TSTP Solution File: GRP253-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP253-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Sat Jul 16 11:46:32 EDT 2022
% Result : Unsatisfiable 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : GRP253-1 : TPTP v8.1.0. Released v2.5.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 02:56:21 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.23/0.46
% 0.23/0.46 SPASS V 3.9
% 0.23/0.46 SPASS beiseite: Proof found.
% 0.23/0.46 % SZS status Theorem
% 0.23/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.46 SPASS derived 451 clauses, backtracked 112 clauses, performed 7 splits and kept 270 clauses.
% 0.23/0.46 SPASS allocated 63409 KBytes.
% 0.23/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.23/0.46 0:00:00.04 for the input.
% 0.23/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.46 0:00:00.00 for inferences.
% 0.23/0.46 0:00:00.00 for the backtracking.
% 0.23/0.46 0:00:00.02 for the reduction.
% 0.23/0.46
% 0.23/0.46
% 0.23/0.46 Here is a proof with depth 5, length 143 :
% 0.23/0.46 % SZS output start Refutation
% 0.23/0.46 1[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.23/0.46 2[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.46 3[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.46 4[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.23/0.46 5[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.23/0.46 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.23/0.46 7[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.46 8[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.46 9[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.46 10[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.23/0.46 11[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.23/0.46 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.23/0.46 13[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.23/0.46 14[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c3),sk_c6)**.
% 0.23/0.46 15[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c3),sk_c6)**.
% 0.23/0.46 18[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.23/0.46 19[0:Inp] || equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(v,sk_c6),sk_c5)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(w,sk_c5),sk_c6)** equal(multiply(x,sk_c7),sk_c6)** equal(inverse(x),sk_c7) equal(inverse(sk_c5),sk_c6) -> .
% 0.23/0.46 20[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.23/0.46 21[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.23/0.46 22[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.23/0.46 23[0:Con:19.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.23/0.46 24[1:Spt:23.2,23.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.23/0.46 27[2:Spt:14.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.23/0.46 31[3:Spt:13.1] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.23/0.46 33[3:SpL:31.0,24.1] || equal(inverse(sk_c4),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.23/0.46 34[3:Obv:33.1] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.23/0.46 35[3:Rew:27.0,34.0] || equal(sk_c7,sk_c7)* -> .
% 0.23/0.46 36[3:Obv:35.0] || -> .
% 0.23/0.46 37[3:Spt:36.0,13.1,31.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.23/0.46 38[3:Spt:36.0,13.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.23/0.46 40[3:MRR:4.1,37.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.23/0.46 43[3:MRR:1.0,37.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.46 50[3:SpL:43.0,24.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.23/0.46 51[3:Obv:50.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.23/0.46 52[3:Rew:40.0,51.0] || equal(sk_c7,sk_c7)* -> .
% 0.23/0.46 53[3:Obv:52.0] || -> .
% 0.23/0.46 54[2:Spt:53.0,14.0,27.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.23/0.46 55[2:Spt:53.0,14.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.23/0.46 57[2:MRR:5.0,54.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.23/0.46 60[2:MRR:2.0,54.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.46 67[2:SpL:60.0,24.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.23/0.46 68[2:Obv:67.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.23/0.46 69[2:Rew:57.0,68.0] || equal(sk_c7,sk_c7)* -> .
% 0.23/0.46 70[2:Obv:69.0] || -> .
% 0.23/0.46 71[1:Spt:70.0,23.0,23.1,23.3,23.4,23.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(sk_c5),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.23/0.46 72[1:SpL:20.0,71.3] || equal(inverse(identity),sk_c6) equal(inverse(u),sk_c6) equal(inverse(sk_c5),sk_c6) equal(sk_c6,sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.23/0.46 73[2:Spt:15.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.23/0.46 75[2:Rew:73.0,72.2] || equal(inverse(identity),sk_c6) equal(inverse(u),sk_c6) equal(sk_c6,sk_c6) equal(sk_c6,sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.23/0.46 76[2:Obv:75.2] || equal(inverse(identity),sk_c6) equal(inverse(u),sk_c6) equal(sk_c6,sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.23/0.46 79[3:Spt:11.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.23/0.46 81[4:Spt:10.1] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.23/0.46 84[2:SpR:73.0,21.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.23/0.46 85[3:SpR:79.0,21.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.23/0.46 90[0:SpR:21.0,22.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.23/0.46 94[0:Rew:20.0,90.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.23/0.46 96[3:SpR:85.0,22.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.23/0.46 98[3:Rew:20.0,96.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.23/0.46 104[4:SpR:81.0,98.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.23/0.46 109[0:SpR:94.0,94.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.23/0.46 112[0:SpR:21.0,94.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.23/0.46 118[3:SpR:98.0,94.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c4,u))**.
% 0.23/0.46 119[4:SpR:104.0,94.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.23/0.46 123[4:Rew:21.0,119.0] || -> equal(sk_c6,identity)**.
% 0.23/0.46 124[4:Rew:123.0,73.0] || -> equal(inverse(sk_c5),identity)**.
% 0.23/0.46 126[4:Rew:123.0,84.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.23/0.46 129[4:Rew:123.0,76.0] || equal(inverse(identity),identity) equal(inverse(u),sk_c6) equal(sk_c6,sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.23/0.46 134[4:Rew:20.0,126.0] || -> equal(identity,sk_c5)**.
% 0.23/0.46 140[4:Rew:134.0,123.0] || -> equal(sk_c6,sk_c5)**.
% 0.23/0.46 141[4:Rew:134.0,124.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.23/0.46 146[4:Rew:134.0,112.0] || -> equal(multiply(inverse(inverse(u)),sk_c5),u)**.
% 0.23/0.46 151[4:Rew:109.0,146.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.23/0.46 155[4:Rew:151.0,129.3,140.0,129.3,140.0,129.2,140.0,129.1,141.0,129.0,134.0,129.0] || equal(sk_c5,sk_c5) equal(inverse(u),sk_c5)** equal(sk_c5,sk_c5) equal(u,sk_c5) -> .
% 0.23/0.46 156[4:Obv:155.2] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.23/0.46 254[4:SpL:141.0,156.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.23/0.46 257[4:Obv:254.1] || -> .
% 0.23/0.46 258[4:Spt:257.0,10.1,81.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.23/0.46 259[4:Spt:257.0,10.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.23/0.46 262[4:MRR:4.1,258.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.23/0.46 264[0:Rew:109.0,112.0] || -> equal(multiply(u,identity),u)**.
% 0.23/0.46 266[4:MRR:7.0,258.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.46 267[4:MRR:1.0,258.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.46 291[4:SpR:266.0,94.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.23/0.46 293[4:Rew:84.0,291.0,259.0,291.0] || -> equal(sk_c6,identity)**.
% 0.23/0.46 297[4:Rew:293.0,84.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.23/0.46 300[4:Rew:293.0,258.0] || equal(multiply(sk_c4,sk_c7),identity)** -> .
% 0.23/0.46 303[4:Rew:293.0,267.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.23/0.46 310[4:Rew:20.0,297.0] || -> equal(identity,sk_c5)**.
% 0.23/0.46 313[4:Rew:310.0,21.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.23/0.46 315[4:Rew:310.0,264.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.23/0.46 322[4:Rew:310.0,303.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.23/0.46 328[4:Rew:310.0,300.0] || equal(multiply(sk_c4,sk_c7),sk_c5)** -> .
% 0.23/0.46 374[4:SpR:262.0,313.0] || -> equal(multiply(sk_c7,sk_c1),sk_c5)**.
% 0.23/0.46 380[4:SpR:374.0,94.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c1)**.
% 0.23/0.46 382[4:Rew:315.0,380.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.23/0.46 383[4:Rew:382.0,118.0] || -> equal(multiply(sk_c4,u),multiply(sk_c1,u))**.
% 0.23/0.46 384[4:Rew:383.0,328.0] || equal(multiply(sk_c1,sk_c7),sk_c5)** -> .
% 0.23/0.46 386[4:Rew:322.0,384.0] || equal(sk_c5,sk_c5)* -> .
% 0.23/0.46 387[4:Obv:386.0] || -> .
% 0.23/0.46 389[3:Spt:387.0,11.0,79.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.23/0.46 390[3:Spt:387.0,11.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.23/0.46 394[3:MRR:8.0,389.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.46 414[3:SpR:394.0,94.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.23/0.46 416[3:Rew:84.0,414.0,390.0,414.0] || -> equal(sk_c6,identity)**.
% 0.23/0.47 418[3:Rew:416.0,73.0] || -> equal(inverse(sk_c5),identity)**.
% 0.23/0.47 420[3:Rew:416.0,84.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.23/0.47 426[3:Rew:416.0,76.0] || equal(inverse(identity),identity) equal(inverse(u),sk_c6) equal(sk_c6,sk_c5) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.23/0.47 432[3:Rew:20.0,420.0] || -> equal(identity,sk_c5)**.
% 0.23/0.47 433[3:Rew:432.0,264.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.23/0.47 437[3:Rew:432.0,416.0] || -> equal(sk_c6,sk_c5)**.
% 0.23/0.47 439[3:Rew:432.0,418.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.23/0.47 456[3:Rew:433.0,426.3,437.0,426.3,437.0,426.2,437.0,426.1,439.0,426.0,432.0,426.0] || equal(sk_c5,sk_c5) equal(inverse(u),sk_c5)** equal(sk_c5,sk_c5) equal(u,sk_c5) -> .
% 0.23/0.47 457[3:Obv:456.2] || equal(inverse(u),sk_c5)** equal(u,sk_c5) -> .
% 0.23/0.47 561[3:SpL:439.0,457.0] || equal(sk_c5,sk_c5)* equal(sk_c5,sk_c5)* -> .
% 0.23/0.47 564[3:Obv:561.1] || -> .
% 0.23/0.47 565[2:Spt:564.0,15.0,73.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.23/0.47 566[2:Spt:564.0,15.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.23/0.47 567[2:MRR:12.0,565.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.23/0.47 568[2:MRR:6.0,565.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.23/0.47 569[2:MRR:18.0,565.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.23/0.47 570[2:MRR:9.0,565.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.23/0.47 571[2:MRR:3.0,565.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.23/0.47 579[2:SpR:569.0,94.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c5)**.
% 0.23/0.47 581[2:Rew:566.0,579.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.23/0.47 583[2:SpR:570.0,94.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.23/0.47 585[2:Rew:567.0,583.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.23/0.47 587[2:SpR:571.0,94.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.23/0.47 589[2:Rew:568.0,587.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.23/0.47 591[2:SpR:581.0,94.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.23/0.47 597[2:SpR:585.0,94.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.23/0.47 599[2:Rew:21.0,597.0] || -> equal(identity,sk_c5)**.
% 0.23/0.47 601[2:Rew:599.0,264.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.23/0.47 602[2:Rew:599.0,21.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.23/0.47 607[2:Rew:601.0,569.0] || -> equal(sk_c6,sk_c3)**.
% 0.23/0.47 608[2:Rew:601.0,591.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.23/0.47 611[2:Rew:607.0,565.0] || equal(inverse(sk_c5),sk_c3)** -> .
% 0.23/0.47 618[2:Rew:607.0,589.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.23/0.47 619[2:Rew:607.0,608.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.23/0.47 648[2:SpR:618.0,94.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.23/0.47 650[2:Rew:602.0,648.0] || -> equal(sk_c3,sk_c5)**.
% 0.23/0.47 652[2:Rew:650.0,619.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.23/0.47 654[2:Rew:650.0,611.0] || equal(inverse(sk_c5),sk_c5)** -> .
% 0.23/0.47 664[2:Rew:652.0,654.0] || equal(sk_c5,sk_c5)* -> .
% 0.23/0.47 665[2:Obv:664.0] || -> .
% 0.23/0.47 % SZS output end Refutation
% 0.23/0.47 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_18 prove_this_19 left_identity left_inverse associativity
% 0.23/0.47
%------------------------------------------------------------------------------