TSTP Solution File: GRP124-2.004 by SPASS---3.9
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% File : SPASS---3.9
% Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:45:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Tue Jun 14 06:01:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 295 clauses, backtracked 37 clauses, performed 5 splits and kept 217 clauses.
% 0.19/0.46 SPASS allocated 75902 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.01 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 9, length 70 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 2[0:Inp] || -> next(e_2,e_3)*.
% 0.19/0.46 9[0:Inp] || -> greater(e_4,e_3)*.
% 0.19/0.46 10[0:Inp] || greater(u,v)* next(w,v)* product(w,e_1,u)*+ -> .
% 0.19/0.46 11[0:Inp] || -> group_element(e_1)*.
% 0.19/0.46 12[0:Inp] || -> group_element(e_2)*.
% 0.19/0.46 13[0:Inp] || -> group_element(e_3)*.
% 0.19/0.46 15[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.19/0.46 16[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.19/0.46 18[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.19/0.46 19[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.19/0.46 21[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.19/0.46 22[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.19/0.46 26[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.19/0.46 27[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_4) product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 0.19/0.46 28[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.19/0.46 29[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.19/0.46 30[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.19/0.46 31[0:Inp] || -> product(u,u,u)*.
% 0.19/0.46 32[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(x,v)*.
% 0.19/0.46 51[0:Res:31.0,32.1] || product(u,v,v)*+ product(u,w,x)* product(w,x,v)* -> equalish(w,v).
% 0.19/0.46 71[0:Res:31.0,30.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.19/0.46 72[0:Res:31.0,29.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.19/0.46 76[0:Res:27.5,72.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.19/0.46 81[0:Res:27.5,71.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.19/0.46 82[0:SSi:81.0,11.0] group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.19/0.46 83[0:SSi:76.1,11.0] group_element(u) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.19/0.46 88[0:Res:82.3,72.0] group_element(e_2) || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.46 94[0:SSi:88.0,12.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.46 95[0:MRR:94.2,94.3,18.0,15.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 0.19/0.46 97[0:Res:95.1,28.0] || product(e_2,e_1,u)*+ -> product(e_2,e_1,e_4)* equalish(u,e_3).
% 0.19/0.46 106[1:Spt:97.1] || -> product(e_2,e_1,e_4)*.
% 0.19/0.46 107[1:Res:106.0,10.2] || greater(e_4,u)+ next(e_2,u)* -> .
% 0.19/0.46 112[1:Res:9.0,107.0] || next(e_2,e_3)* -> .
% 0.19/0.46 115[1:MRR:112.0,2.0] || -> .
% 0.19/0.46 116[1:Spt:115.0,97.1,106.0] || product(e_2,e_1,e_4)*+ -> .
% 0.19/0.46 117[1:Spt:115.0,97.0,97.2] || product(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.19/0.46 118[1:MRR:95.0,116.0] || -> product(e_2,e_1,e_3)*.
% 0.19/0.46 147[0:Res:83.3,71.0] group_element(e_2) || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.46 149[0:SSi:147.0,12.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.46 150[0:MRR:149.2,149.3,18.0,15.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)*.
% 0.19/0.46 153[0:Res:150.1,28.0] || product(e_1,e_2,u)*+ -> product(e_1,e_2,e_4)* equalish(u,e_3).
% 0.19/0.46 156[0:Res:31.0,51.0] || product(u,v,w)*+ product(v,w,u)* -> equalish(v,u).
% 0.19/0.46 160[2:Spt:153.0,153.2] || product(e_1,e_2,u)*+ -> equalish(u,e_3).
% 0.19/0.46 172[1:Res:118.0,156.0] || product(e_1,e_3,e_2)* -> equalish(e_1,e_2).
% 0.19/0.46 173[0:Res:150.1,156.0] || product(e_2,e_3,e_1) -> product(e_1,e_2,e_4)* equalish(e_2,e_1).
% 0.19/0.46 174[1:MRR:172.1,15.0] || product(e_1,e_3,e_2)*+ -> .
% 0.19/0.46 175[0:MRR:173.2,18.0] || product(e_2,e_3,e_1)+ -> product(e_1,e_2,e_4)*.
% 0.19/0.46 181[1:Res:83.3,174.0] group_element(e_3) || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 0.19/0.46 182[1:SSi:181.0,13.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 0.19/0.46 183[1:MRR:182.2,21.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)*.
% 0.19/0.46 192[1:Res:183.1,71.0] || -> product(e_1,e_3,e_4)* equalish(e_1,e_3).
% 0.19/0.46 194[1:MRR:192.1,16.0] || -> product(e_1,e_3,e_4)*.
% 0.19/0.46 199[1:Res:194.0,29.0] || product(e_1,u,e_4)*+ -> equalish(u,e_3).
% 0.19/0.46 200[1:Res:194.0,30.0] || product(u,e_3,e_4)*+ -> equalish(u,e_1).
% 0.19/0.46 221[0:Res:27.5,175.0] group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_2,e_4)*.
% 0.19/0.46 222[0:SSi:221.1,221.0,12.0,13.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_2,e_4)*.
% 0.19/0.46 293[3:Spt:222.3] || -> product(e_1,e_2,e_4)*.
% 0.19/0.46 306[3:Res:293.0,160.0] || -> equalish(e_4,e_3)*.
% 0.19/0.46 308[3:MRR:306.0,26.0] || -> .
% 0.19/0.46 311[3:Spt:308.0,222.3,293.0] || product(e_1,e_2,e_4)*+ -> .
% 0.19/0.46 312[3:Spt:308.0,222.0,222.1,222.2] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2)*.
% 0.19/0.46 320[3:Res:312.2,72.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3)* equalish(e_3,e_2).
% 0.19/0.46 332[3:MRR:320.2,22.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3)*.
% 0.19/0.46 361[3:Res:332.1,71.0] || -> product(e_2,e_3,e_4)* equalish(e_2,e_3).
% 0.19/0.46 365[3:MRR:361.1,19.0] || -> product(e_2,e_3,e_4)*.
% 0.19/0.46 377[3:Res:365.0,200.0] || -> equalish(e_2,e_1)*.
% 0.19/0.46 378[3:MRR:377.0,18.0] || -> .
% 0.19/0.46 382[2:Spt:378.0,153.1] || -> product(e_1,e_2,e_4)*.
% 0.19/0.46 394[2:Res:382.0,199.0] || -> equalish(e_2,e_3)*.
% 0.19/0.46 395[2:MRR:394.0,19.0] || -> .
% 0.19/0.46 % SZS output end Refutation
% 0.19/0.46 Formulae used in the proof : e_2_then_e_3 e_4_greater_e_3 no_redundancy element_1 element_2 element_3 e_1_is_not_e_2 e_1_is_not_e_3 e_2_is_not_e_1 e_2_is_not_e_3 e_3_is_not_e_1 e_3_is_not_e_2 e_4_is_not_e_3 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg2_1
% 0.19/0.46
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