63 6801[0:Rew:867.0,209.1] || SkC3* -> leq(skc11,n5).
% 2.44/2.63 6832[0:Rew:867.0,200.0] || leq(u,n5) leq(v,pred(pv57)) leq(n0,u) leq(n0,v) -> equal(a_select3(id_ds1_filter,v,u),a_select3(id_ds1_filter,u,v))*.
% 2.44/2.63 6834[0:Rew:867.0,214.3,867.0,214.2] || equal(u,pv57) lt(v,n6) leq(v,n5) leq(u,n5) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.44/2.63 7263[2:Spt:51.0] || -> SkC3*.
% 2.44/2.63 7264[2:MRR:6801.0,7263.0] || -> leq(skc11,n5)*l.
% 2.44/2.63 7265[2:MRR:211.0,7263.0] || -> leq(skc10,pred(pv57))*r.
% 2.44/2.63 7266[2:MRR:213.0,7263.0] || equal(a_select3(id_ds1_filter,skc11,skc10),a_select3(id_ds1_filter,skc10,skc11))** -> .
% 2.51/2.67 7569[0:Res:6800.0,103.0] || -> gt(succ(n5),pv57)*l.
% 2.51/2.67 7579[0:Rew:191.0,7569.0] || -> gt(n6,pv57)*l.
% 2.51/2.67 7897[0:NCh:130.2,130.0,7579.0,101.0] || equal(pv57,u)* -> leq(u,pred(n6))*.
% 2.51/2.67 7902[0:Rew:867.0,7897.1] || equal(pv57,u)* -> leq(u,n5)*.
% 2.51/2.67 7904[0:MRR:6834.3,7902.1] || equal(u,pv57) lt(v,n6) leq(v,n5) leq(n0,v) leq(n0,u) -> equal(a_select3(id_ds1_filter,u,v),a_select3(id_ds1_filter,v,u))*.
% 2.51/2.67 9835[2:SpL:6832.4,7266.0] || leq(skc11,n5) leq(skc10,pred(pv57)) leq(n0,skc11) leq(n0,skc10) equal(a_select3(id_ds1_filter,skc10,skc11),a_select3(id_ds1_filter,skc10,skc11))* -> .
% 2.51/2.67 9836[2:Obv:9835.4] || leq(skc11,n5) leq(skc10,pred(pv57))*r leq(n0,skc11) leq(n0,skc10) -> .
% 2.51/2.67 9837[2:MRR:9836.0,9836.1,9836.2,9836.3,7264.0,7265.0,9.0,10.0] || -> .
% 2.51/2.67 9852[2:Spt:9837.0,51.0,7263.0] || SkC3* -> .
% 2.51/2.67 9853[2:Spt:9837.0,51.1] || -> leq(n0,skc18)*r.
% 2.51/2.67 9866[2:MRR:50.0,9852.0] || -> leq(skc19,pv57)*l.
% 2.51/2.67 9867[2:MRR:128.1,9852.0] || equal(a_select3(id_ds1_filter,skc19,skc18),a_select3(id_ds1_filter,skc18,skc19))** -> .
% 2.51/2.67 9885[2:Res:9866.0,124.0] || -> gt(pv57,skc19)*r equal(skc19,pv57).
% 2.51/2.67 9943[2:SpL:6832.4,9867.0] || leq(skc18,n5) leq(skc19,pred(pv57)) leq(n0,skc18) leq(n0,skc19) equal(a_select3(id_ds1_filter,skc18,skc19),a_select3(id_ds1_filter,skc18,skc19))* -> .
% 2.51/2.67 9946[2:SpL:7904.5,9867.0] || equal(skc19,pv57) lt(skc18,n6) leq(skc18,n5) leq(n0,skc18) leq(n0,skc19) equal(a_select3(id_ds1_filter,skc18,skc19),a_select3(id_ds1_filter,skc18,skc19))* -> .
% 2.51/2.67 9947[2:Obv:9946.5] || equal(skc19,pv57) lt(skc18,n6)* leq(skc18,n5) leq(n0,skc18) leq(n0,skc19) -> .
% 2.51/2.67 9948[2:MRR:9947.2,9947.3,9947.4,888.0,9853.0,5.0] || equal(skc19,pv57) lt(skc18,n6)* -> .
% 2.51/2.67 9953[2:Obv:9943.4] || leq(skc18,n5) leq(skc19,pred(pv57))*r leq(n0,skc18) leq(n0,skc19) -> .
% 2.51/2.67 9954[2:MRR:9953.0,9953.2,9953.3,888.0,9853.0,5.0] || leq(skc19,pred(pv57))*r -> .
% 2.51/2.67 9955[2:Res:91.1,9948.1] || gt(n6,skc18) equal(skc19,pv57)** -> .
% 2.51/2.67 9956[2:MRR:9955.0,3498.0] || equal(skc19,pv57)** -> .
% 2.51/2.67 9957[2:MRR:9885.1,9956.0] || -> gt(pv57,skc19)*r.
% 2.51/2.67 9958[2:Res:9957.0,101.0] || -> leq(skc19,pred(pv57))*r.
% 2.51/2.67 9968[2:MRR:9958.0,9954.0] || -> .
% 2.51/2.67 % SZS output end Refutation
% 2.51/2.67 Formulae used in the proof : quaternion_ds1_symm_0004 gt_succ leq_succ_gt_equiv gt_5_0 successor_1 irreflexivity_gt succ_tptp_minus_1 successor_2 pred_succ succ_pred successor_3 succ_plus_1_l pred_minus_1 successor_4 lt_gt leq_gt1 successor_5 leq_gt_pred successor_6 leq_gt2 finite_domain_0 transitivity_gt transitivity_leq finite_domain_1
% 2.51/2.67
%------------------------------------------------------------------------------