TSTP Solution File: SWC322-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC322-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : Tue Jul 19 22:03:18 EDT 2022
% Result : Unsatisfiable 3.65s 3.84s
% Output : Refutation 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC322-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 00:27:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.65/3.84
% 3.65/3.84 SPASS V 3.9
% 3.65/3.84 SPASS beiseite: Proof found.
% 3.65/3.84 % SZS status Theorem
% 3.65/3.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/3.84 SPASS derived 8822 clauses, backtracked 3109 clauses, performed 93 splits and kept 7315 clauses.
% 3.65/3.84 SPASS allocated 85078 KBytes.
% 3.65/3.84 SPASS spent 0:00:03.49 on the problem.
% 3.65/3.84 0:00:00.04 for the input.
% 3.65/3.84 0:00:00.00 for the FLOTTER CNF translation.
% 3.65/3.84 0:00:00.08 for inferences.
% 3.65/3.84 0:00:00.08 for the backtracking.
% 3.65/3.84 0:00:03.08 for the reduction.
% 3.65/3.84
% 3.65/3.84
% 3.65/3.84 Here is a proof with depth 3, length 119 :
% 3.65/3.84 % SZS output start Refutation
% 3.65/3.84 1[0:Inp] || -> ssList(sk1)*.
% 3.65/3.84 4[0:Inp] || -> ssList(sk4)*.
% 3.65/3.84 5[0:Inp] || -> equal(sk2,sk4)**.
% 3.65/3.84 6[0:Inp] || -> equal(sk3,sk1)**.
% 3.65/3.84 7[0:Inp] ssItem(u) ssList(v) || equal(app(v,cons(u,nil)),sk4)** -> equal(app(cons(u,nil),v),sk3)**.
% 3.65/3.84 8[0:Inp] || equal(nil,sk4)** -> equal(nil,sk3).
% 3.65/3.84 11[0:Inp] || -> ssList(sk6)* equal(sk2,nil).
% 3.65/3.84 12[0:Inp] || -> equal(app(sk6,cons(sk5,nil)),sk2)** equal(sk2,nil).
% 3.65/3.84 13[0:Inp] || equal(app(cons(sk5,nil),sk6),sk1)** -> equal(sk2,nil).
% 3.65/3.84 14[0:Inp] || equal(nil,sk1) -> ssList(sk6)*.
% 3.65/3.84 15[0:Inp] || equal(nil,sk1) -> equal(app(sk6,cons(sk5,nil)),sk2)**.
% 3.65/3.84 29[0:Inp] || -> ssList(skaf82(u))*.
% 3.65/3.84 63[0:Inp] || -> ssItem(skaf44(u))*.
% 3.65/3.84 70[0:Inp] || equal(skac2,skac3)** -> .
% 3.65/3.84 80[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.65/3.84 81[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.65/3.84 82[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.65/3.84 83[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.65/3.84 84[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.65/3.84 85[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.65/3.84 86[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.65/3.84 88[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 3.65/3.84 89[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 3.65/3.84 90[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.65/3.84 101[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 3.65/3.84 102[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 3.65/3.84 113[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 3.65/3.84 114[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 3.65/3.84 136[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.65/3.84 139[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 3.65/3.84 173[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 3.65/3.84 186[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.65/3.84 193[0:Inp] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(nil,v) equal(nil,u).
% 3.65/3.84 195[0:Inp] ssList(u) duplicatefreeP(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 3.65/3.84 204[0:Rew:5.0,11.1] || -> ssList(sk6)* equal(nil,sk4).
% 3.65/3.84 206[0:Rew:204.1,14.0] || equal(sk4,sk1) -> ssList(sk6)*.
% 3.65/3.84 208[0:Rew:6.0,8.1] || equal(nil,sk4)** -> equal(nil,sk1).
% 3.65/3.84 209[0:Rew:5.0,12.1,5.0,12.0] || -> equal(nil,sk4) equal(app(sk6,cons(sk5,nil)),sk4)**.
% 3.65/3.84 210[0:Rew:5.0,15.1] || equal(nil,sk1) -> equal(app(sk6,cons(sk5,nil)),sk4)**.
% 3.65/3.84 211[0:Rew:5.0,13.1] || equal(app(cons(sk5,nil),sk6),sk1)** -> equal(nil,sk4).
% 3.65/3.84 213[0:Rew:136.2,7.3,6.0,7.3] ssList(u) ssItem(v) || equal(app(u,cons(v,nil)),sk4)** -> equal(cons(v,u),sk1).
% 3.65/3.84 356[0:Res:4.0,102.1] ssItem(u) || -> ssList(cons(u,sk4))*.
% 3.65/3.84 486[0:Res:1.0,193.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 3.65/3.84 516[0:Res:1.0,139.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 3.65/3.84 523[0:Res:1.0,113.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 3.65/3.84 528[0:Res:1.0,102.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 3.65/3.84 539[0:Res:1.0,173.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 3.65/3.84 572[1:Spt:88.1] || -> ssItem(u)*.
% 3.65/3.84 575[1:MRR:528.0,572.0] || -> ssList(cons(u,sk1))*.
% 3.65/3.84 578[1:MRR:86.0,572.0] || -> cyclefreeP(cons(u,nil))*.
% 3.65/3.84 579[1:MRR:85.0,572.0] || -> totalorderP(cons(u,nil))*.
% 3.65/3.84 580[1:MRR:84.0,572.0] || -> strictorderP(cons(u,nil))*.
% 3.65/3.84 581[1:MRR:83.0,572.0] || -> totalorderedP(cons(u,nil))*.
% 3.65/3.84 582[1:MRR:82.0,572.0] || -> strictorderedP(cons(u,nil))*.
% 3.65/3.84 583[1:MRR:81.0,572.0] || -> duplicatefreeP(cons(u,nil))*.
% 3.65/3.84 584[1:MRR:80.0,572.0] || -> equalelemsP(cons(u,nil))*.
% 3.65/3.84 588[1:MRR:523.0,572.0] || -> equal(hd(cons(u,sk1)),u)**.
% 3.65/3.84 701[1:MRR:114.1,572.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 3.65/3.84 705[1:MRR:136.1,572.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.65/3.84 706[1:MRR:539.1,572.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 3.65/3.84 710[1:MRR:213.1,572.0] ssList(u) || equal(app(u,cons(v,nil)),sk4)** -> equal(cons(v,u),sk1).
% 3.65/3.84 770[1:MRR:186.3,186.2,572.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.65/3.84 771[2:Spt:516.0,516.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 3.65/3.84 779[3:Spt:486.5] || -> equal(nil,sk1)**.
% 3.65/3.84 863[3:Rew:779.0,90.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 3.65/3.84 864[3:Rew:779.0,89.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 3.65/3.84 869[3:Rew:779.0,578.0] || -> cyclefreeP(cons(u,sk1))*.
% 3.65/3.84 870[3:Rew:779.0,579.0] || -> totalorderP(cons(u,sk1))*.
% 3.65/3.84 871[3:Rew:779.0,580.0] || -> strictorderP(cons(u,sk1))*.
% 3.65/3.84 872[3:Rew:779.0,581.0] || -> totalorderedP(cons(u,sk1))*.
% 3.65/3.84 873[3:Rew:779.0,582.0] || -> strictorderedP(cons(u,sk1))*.
% 3.65/3.84 874[3:Rew:779.0,583.0] || -> duplicatefreeP(cons(u,sk1))*.
% 3.65/3.84 875[3:Rew:779.0,584.0] || -> equalelemsP(cons(u,sk1))*.
% 3.65/3.84 926[3:Rew:863.1,771.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 3.65/3.84 949[3:Rew:864.1,706.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 3.65/3.84 1233[3:SpR:926.1,588.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 3.65/3.84 1238[3:SSi:1233.0,575.0,869.0,870.0,871.0,872.0,873.0,874.0,875.0] || -> equal(hd(sk1),u)*.
% 3.65/3.84 1271[3:Rew:1238.0,949.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 3.65/3.84 1364[3:Rew:1238.0,770.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 3.65/3.84 1446[3:Con:1364.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 3.65/3.84 1447[3:AED:70.0,1446.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 3.65/3.84 1448[3:Rew:1271.1,1447.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 3.65/3.84 1449[3:Obv:1448.1] ssList(u) || -> .
% 3.65/3.84 1450[3:UnC:1449.0,29.0] || -> .
% 3.65/3.84 1548[3:Spt:1450.0,486.5,779.0] || equal(nil,sk1)** -> .
% 3.65/3.84 1549[3:Spt:1450.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 3.65/3.84 1554[3:MRR:208.1,1548.0] || equal(nil,sk4)** -> .
% 3.65/3.84 1555[3:MRR:204.1,1554.0] || -> ssList(sk6)*.
% 3.65/3.84 1566[3:MRR:209.0,1554.0] || -> equal(app(sk6,cons(sk5,nil)),sk4)**.
% 3.65/3.84 1569[3:MRR:211.1,1554.0] || equal(app(cons(sk5,nil),sk6),sk1)** -> .
% 3.65/3.84 1938[3:SpL:705.1,1569.0] ssList(sk6) || equal(cons(sk5,sk6),sk1)** -> .
% 3.65/3.84 1939[3:SSi:1938.0,1555.0] || equal(cons(sk5,sk6),sk1)** -> .
% 3.65/3.84 2444[3:SpL:1566.0,710.1] ssList(sk6) || equal(sk4,sk4) -> equal(cons(sk5,sk6),sk1)**.
% 3.65/3.84 2447[3:Obv:2444.1] ssList(sk6) || -> equal(cons(sk5,sk6),sk1)**.
% 3.65/3.84 2448[3:SSi:2447.0,1555.0] || -> equal(cons(sk5,sk6),sk1)**.
% 3.65/3.84 2449[3:MRR:2448.0,1939.0] || -> .
% 3.65/3.84 2455[2:Spt:2449.0,516.1] || -> equal(nil,sk1)**.
% 3.65/3.84 2508[2:Rew:2455.0,701.1] ssList(u) || equal(cons(v,u),sk1)** -> .
% 3.65/3.84 2511[2:Rew:2455.0,710.1] ssList(u) || equal(app(u,cons(v,sk1)),sk4)** -> equal(cons(v,u),sk1).
% 3.65/3.84 2557[2:Rew:2455.0,204.1] || -> ssList(sk6)* equal(sk4,sk1).
% 3.65/3.84 2559[2:Rew:2557.1,206.0] || equal(sk1,sk1) -> ssList(sk6)*.
% 3.65/3.84 2560[2:Obv:2559.0] || -> ssList(sk6)*.
% 3.65/3.84 2630[2:Rew:2455.0,210.1,2455.0,210.0] || equal(sk1,sk1) -> equal(app(sk6,cons(sk5,sk1)),sk4)**.
% 3.65/3.84 2631[2:Obv:2630.0] || -> equal(app(sk6,cons(sk5,sk1)),sk4)**.
% 3.65/3.84 2671[2:MRR:2511.2,2508.1] ssList(u) || equal(app(u,cons(v,sk1)),sk4)** -> .
% 3.65/3.84 3106[2:SpL:2631.0,2671.1] ssList(sk6) || equal(sk4,sk4)* -> .
% 3.65/3.84 3107[2:Obv:3106.1] ssList(sk6) || -> .
% 3.65/3.84 3108[2:SSi:3107.0,2560.0] || -> .
% 3.65/3.84 3109[1:Spt:3108.0,88.0,88.2] ssList(u) || -> duplicatefreeP(u)*.
% 3.65/3.84 3118[1:MRR:195.1,3109.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 3.65/3.84 10954[0:SpR:173.3,101.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 3.65/3.84 10999[0:Obv:10954.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 3.65/3.84 11000[0:SSi:10999.2,102.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 3.65/3.84 12570[1:EqR:3118.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 3.65/3.84 12607[1:SSi:12570.0,101.2,101.2,102.2,102.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 4.06/4.26 12608[1:MRR:11000.3,12607.1] ssList(u) ssItem(v) ssList(w) || -> .
% 4.06/4.26 12611[1:Con:12608.2] ssList(u) ssItem(v) || -> .
% 4.06/4.26 12613[1:MRR:356.1,12611.0] ssItem(u) || -> .
% 4.06/4.26 12615[1:UnC:12613.0,63.0] || -> .
% 4.06/4.26 % SZS output end Refutation
% 4.06/4.26 Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_11 co1_12 co1_13 co1_14 co1_15 clause13 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause85 clause86 clause97 clause98 clause120 clause123 clause157 clause170 clause177 clause179
% 4.06/4.26
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