TSTP Solution File: GRP135-1.002 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP135-1.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP135-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 20:51:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 461 clauses, backtracked 89 clauses, performed 9 splits and kept 339 clauses.
% 0.20/0.52 SPASS allocated 76100 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.52 0:00:00.03 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.10 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 13, length 96 :
% 0.20/0.52 % SZS output start Refutation
% 0.20/0.52 1[0:Inp] || -> group_element(e_1)*.
% 0.20/0.52 2[0:Inp] || -> group_element(e_2)*.
% 0.20/0.52 3[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.20/0.52 4[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.20/0.52 5[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_2) product(v,u,e_1)*.
% 0.20/0.52 6[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.20/0.52 7[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.20/0.52 8[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.20/0.52 9[0:Inp] || product(u,v,w)*+ product(v,x,u)* -> product(w,v,x)*.
% 0.20/0.52 12[0:Res:5.3,6.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_2)* equalish(w,e_1).
% 0.20/0.52 13[0:Res:5.3,7.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_2)* equalish(w,u)*.
% 0.20/0.52 15[0:Res:5.3,9.0] group_element(u) group_element(v) || product(u,w,v)*+ -> product(v,u,e_2)* product(e_1,u,w)*.
% 0.20/0.52 16[0:Res:5.3,12.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_2)* product(v,u,e_2)* equalish(e_1,e_1).
% 0.20/0.52 17[0:Obv:16.4] group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(e_1,e_1).
% 0.20/0.52 18[1:Spt:17.0,17.1,17.2] group_element(u) group_element(v) || -> product(v,u,e_2)*.
% 0.20/0.52 21[1:Res:18.2,7.0] group_element(u) group_element(v) || product(v,w,e_2)*+ -> equalish(w,u)*.
% 0.20/0.52 28[1:Res:18.2,21.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 0.20/0.52 29[1:Obv:28.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 0.20/0.52 30[1:Con:29.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.20/0.52 32[1:Res:30.2,3.0] group_element(e_1) group_element(e_2) || -> .
% 0.20/0.52 34[1:SSi:32.1,32.0,2.0,1.0] || -> .
% 0.20/0.52 35[1:Spt:34.0,17.3] || -> equalish(e_1,e_1)*.
% 0.20/0.52 46[0:Res:5.3,15.2] group_element(u) group_element(v) group_element(v) group_element(e_1) || -> product(v,u,e_2)* product(e_1,v,e_2)* product(e_1,v,u)*.
% 0.20/0.52 47[0:Obv:46.1] group_element(u) group_element(v) group_element(e_1) || -> product(v,u,e_2)* product(e_1,v,e_2)* product(e_1,v,u)*.
% 0.20/0.52 48[0:SSi:47.2,1.0] group_element(u) group_element(v) || -> product(v,u,e_2)* product(e_1,v,e_2)* product(e_1,v,u)*.
% 0.20/0.52 49[0:Fac:48.3,48.4] group_element(e_2) group_element(u) || -> product(u,e_2,e_2)* product(e_1,u,e_2)*.
% 0.20/0.52 55[0:Res:48.2,15.2] group_element(u) group_element(v) group_element(v) group_element(e_2) || -> product(e_1,v,e_2)* product(e_1,v,u)* product(e_2,v,e_2) product(e_1,v,u)*.
% 0.20/0.52 70[0:SSi:49.0,2.0] group_element(u) || -> product(u,e_2,e_2)* product(e_1,u,e_2)*.
% 0.20/0.52 80[0:Obv:55.5] group_element(u) group_element(v) group_element(e_2) || -> product(e_1,v,e_2)* product(e_2,v,e_2) product(e_1,v,u)*.
% 0.20/0.52 81[0:Con:80.0] group_element(u) group_element(e_2) || -> product(e_1,u,e_2)* product(e_2,u,e_2).
% 0.20/0.52 82[0:SSi:81.1,2.0] group_element(u) || -> product(e_1,u,e_2)* product(e_2,u,e_2).
% 0.20/0.52 86[0:Res:70.1,8.0] group_element(u) || product(v,e_2,e_2)* -> product(e_1,u,e_2)* equalish(v,u)*.
% 0.20/0.52 94[0:Res:70.2,15.2] group_element(u) group_element(e_1) group_element(e_2) || -> product(u,e_2,e_2)* product(e_2,e_1,e_2) product(e_1,e_1,u)*.
% 0.20/0.52 97[0:SSi:94.2,94.1,2.0,1.0] group_element(u) || -> product(u,e_2,e_2)* product(e_2,e_1,e_2) product(e_1,e_1,u)*.
% 0.20/0.52 136[2:Spt:97.0,97.1,97.3] group_element(u) || -> product(u,e_2,e_2)* product(e_1,e_1,u)*.
% 0.20/0.52 148[2:Res:136.2,13.2] group_element(e_1) group_element(u) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_1,u,e_2)* equalish(e_1,u).
% 0.20/0.52 153[2:Obv:148.0] group_element(u) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_1,u,e_2)* equalish(e_1,u).
% 0.20/0.52 154[2:SSi:153.1,1.0] group_element(u) || -> product(e_1,e_2,e_2)* product(e_1,u,e_2)* equalish(e_1,u).
% 0.20/0.52 155[2:MRR:154.1,86.1] group_element(u) || -> product(e_1,u,e_2)* equalish(e_1,u).
% 0.20/0.52 167[2:Res:155.1,15.2] group_element(u) group_element(e_1) group_element(e_2) || -> equalish(e_1,u) product(e_2,e_1,e_2) product(e_1,e_1,u)*.
% 0.20/0.52 169[2:SSi:167.2,167.1,2.0,1.0] group_element(u) || -> equalish(e_1,u) product(e_2,e_1,e_2) product(e_1,e_1,u)*.
% 0.20/0.52 217[3:Spt:169.0,169.1,169.3] group_element(u) || -> equalish(e_1,u) product(e_1,e_1,u)*.
% 0.20/0.52 222[3:Res:217.2,12.2] group_element(u) group_element(e_1) group_element(e_1) || -> equalish(e_1,u)* product(e_1,e_1,e_2)* equalish(u,e_1)*.
% 0.20/0.52 226[3:Obv:222.1] group_element(u) group_element(e_1) || -> equalish(e_1,u)* product(e_1,e_1,e_2)* equalish(u,e_1)*.
% 0.20/0.52 227[3:SSi:226.1,1.0] group_element(u) || -> equalish(e_1,u)* product(e_1,e_1,e_2)* equalish(u,e_1)*.
% 0.20/0.52 231[4:Spt:227.0,227.1,227.3] group_element(u) || -> equalish(e_1,u)* equalish(u,e_1)*.
% 0.20/0.52 233[4:Res:231.1,3.0] group_element(e_2) || -> equalish(e_2,e_1)*.
% 0.20/0.52 234[4:SSi:233.0,2.0] || -> equalish(e_2,e_1)*.
% 0.20/0.52 235[4:MRR:234.0,4.0] || -> .
% 0.20/0.52 236[4:Spt:235.0,227.2] || -> product(e_1,e_1,e_2)*.
% 0.20/0.52 238[4:Res:236.0,6.0] || product(e_1,e_1,u)*+ -> equalish(u,e_2).
% 0.20/0.52 239[4:Res:236.0,7.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 0.20/0.52 242[4:Res:236.0,15.2] group_element(e_1) group_element(e_2) || -> product(e_2,e_1,e_2) product(e_1,e_1,e_1)*.
% 0.20/0.52 244[4:SSi:242.1,242.0,2.0,1.0] || -> product(e_2,e_1,e_2) product(e_1,e_1,e_1)*.
% 0.20/0.52 263[5:Spt:244.0] || -> product(e_2,e_1,e_2)*.
% 0.20/0.52 266[5:Res:263.0,7.0] || product(e_2,u,e_2)* -> equalish(u,e_1).
% 0.20/0.52 361[4:Res:82.1,239.0] group_element(u) || -> product(e_2,u,e_2)* equalish(u,e_1).
% 0.20/0.52 374[5:MRR:361.1,266.0] group_element(u) || -> equalish(u,e_1)*.
% 0.20/0.52 377[5:Res:374.1,4.0] group_element(e_2) || -> .
% 0.20/0.52 378[5:SSi:377.0,2.0] || -> .
% 0.20/0.52 379[5:Spt:378.0,244.0,263.0] || product(e_2,e_1,e_2)* -> .
% 0.20/0.52 380[5:Spt:378.0,244.1] || -> product(e_1,e_1,e_1)*.
% 0.20/0.52 399[5:Res:380.0,238.0] || -> equalish(e_1,e_2)*.
% 0.20/0.52 400[5:MRR:399.0,3.0] || -> .
% 0.20/0.52 403[3:Spt:400.0,169.2] || -> product(e_2,e_1,e_2)*.
% 0.20/0.52 406[3:Res:403.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 0.20/0.52 407[3:Res:403.0,8.0] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 0.20/0.52 409[3:Res:403.0,15.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 410[3:Obv:409.0] group_element(e_2) || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 411[3:SSi:410.0,2.0] || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 419[3:Res:411.1,15.2] group_element(e_1) group_element(e_1) || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)* product(e_1,e_1,e_2)*.
% 0.20/0.52 423[3:Obv:419.3] group_element(e_1) || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.20/0.52 424[3:SSi:423.0,1.0] || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.20/0.52 425[4:Spt:424.0] || -> product(e_2,e_2,e_2)*.
% 0.20/0.52 470[4:Res:425.0,406.0] || -> equalish(e_2,e_1)*.
% 0.20/0.52 471[4:MRR:470.0,4.0] || -> .
% 0.20/0.52 479[4:Spt:471.0,424.0,425.0] || product(e_2,e_2,e_2)*+ -> .
% 0.20/0.52 480[4:Spt:471.0,424.1] || -> product(e_1,e_1,e_2)*.
% 0.20/0.52 534[4:Res:480.0,407.0] || -> equalish(e_1,e_2)*.
% 0.20/0.52 536[4:MRR:534.0,3.0] || -> .
% 0.20/0.52 543[2:Spt:536.0,97.2] || -> product(e_2,e_1,e_2)*.
% 0.20/0.52 548[2:Res:543.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 0.20/0.52 549[2:Res:543.0,8.0] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 0.20/0.52 551[2:Res:543.0,15.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 552[2:Obv:551.0] group_element(e_2) || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 553[2:SSi:552.0,2.0] || -> product(e_2,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.20/0.52 561[2:Res:553.1,15.2] group_element(e_1) group_element(e_1) || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)* product(e_1,e_1,e_2)*.
% 0.20/0.52 565[2:Obv:561.3] group_element(e_1) || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.20/0.52 566[2:SSi:565.0,1.0] || -> product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.20/0.52 567[3:Spt:566.0] || -> product(e_2,e_2,e_2)*.
% 0.20/0.52 633[3:Res:567.0,548.0] || -> equalish(e_2,e_1)*.
% 0.20/0.52 634[3:MRR:633.0,4.0] || -> .
% 0.20/0.52 642[3:Spt:634.0,566.0,567.0] || product(e_2,e_2,e_2)*+ -> .
% 0.20/0.52 643[3:Spt:634.0,566.1] || -> product(e_1,e_1,e_2)*.
% 0.20/0.52 708[3:Res:643.0,549.0] || -> equalish(e_1,e_2)*.
% 0.20/0.52 709[3:MRR:708.0,3.0] || -> .
% 0.20/0.52 % SZS output end Refutation
% 0.20/0.52 Formulae used in the proof : element_1 element_2 e_1_is_not_e_2 e_2_is_not_e_1 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation qg3
% 0.20/0.53
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