TSTP Solution File: SWV153+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV153+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 21:41:27 EDT 2022
% Result : Theorem 4.43s 4.63s
% Output : Refutation 4.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV153+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 04:48:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.43/4.63
% 4.43/4.63 SPASS V 3.9
% 4.43/4.63 SPASS beiseite: Proof found.
% 4.43/4.63 % SZS status Theorem
% 4.43/4.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.43/4.63 SPASS derived 10876 clauses, backtracked 1846 clauses, performed 8 splits and kept 6390 clauses.
% 4.43/4.63 SPASS allocated 94707 KBytes.
% 4.43/4.63 SPASS spent 0:00:04.25 on the problem.
% 4.43/4.63 0:00:00.04 for the input.
% 4.43/4.63 0:00:00.07 for the FLOTTER CNF translation.
% 4.43/4.63 0:00:00.09 for inferences.
% 4.43/4.63 0:00:00.15 for the backtracking.
% 4.43/4.63 0:00:03.76 for the reduction.
% 4.43/4.63
% 4.43/4.63
% 4.43/4.63 Here is a proof with depth 4, length 96 :
% 4.43/4.63 % SZS output start Refutation
% 4.43/4.63 2[0:Inp] || -> leq(n0,skc1)*r.
% 4.43/4.63 4[0:Inp] || -> leq(n0,pv12)*r.
% 4.43/4.63 6[0:Inp] || -> leq(pv12,n4)*l.
% 4.43/4.63 7[0:Inp] || -> leq(skc1,pv12)*l.
% 4.43/4.63 21[0:Inp] || -> gt(n1,n0)*l.
% 4.43/4.63 36[0:Inp] || -> leq(u,u)*.
% 4.43/4.63 37[0:Inp] || equal(skc1,pv12)** -> .
% 4.43/4.63 38[0:Inp] || -> equal(succ(n0),n1)**.
% 4.43/4.63 43[0:Inp] || -> equal(succ(succ(n0)),n2)**.
% 4.43/4.63 60[0:Inp] || -> equal(pred(succ(u)),u)**.
% 4.43/4.63 62[0:Inp] || -> equal(succ(succ(succ(n0))),n3)**.
% 4.43/4.63 69[0:Inp] || -> equal(succ(succ(succ(succ(n0)))),n4)**.
% 4.43/4.63 74[0:Inp] || gt(u,v)* -> leq(v,u).
% 4.43/4.63 81[0:Inp] || gt(u,v)*+ -> leq(v,pred(u))*.
% 4.43/4.63 103[0:Inp] || leq(u,v)* -> gt(v,u) equal(u,v).
% 4.43/4.63 107[0:Inp] || leq(u,n0)*+ leq(n0,u)* -> equal(u,n0).
% 4.43/4.63 109[0:Inp] || leq(u,v)* leq(v,w)* -> leq(u,w)*.
% 4.43/4.63 113[0:Inp] || leq(u,n1)* leq(n0,u) -> equal(u,n1) equal(u,n0).
% 4.43/4.63 115[0:Inp] || leq(u,n2)* leq(n0,u) -> equal(u,n2) equal(u,n1) equal(u,n0).
% 4.43/4.63 123[0:Inp] || leq(u,n4)* leq(n0,u) -> equal(u,n4) equal(u,n3)* equal(u,n2) equal(u,n1) equal(u,n0).
% 4.43/4.63 124[0:Inp] || -> equal(sum__dfg(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10))))),pv70)**.
% 4.43/4.63 147[0:Inp] || equal(divide(sqrt(times(minus(a_select3(center,skc1,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,skc1,n0),a_select2(x__dfg,pv10)))),sum__dfg(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10)))))),a_select3(q,pv10,skc1))** -> .
% 4.43/4.63 150[0:Inp] || leq(n0,u) leq(u,pred(pv12)) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),sum__dfg(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x__dfg,pv10)))))),a_select3(q,pv10,u))**.
% 4.43/4.63 152[0:Rew:38.0,43.0] || -> equal(succ(n1),n2)**.
% 4.43/4.63 155[0:Rew:152.0,62.0,38.0,62.0] || -> equal(succ(n2),n3)**.
% 4.43/4.63 157[0:Rew:155.0,69.0,152.0,69.0,38.0,69.0] || -> equal(succ(n3),n4)**.
% 4.43/4.63 165[0:Rew:124.0,147.0] || equal(divide(sqrt(times(minus(a_select3(center,skc1,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,skc1,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,skc1))** -> .
% 4.43/4.63 166[0:Rew:124.0,150.2] || leq(u,pred(pv12)) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.43/4.63 191[0:Res:7.0,103.0] || -> equal(skc1,pv12) gt(pv12,skc1)*r.
% 4.43/4.63 281[0:Res:6.0,123.1] || leq(n0,pv12) -> equal(pv12,n0) equal(n1,pv12) equal(n2,pv12) equal(n3,pv12)** equal(pv12,n4).
% 4.43/4.63 353[0:MRR:191.0,37.0] || -> gt(pv12,skc1)*r.
% 4.43/4.63 354[0:MRR:281.0,4.0] || -> equal(pv12,n4) equal(n3,pv12)** equal(n2,pv12) equal(n1,pv12) equal(pv12,n0).
% 4.43/4.63 444[1:Spt:354.0] || -> equal(pv12,n4)**.
% 4.43/4.63 500[1:Rew:444.0,353.0] || -> gt(n4,skc1)*r.
% 4.43/4.63 530[1:Rew:444.0,166.0] || leq(u,pred(n4)) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.43/4.63 658[0:SpR:38.0,60.0] || -> equal(pred(n1),n0)**.
% 4.43/4.63 659[0:SpR:152.0,60.0] || -> equal(pred(n2),n1)**.
% 4.43/4.63 660[0:SpR:155.0,60.0] || -> equal(pred(n3),n2)**.
% 4.43/4.63 661[0:SpR:157.0,60.0] || -> equal(pred(n4),n3)**.
% 4.43/4.63 664[1:Rew:661.0,530.0] || leq(u,n3) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.43/4.63 2915[0:Res:21.0,74.0] || -> leq(n0,n1)*r.
% 4.43/4.63 3207[1:Res:500.0,81.0] || -> leq(skc1,pred(n4))*r.
% 4.43/4.63 3337[1:Rew:661.0,3207.0] || -> leq(skc1,n3)*l.
% 4.43/4.63 7613[1:SpL:664.2,165.0] || leq(skc1,n3) leq(n0,skc1) equal(a_select3(q,pv10,skc1),a_select3(q,pv10,skc1))* -> .
% 4.43/4.63 7614[1:Obv:7613.2] || leq(skc1,n3)*l leq(n0,skc1) -> .
% 4.43/4.63 7615[1:MRR:7614.0,7614.1,3337.0,2.0] || -> .
% 4.43/4.63 7616[1:Spt:7615.0,354.0,444.0] || equal(pv12,n4)** -> .
% 4.43/4.63 7617[1:Spt:7615.0,354.1,354.2,354.3,354.4] || -> equal(n3,pv12)** equal(n2,pv12) equal(n1,pv12) equal(pv12,n0).
% 4.43/4.63 7631[2:Spt:7617.0] || -> equal(n3,pv12)**.
% 4.43/4.63 7634[2:Rew:7631.0,660.0] || -> equal(pred(pv12),n2)**.
% 4.43/4.63 8155[2:Rew:7634.0,166.0] || leq(u,n2) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.43/4.63 8520[0:NCh:109.2,109.0,7.0,107.0] || equal(pv12,n0) leq(n0,skc1)*r -> equal(skc1,n0).
% 4.43/4.63 8522[0:NCh:109.2,109.0,7.0,113.0] || equal(n1,pv12) leq(n0,skc1)*r -> equal(skc1,n1) equal(skc1,n0).
% 4.43/4.63 8524[0:NCh:109.2,109.0,7.0,115.0] || equal(n2,pv12) leq(n0,skc1)*r -> equal(skc1,n2) equal(skc1,n1) equal(skc1,n0).
% 4.43/4.63 8527[0:MRR:8520.1,2.0] || equal(pv12,n0) -> equal(skc1,n0)**.
% 4.43/4.63 8528[0:MRR:8522.1,2.0] || equal(n1,pv12) -> equal(skc1,n1)** equal(skc1,n0).
% 4.43/4.63 8540[0:SpL:8527.1,37.0] || equal(pv12,n0)** equal(pv12,n0)** -> .
% 4.43/4.63 8541[0:Obv:8540.0] || equal(pv12,n0)** -> .
% 4.43/4.63 8605[0:Res:353.0,81.0] || -> leq(skc1,pred(pv12))*r.
% 4.43/4.63 8615[2:Rew:7634.0,8605.0] || -> leq(skc1,n2)*l.
% 4.43/4.63 9658[2:SpL:8155.2,165.0] || leq(skc1,n2) leq(n0,skc1) equal(a_select3(q,pv10,skc1),a_select3(q,pv10,skc1))* -> .
% 4.43/4.63 9659[2:Obv:9658.2] || leq(skc1,n2)*l leq(n0,skc1) -> .
% 4.43/4.63 9660[2:MRR:9659.0,9659.1,8615.0,2.0] || -> .
% 4.43/4.63 9661[2:Spt:9660.0,7617.0,7631.0] || equal(n3,pv12)** -> .
% 4.43/4.63 9662[2:Spt:9660.0,7617.1,7617.2,7617.3] || -> equal(n2,pv12)** equal(n1,pv12) equal(pv12,n0).
% 4.43/4.63 9664[2:MRR:9662.2,8541.0] || -> equal(n2,pv12)** equal(n1,pv12).
% 4.43/4.63 9666[0:MRR:8524.1,2.0] || equal(n2,pv12) -> equal(skc1,n2)** equal(skc1,n1) equal(skc1,n0).
% 4.43/4.63 9865[3:Spt:9664.0] || -> equal(n2,pv12)**.
% 4.43/4.63 9867[3:Rew:9865.0,659.0] || -> equal(pred(pv12),n1)**.
% 4.43/4.63 10298[3:Rew:9865.0,9666.0] || equal(pv12,pv12) -> equal(skc1,n2)** equal(skc1,n1) equal(skc1,n0).
% 4.43/4.63 10352[3:Rew:9867.0,166.0] || leq(u,n1) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.43/4.63 10368[3:Obv:10298.0] || -> equal(skc1,n2)** equal(skc1,n1) equal(skc1,n0).
% 4.43/4.63 10369[3:Rew:9865.0,10368.0] || -> equal(skc1,pv12) equal(skc1,n1)** equal(skc1,n0).
% 4.43/4.63 10370[3:MRR:10369.0,37.0] || -> equal(skc1,n1)** equal(skc1,n0).
% 4.43/4.63 10571[4:Spt:10370.0] || -> equal(skc1,n1)**.
% 4.43/4.63 10573[4:Rew:10571.0,165.0] || equal(divide(sqrt(times(minus(a_select3(center,n1,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,n1,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,n1))** -> .
% 4.43/4.63 12198[4:SpL:10352.2,10573.0] || leq(n1,n1) leq(n0,n1) equal(a_select3(q,pv10,n1),a_select3(q,pv10,n1))* -> .
% 4.43/4.63 12199[4:Obv:12198.2] || leq(n1,n1)* leq(n0,n1) -> .
% 4.43/4.63 12200[4:MRR:12199.0,12199.1,36.0,2915.0] || -> .
% 4.43/4.63 12201[4:Spt:12200.0,10370.0,10571.0] || equal(skc1,n1)** -> .
% 4.43/4.63 12202[4:Spt:12200.0,10370.1] || -> equal(skc1,n0)**.
% 4.43/4.63 12297[4:Rew:12202.0,165.0] || equal(divide(sqrt(times(minus(a_select3(center,n0,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,n0,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,n0))** -> .
% 4.43/4.63 12388[4:SpL:10352.2,12297.0] || leq(n0,n1) leq(n0,n0) equal(a_select3(q,pv10,n0),a_select3(q,pv10,n0))* -> .
% 4.43/4.63 12389[4:Obv:12388.2] || leq(n0,n1)*r leq(n0,n0) -> .
% 4.43/4.63 12390[4:MRR:12389.0,12389.1,2915.0,36.0] || -> .
% 4.43/4.63 12391[3:Spt:12390.0,9664.0,9865.0] || equal(n2,pv12)** -> .
% 4.43/4.63 12392[3:Spt:12390.0,9664.1] || -> equal(n1,pv12)**.
% 4.43/4.63 12394[3:Rew:12392.0,658.0] || -> equal(pred(pv12),n0)**.
% 4.43/4.63 12608[3:Rew:12392.0,8528.1,12392.0,8528.0] || equal(pv12,pv12) -> equal(skc1,pv12)** equal(skc1,n0).
% 4.43/4.63 12609[3:Obv:12608.0] || -> equal(skc1,pv12)** equal(skc1,n0).
% 4.43/4.63 12610[3:MRR:12609.0,37.0] || -> equal(skc1,n0)**.
% 4.43/4.63 12800[3:Rew:12610.0,165.0] || equal(divide(sqrt(times(minus(a_select3(center,n0,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,n0,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,n0))** -> .
% 4.52/4.68 12964[3:Rew:12394.0,166.0] || leq(u,n0) leq(n0,u) -> equal(divide(sqrt(times(minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)),minus(a_select3(center,u,n0),a_select2(x__dfg,pv10)))),pv70),a_select3(q,pv10,u))**.
% 4.52/4.68 14706[3:SpL:12964.2,12800.0] || leq(n0,n0) leq(n0,n0) equal(a_select3(q,pv10,n0),a_select3(q,pv10,n0))* -> .
% 4.52/4.68 14707[3:Obv:14706.2] || leq(n0,n0)* -> .
% 4.52/4.68 14708[3:MRR:14707.0,36.0] || -> .
% 4.52/4.68 % SZS output end Refutation
% 4.52/4.68 Formulae used in the proof : cl5_nebula_norm_0003 gt_1_0 reflexivity_leq successor_1 successor_2 pred_succ successor_3 successor_4 leq_gt1 leq_gt_pred leq_gt2 finite_domain_0 transitivity_leq finite_domain_1 finite_domain_2 finite_domain_4
% 4.52/4.68
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