TSTP Solution File: GRP025-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:44:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 05:07:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 350 clauses, backtracked 194 clauses, performed 12 splits and kept 392 clauses.
% 0.19/0.48 SPASS allocated 63430 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 4, length 125 :
% 0.19/0.48 % SZS output start Refutation
% 0.19/0.48 5[0:Inp] || group_member(u,g1)* -> equal(u,b) equal(u,a).
% 0.19/0.48 6[0:Inp] || group_member(u,g2)* -> equal(u,d) equal(u,c).
% 0.19/0.48 8[0:Inp] || -> product(g1,a,b,b)*.
% 0.19/0.48 10[0:Inp] || -> product(g1,b,b,a)*.
% 0.19/0.48 14[0:Inp] || -> product(g2,d,d,c)*.
% 0.19/0.48 15[0:Inp] || -> equal(an_isomorphism(a),c)**.
% 0.19/0.48 16[0:Inp] || -> equal(an_isomorphism(b),d)**.
% 0.19/0.48 17[0:Inp] || -> group_member(d1,g1)*.
% 0.19/0.48 18[0:Inp] || -> group_member(d2,g1)*.
% 0.19/0.48 19[0:Inp] || -> group_member(d3,g1)*.
% 0.19/0.48 20[0:Inp] || -> product(g1,d1,d2,d3)*.
% 0.19/0.48 21[0:Inp] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3))* -> .
% 0.19/0.48 22[0:Inp] || -> group_member(identity_for(u),u)*.
% 0.19/0.48 23[0:Inp] || -> product(u,identity_for(u),v,v)*.
% 0.19/0.48 24[0:Inp] || -> product(u,v,identity_for(u),v)*.
% 0.19/0.48 30[0:Inp] || product(u,v,w,x)*+ product(u,v,w,y)* -> equal(x,y)*.
% 0.19/0.48 39[0:Res:22.0,6.0] || -> equal(identity_for(g2),d)** equal(identity_for(g2),c).
% 0.19/0.48 43[0:SpR:39.0,23.0] || -> equal(identity_for(g2),c) product(g2,d,u,u)*.
% 0.19/0.48 55[1:Spt:43.0] || -> equal(identity_for(g2),c)**.
% 0.19/0.48 57[1:SpR:55.0,23.0] || -> product(g2,c,u,u)*.
% 0.19/0.48 58[1:SpR:55.0,24.0] || -> product(g2,u,c,u)*.
% 0.19/0.48 62[0:Res:19.0,5.0] || -> equal(d3,b)** equal(d3,a).
% 0.19/0.48 63[0:Res:18.0,5.0] || -> equal(d2,b)** equal(d2,a).
% 0.19/0.48 64[0:Res:17.0,5.0] || -> equal(d1,b)** equal(d1,a).
% 0.19/0.48 67[0:Res:22.0,5.0] || -> equal(identity_for(g1),b)** equal(identity_for(g1),a).
% 0.19/0.48 69[2:Spt:62.0] || -> equal(d3,b)**.
% 0.19/0.48 71[2:Rew:69.0,20.0] || -> product(g1,d1,d2,b)*.
% 0.19/0.48 72[2:Rew:69.0,21.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b))* -> .
% 0.19/0.48 75[2:Rew:16.0,72.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),d)* -> .
% 0.19/0.48 79[3:Spt:63.0] || -> equal(d2,b)**.
% 0.19/0.48 81[3:Rew:79.0,71.0] || -> product(g1,d1,b,b)*.
% 0.19/0.48 82[3:Rew:79.0,75.0] || product(g2,an_isomorphism(d1),an_isomorphism(b),d)* -> .
% 0.19/0.48 85[3:Rew:16.0,82.0] || product(g2,an_isomorphism(d1),d,d)* -> .
% 0.19/0.48 89[4:Spt:64.0] || -> equal(d1,b)**.
% 0.19/0.48 91[4:Rew:89.0,81.0] || -> product(g1,b,b,b)*.
% 0.19/0.48 92[4:Rew:89.0,85.0] || product(g2,an_isomorphism(b),d,d)* -> .
% 0.19/0.48 95[4:Rew:16.0,92.0] || product(g2,d,d,d)* -> .
% 0.19/0.48 101[0:SpR:67.0,23.0] || -> equal(identity_for(g1),a) product(g1,b,u,u)*.
% 0.19/0.48 102[0:SpR:67.0,24.0] || -> equal(identity_for(g1),a) product(g1,u,b,u)*.
% 0.19/0.48 122[0:Res:10.0,30.0] || product(g1,b,b,u)* -> equal(a,u).
% 0.19/0.48 127[0:Res:14.0,30.0] || product(g2,d,d,u)* -> equal(c,u).
% 0.19/0.48 138[4:Res:91.0,122.0] || -> equal(b,a)**.
% 0.19/0.48 140[4:Rew:138.0,16.0] || -> equal(an_isomorphism(a),d)**.
% 0.19/0.48 151[4:Rew:15.0,140.0] || -> equal(d,c)**.
% 0.19/0.48 155[4:Rew:151.0,95.0] || product(g2,c,c,c)* -> .
% 0.19/0.48 161[4:MRR:155.0,58.0] || -> .
% 0.19/0.48 171[4:Spt:161.0,64.0,89.0] || equal(d1,b)** -> .
% 0.19/0.48 172[4:Spt:161.0,64.1] || -> equal(d1,a)**.
% 0.19/0.48 176[4:Rew:172.0,85.0] || product(g2,an_isomorphism(a),d,d)* -> .
% 0.19/0.48 177[4:Rew:15.0,176.0] || product(g2,c,d,d)* -> .
% 0.19/0.48 178[4:MRR:177.0,57.0] || -> .
% 0.19/0.48 183[3:Spt:178.0,63.0,79.0] || equal(d2,b)** -> .
% 0.19/0.48 184[3:Spt:178.0,63.1] || -> equal(d2,a)**.
% 0.19/0.48 186[3:Rew:184.0,183.0] || equal(b,a)** -> .
% 0.19/0.48 187[3:Rew:184.0,71.0] || -> product(g1,d1,a,b)*.
% 0.19/0.48 188[3:Rew:184.0,75.0] || product(g2,an_isomorphism(d1),an_isomorphism(a),d)* -> .
% 0.19/0.48 189[3:Rew:15.0,188.0] || product(g2,an_isomorphism(d1),c,d)* -> .
% 0.19/0.48 197[0:Res:8.0,30.0] || product(g1,a,b,u)* -> equal(b,u).
% 0.19/0.48 202[3:Res:187.0,30.0] || product(g1,d1,a,u)* -> equal(b,u).
% 0.19/0.48 203[4:Spt:64.0] || -> equal(d1,b)**.
% 0.19/0.48 206[4:Rew:203.0,189.0] || product(g2,an_isomorphism(b),c,d)* -> .
% 0.19/0.48 210[4:Rew:16.0,206.0] || product(g2,d,c,d)* -> .
% 0.19/0.48 211[4:MRR:210.0,58.0] || -> .
% 0.19/0.48 214[4:Spt:211.0,64.0,203.0] || equal(d1,b)** -> .
% 0.19/0.48 215[4:Spt:211.0,64.1] || -> equal(d1,a)**.
% 0.19/0.48 221[4:Rew:215.0,202.0] || product(g1,a,a,u)* -> equal(b,u).
% 0.19/0.48 228[5:Spt:67.0] || -> equal(identity_for(g1),b)**.
% 0.19/0.48 232[5:Rew:228.0,102.0] || -> equal(b,a) product(g1,u,b,u)*.
% 0.19/0.48 234[5:MRR:232.0,186.0] || -> product(g1,u,b,u)*.
% 0.19/0.48 245[0:Res:22.0,5.0] || -> equal(identity_for(g1),b)** equal(identity_for(g1),a).
% 0.19/0.48 259[5:Res:234.0,122.0] || -> equal(b,a)**.
% 0.19/0.48 261[5:MRR:259.0,186.0] || -> .
% 0.19/0.48 262[5:Spt:261.0,67.0,228.0] || equal(identity_for(g1),b)** -> .
% 0.19/0.48 263[5:Spt:261.0,67.1] || -> equal(identity_for(g1),a)**.
% 0.19/0.48 267[5:SpR:263.0,24.0] || -> product(g1,u,a,u)*.
% 0.19/0.48 311[5:Res:267.0,221.0] || -> equal(b,a)**.
% 0.19/0.48 314[5:MRR:311.0,186.0] || -> .
% 0.19/0.48 317[2:Spt:314.0,62.0,69.0] || equal(d3,b)** -> .
% 0.19/0.48 318[2:Spt:314.0,62.1] || -> equal(d3,a)**.
% 0.19/0.48 320[2:Rew:318.0,317.0] || equal(b,a)** -> .
% 0.19/0.48 321[2:Rew:318.0,20.0] || -> product(g1,d1,d2,a)*.
% 0.19/0.48 322[2:Rew:318.0,21.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))* -> .
% 0.19/0.48 323[2:Rew:15.0,322.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),c)* -> .
% 0.19/0.48 338[2:Res:321.0,30.0] || product(g1,d1,d2,u)* -> equal(a,u).
% 0.19/0.48 339[3:Spt:64.0] || -> equal(d1,b)**.
% 0.19/0.48 342[3:Rew:339.0,323.0] || product(g2,an_isomorphism(b),an_isomorphism(d2),c)* -> .
% 0.19/0.48 345[3:Rew:339.0,338.0] || product(g1,b,d2,u)* -> equal(a,u).
% 0.19/0.48 347[3:Rew:16.0,342.0] || product(g2,d,an_isomorphism(d2),c)* -> .
% 0.19/0.48 353[4:Spt:63.0] || -> equal(d2,b)**.
% 0.19/0.48 356[4:Rew:353.0,347.0] || product(g2,d,an_isomorphism(b),c)* -> .
% 0.19/0.48 361[4:Rew:16.0,356.0] || product(g2,d,d,c)* -> .
% 0.19/0.48 362[4:MRR:361.0,14.0] || -> .
% 0.19/0.48 366[4:Spt:362.0,63.0,353.0] || equal(d2,b)** -> .
% 0.19/0.48 367[4:Spt:362.0,63.1] || -> equal(d2,a)**.
% 0.19/0.48 373[4:Rew:367.0,345.0] || product(g1,b,a,u)* -> equal(a,u).
% 0.19/0.48 382[5:Spt:245.0] || -> equal(identity_for(g1),b)**.
% 0.19/0.48 385[5:Rew:382.0,101.0] || -> equal(b,a) product(g1,b,u,u)*.
% 0.19/0.48 387[5:MRR:385.0,320.0] || -> product(g1,b,u,u)*.
% 0.19/0.48 414[5:Res:387.0,122.0] || -> equal(b,a)**.
% 0.19/0.48 415[5:MRR:414.0,320.0] || -> .
% 0.19/0.48 416[5:Spt:415.0,245.0,382.0] || equal(identity_for(g1),b)** -> .
% 0.19/0.48 417[5:Spt:415.0,245.1] || -> equal(identity_for(g1),a)**.
% 0.19/0.48 421[5:SpR:417.0,24.0] || -> product(g1,u,a,u)*.
% 0.19/0.48 435[5:Res:421.0,373.0] || -> equal(b,a)**.
% 0.19/0.48 437[5:MRR:435.0,320.0] || -> .
% 0.19/0.48 439[3:Spt:437.0,64.0,339.0] || equal(d1,b)** -> .
% 0.19/0.48 440[3:Spt:437.0,64.1] || -> equal(d1,a)**.
% 0.19/0.48 443[3:Rew:440.0,321.0] || -> product(g1,a,d2,a)*.
% 0.19/0.48 444[3:Rew:440.0,323.0] || product(g2,an_isomorphism(a),an_isomorphism(d2),c)* -> .
% 0.19/0.48 445[3:Rew:15.0,444.0] || product(g2,c,an_isomorphism(d2),c)* -> .
% 0.19/0.48 466[4:Spt:63.0] || -> equal(d2,b)**.
% 0.19/0.48 468[4:Rew:466.0,443.0] || -> product(g1,a,b,a)*.
% 0.19/0.48 517[4:Res:468.0,197.0] || -> equal(b,a)**.
% 0.19/0.48 518[4:MRR:517.0,320.0] || -> .
% 0.19/0.48 519[4:Spt:518.0,63.0,466.0] || equal(d2,b)** -> .
% 0.19/0.48 520[4:Spt:518.0,63.1] || -> equal(d2,a)**.
% 0.19/0.48 524[4:Rew:520.0,445.0] || product(g2,c,an_isomorphism(a),c)* -> .
% 0.19/0.48 525[4:Rew:15.0,524.0] || product(g2,c,c,c)* -> .
% 0.19/0.48 526[4:MRR:525.0,58.0] || -> .
% 0.19/0.48 536[1:Spt:526.0,43.0,55.0] || equal(identity_for(g2),c)** -> .
% 0.19/0.48 537[1:Spt:526.0,43.1] || -> product(g2,d,u,u)*.
% 0.19/0.48 538[1:MRR:39.1,536.0] || -> equal(identity_for(g2),d)**.
% 0.19/0.48 539[1:Rew:538.0,536.0] || equal(d,c)** -> .
% 0.19/0.48 546[1:Res:537.0,127.0] || -> equal(d,c)**.
% 0.19/0.48 550[1:MRR:546.0,539.0] || -> .
% 0.19/0.48 % SZS output end Refutation
% 0.19/0.48 Formulae used in the proof : a_and_b_only_members_of_group1 c_and_d_only_members_of_group2 a_times_b_is_b b_times_b_is_a d_times_d_is_c a_maps_to_c b_maps_to_d d1_member_of_group1 d2_member_of_group1 d3_member_of_group1 d1_times_d2_is_d3 prove_product_holds_in_group2 identity_in_group left_identity right_identity total_function2
% 0.19/0.48
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