TSTP Solution File: GRP026-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP026-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:44:50 EDT 2022
% Result : Unsatisfiable 0.40s 0.61s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP026-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 18:06:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.40/0.61
% 0.40/0.61 SPASS V 3.9
% 0.40/0.61 SPASS beiseite: Proof found.
% 0.40/0.61 % SZS status Theorem
% 0.40/0.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.61 SPASS derived 1351 clauses, backtracked 720 clauses, performed 27 splits and kept 1311 clauses.
% 0.40/0.61 SPASS allocated 64092 KBytes.
% 0.40/0.61 SPASS spent 0:00:00.26 on the problem.
% 0.40/0.61 0:00:00.03 for the input.
% 0.40/0.61 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.61 0:00:00.01 for inferences.
% 0.40/0.61 0:00:00.00 for the backtracking.
% 0.40/0.61 0:00:00.18 for the reduction.
% 0.40/0.61
% 0.40/0.61
% 0.40/0.61 Here is a proof with depth 3, length 290 :
% 0.40/0.61 % SZS output start Refutation
% 0.40/0.61 1[0:Inp] || -> group_member(a,g1)*.
% 0.40/0.61 2[0:Inp] || -> group_member(b,g1)*.
% 0.40/0.61 3[0:Inp] || -> group_member(c,g1)*.
% 0.40/0.61 7[0:Inp] || group_member(u,g1)* -> equal(u,c) equal(u,b) equal(u,a).
% 0.40/0.61 9[0:Inp] || -> product(g1,a,a,a)*.
% 0.40/0.61 10[0:Inp] || -> product(g1,a,b,b)*.
% 0.40/0.61 11[0:Inp] || -> product(g1,b,a,b)*.
% 0.40/0.61 12[0:Inp] || -> product(g1,a,c,c)*.
% 0.40/0.61 13[0:Inp] || -> product(g1,c,a,c)*.
% 0.40/0.61 14[0:Inp] || -> product(g1,b,b,c)*.
% 0.40/0.61 15[0:Inp] || -> product(g1,b,c,a)*.
% 0.40/0.61 16[0:Inp] || -> product(g1,c,b,a)*.
% 0.40/0.61 17[0:Inp] || -> product(g1,c,c,b)*.
% 0.40/0.61 18[0:Inp] || -> product(g2,f,f,f)*.
% 0.40/0.61 19[0:Inp] || -> product(g2,f,g,g)*.
% 0.40/0.61 20[0:Inp] || -> product(g2,g,f,g)*.
% 0.40/0.61 21[0:Inp] || -> product(g2,f,h,h)*.
% 0.40/0.61 22[0:Inp] || -> product(g2,h,f,h)*.
% 0.40/0.61 23[0:Inp] || -> product(g2,g,g,h)*.
% 0.40/0.61 24[0:Inp] || -> product(g2,g,h,f)*.
% 0.40/0.61 25[0:Inp] || -> product(g2,h,g,f)*.
% 0.40/0.61 26[0:Inp] || -> product(g2,h,h,g)*.
% 0.40/0.61 27[0:Inp] || -> equal(an_isomorphism(a),f)**.
% 0.40/0.61 28[0:Inp] || -> equal(an_isomorphism(b),g)**.
% 0.40/0.61 29[0:Inp] || -> equal(an_isomorphism(c),h)**.
% 0.40/0.61 30[0:Inp] || -> group_member(d1,g1)*.
% 0.40/0.61 31[0:Inp] || -> group_member(d2,g1)*.
% 0.40/0.61 32[0:Inp] || -> group_member(d3,g1)*.
% 0.40/0.61 33[0:Inp] || -> product(g1,d1,d2,d3)*.
% 0.40/0.61 34[0:Inp] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3))* -> .
% 0.40/0.61 41[0:Inp] || group_member(u,v) group_member(w,v) -> product(v,w,u,multiply(v,w,u))*.
% 0.40/0.61 43[0:Inp] || product(u,v,w,x)*+ product(u,v,w,y)* -> equal(x,y)*.
% 0.40/0.61 56[0:Res:32.0,7.0] || -> equal(d3,c)** equal(d3,b) equal(d3,a).
% 0.40/0.61 57[0:Res:31.0,7.0] || -> equal(d2,c)** equal(d2,b) equal(d2,a).
% 0.40/0.61 58[0:Res:30.0,7.0] || -> equal(d1,c)** equal(d1,b) equal(d1,a).
% 0.40/0.61 64[1:Spt:56.0] || -> equal(d3,c)**.
% 0.40/0.61 66[1:Rew:64.0,33.0] || -> product(g1,d1,d2,c)*.
% 0.40/0.61 67[1:Rew:64.0,34.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(c))* -> .
% 0.40/0.61 70[1:Rew:29.0,67.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),h)* -> .
% 0.40/0.61 74[2:Spt:57.0] || -> equal(d2,c)**.
% 0.40/0.61 76[2:Rew:74.0,66.0] || -> product(g1,d1,c,c)*.
% 0.40/0.61 77[2:Rew:74.0,70.0] || product(g2,an_isomorphism(d1),an_isomorphism(c),h)* -> .
% 0.40/0.61 80[2:Rew:29.0,77.0] || product(g2,an_isomorphism(d1),h,h)* -> .
% 0.40/0.61 84[3:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 86[3:Rew:84.0,76.0] || -> product(g1,c,c,c)*.
% 0.40/0.61 87[3:Rew:84.0,80.0] || product(g2,an_isomorphism(c),h,h)* -> .
% 0.40/0.61 90[3:Rew:29.0,87.0] || product(g2,h,h,h)* -> .
% 0.40/0.61 119[0:Res:16.0,43.0] || product(g1,c,b,u)* -> equal(a,u).
% 0.40/0.61 120[0:Res:15.0,43.0] || product(g1,b,c,u)* -> equal(a,u).
% 0.40/0.61 121[0:Res:9.0,43.0] || product(g1,a,a,u)* -> equal(a,u).
% 0.40/0.61 122[0:Res:17.0,43.0] || product(g1,c,c,u)* -> equal(b,u).
% 0.40/0.61 123[0:Res:11.0,43.0] || product(g1,b,a,u)* -> equal(b,u).
% 0.40/0.61 124[0:Res:10.0,43.0] || product(g1,a,b,u)* -> equal(b,u).
% 0.40/0.61 125[0:Res:14.0,43.0] || product(g1,b,b,u)* -> equal(c,u).
% 0.40/0.61 126[0:Res:13.0,43.0] || product(g1,c,a,u)* -> equal(c,u).
% 0.40/0.61 127[0:Res:12.0,43.0] || product(g1,a,c,u)* -> equal(c,u).
% 0.40/0.61 147[0:Res:41.2,119.0] || group_member(b,g1) group_member(c,g1) -> equal(multiply(g1,c,b),a)**.
% 0.40/0.61 149[0:MRR:147.0,147.1,2.0,3.0] || -> equal(multiply(g1,c,b),a)**.
% 0.40/0.61 196[3:Res:86.0,122.0] || -> equal(c,b)**.
% 0.40/0.61 197[0:Res:41.2,122.0] || group_member(c,g1) group_member(c,g1) -> equal(multiply(g1,c,c),b)**.
% 0.40/0.61 199[3:Rew:196.0,29.0] || -> equal(an_isomorphism(b),h)**.
% 0.40/0.61 213[3:Rew:196.0,149.0] || -> equal(multiply(g1,b,b),a)**.
% 0.40/0.61 236[3:Rew:28.0,199.0] || -> equal(h,g)**.
% 0.40/0.61 240[3:Rew:236.0,26.0] || -> product(g2,g,g,g)*.
% 0.40/0.61 245[3:Rew:236.0,90.0] || product(g2,g,g,g)* -> .
% 0.40/0.61 272[0:Obv:197.0] || group_member(c,g1) -> equal(multiply(g1,c,c),b)**.
% 0.40/0.61 273[3:Rew:213.0,272.1,196.0,272.1,196.0,272.0] || group_member(b,g1)* -> equal(b,a).
% 0.40/0.61 274[3:MRR:273.0,2.0] || -> equal(b,a)**.
% 0.40/0.61 276[3:Rew:274.0,28.0] || -> equal(an_isomorphism(a),g)**.
% 0.40/0.61 294[3:Rew:27.0,276.0] || -> equal(g,f)**.
% 0.40/0.61 361[3:Rew:294.0,240.0] || -> product(g2,f,f,f)*.
% 0.40/0.61 364[3:Rew:294.0,245.0] || product(g2,f,f,f)* -> .
% 0.40/0.61 365[3:MRR:364.0,361.0] || -> .
% 0.40/0.61 391[3:Spt:365.0,58.0,84.0] || equal(d1,c)** -> .
% 0.40/0.61 392[3:Spt:365.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 395[4:Spt:392.0] || -> equal(d1,b)**.
% 0.40/0.61 398[4:Rew:395.0,76.0] || -> product(g1,b,c,c)*.
% 0.40/0.61 399[4:Rew:395.0,80.0] || product(g2,an_isomorphism(b),h,h)* -> .
% 0.40/0.61 402[4:Rew:28.0,399.0] || product(g2,g,h,h)* -> .
% 0.40/0.61 467[4:Res:398.0,120.0] || -> equal(c,a)**.
% 0.40/0.61 472[4:Rew:467.0,29.0] || -> equal(an_isomorphism(a),h)**.
% 0.40/0.61 507[4:Rew:27.0,472.0] || -> equal(h,f)**.
% 0.40/0.61 513[4:Rew:507.0,24.0] || -> product(g2,g,f,f)*.
% 0.40/0.61 515[4:Rew:507.0,402.0] || product(g2,g,f,f)* -> .
% 0.40/0.61 542[4:MRR:515.0,513.0] || -> .
% 0.40/0.61 569[4:Spt:542.0,392.0,395.0] || equal(d1,b)** -> .
% 0.40/0.61 570[4:Spt:542.0,392.1] || -> equal(d1,a)**.
% 0.40/0.61 575[4:Rew:570.0,80.0] || product(g2,an_isomorphism(a),h,h)* -> .
% 0.40/0.61 576[4:Rew:27.0,575.0] || product(g2,f,h,h)* -> .
% 0.40/0.61 577[4:MRR:576.0,21.0] || -> .
% 0.40/0.61 583[2:Spt:577.0,57.0,74.0] || equal(d2,c)** -> .
% 0.40/0.61 584[2:Spt:577.0,57.1,57.2] || -> equal(d2,b)** equal(d2,a).
% 0.40/0.61 585[3:Spt:584.0] || -> equal(d2,b)**.
% 0.40/0.61 587[3:Rew:585.0,583.0] || equal(c,b)** -> .
% 0.40/0.61 588[3:Rew:585.0,66.0] || -> product(g1,d1,b,c)*.
% 0.40/0.61 589[3:Rew:585.0,70.0] || product(g2,an_isomorphism(d1),an_isomorphism(b),h)* -> .
% 0.40/0.61 592[3:Rew:28.0,589.0] || product(g2,an_isomorphism(d1),g,h)* -> .
% 0.40/0.61 642[4:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 644[4:Rew:642.0,588.0] || -> product(g1,c,b,c)*.
% 0.40/0.61 669[0:Res:41.2,124.0] || group_member(b,g1) group_member(a,g1) -> equal(multiply(g1,a,b),b)**.
% 0.40/0.61 670[0:MRR:669.0,669.1,2.0,1.0] || -> equal(multiply(g1,a,b),b)**.
% 0.40/0.61 733[0:Res:41.2,126.0] || group_member(a,g1) group_member(c,g1) -> equal(multiply(g1,c,a),c)**.
% 0.40/0.61 734[0:MRR:733.0,733.1,1.0,3.0] || -> equal(multiply(g1,c,a),c)**.
% 0.40/0.61 739[0:Res:41.2,127.0] || group_member(c,g1) group_member(a,g1) -> equal(multiply(g1,a,c),c)**.
% 0.40/0.61 740[0:MRR:739.0,739.1,3.0,1.0] || -> equal(multiply(g1,a,c),c)**.
% 0.40/0.61 745[4:Res:644.0,119.0] || -> equal(c,a)**.
% 0.40/0.61 746[0:Res:41.2,119.0] || group_member(b,g1) group_member(c,g1) -> equal(multiply(g1,c,b),a)**.
% 0.40/0.61 750[4:Rew:745.0,587.0] || equal(b,a)** -> .
% 0.40/0.61 852[4:Rew:745.0,746.2,745.0,746.1] || group_member(b,g1) group_member(a,g1) -> equal(multiply(g1,a,b),a)**.
% 0.40/0.61 853[4:Rew:670.0,852.2] || group_member(b,g1)* group_member(a,g1) -> equal(b,a).
% 0.40/0.61 854[4:MRR:853.0,853.1,2.0,1.0] || -> equal(b,a)**.
% 0.40/0.61 855[4:MRR:854.0,750.0] || -> .
% 0.40/0.61 878[4:Spt:855.0,58.0,642.0] || equal(d1,c)** -> .
% 0.40/0.61 879[4:Spt:855.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 880[5:Spt:879.0] || -> equal(d1,b)**.
% 0.40/0.61 884[5:Rew:880.0,592.0] || product(g2,an_isomorphism(b),g,h)* -> .
% 0.40/0.61 889[5:Rew:28.0,884.0] || product(g2,g,g,h)* -> .
% 0.40/0.61 890[5:MRR:889.0,23.0] || -> .
% 0.40/0.61 895[5:Spt:890.0,879.0,880.0] || equal(d1,b)** -> .
% 0.40/0.61 896[5:Spt:890.0,879.1] || -> equal(d1,a)**.
% 0.40/0.61 900[5:Rew:896.0,588.0] || -> product(g1,a,b,c)*.
% 0.40/0.61 948[5:Res:900.0,124.0] || -> equal(c,b)**.
% 0.40/0.61 952[5:MRR:948.0,587.0] || -> .
% 0.40/0.61 953[3:Spt:952.0,584.0,585.0] || equal(d2,b)** -> .
% 0.40/0.61 954[3:Spt:952.0,584.1] || -> equal(d2,a)**.
% 0.40/0.61 956[3:Rew:954.0,583.0] || equal(c,a)** -> .
% 0.40/0.61 958[3:Rew:954.0,66.0] || -> product(g1,d1,a,c)*.
% 0.40/0.61 959[3:Rew:954.0,70.0] || product(g2,an_isomorphism(d1),an_isomorphism(a),h)* -> .
% 0.40/0.61 960[3:Rew:27.0,959.0] || product(g2,an_isomorphism(d1),f,h)* -> .
% 0.40/0.61 998[4:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 1001[4:Rew:998.0,960.0] || product(g2,an_isomorphism(c),f,h)* -> .
% 0.40/0.61 1007[4:Rew:29.0,1001.0] || product(g2,h,f,h)* -> .
% 0.40/0.61 1008[4:MRR:1007.0,22.0] || -> .
% 0.40/0.61 1013[4:Spt:1008.0,58.0,998.0] || equal(d1,c)** -> .
% 0.40/0.61 1014[4:Spt:1008.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 1015[5:Spt:1014.0] || -> equal(d1,b)**.
% 0.40/0.61 1017[5:Rew:1015.0,1013.0] || equal(c,b)** -> .
% 0.40/0.61 1018[5:Rew:1015.0,958.0] || -> product(g1,b,a,c)*.
% 0.40/0.61 1029[5:Res:1018.0,123.0] || -> equal(c,b)**.
% 0.40/0.61 1033[5:MRR:1029.0,1017.0] || -> .
% 0.40/0.61 1034[5:Spt:1033.0,1014.0,1015.0] || equal(d1,b)** -> .
% 0.40/0.61 1035[5:Spt:1033.0,1014.1] || -> equal(d1,a)**.
% 0.40/0.61 1039[5:Rew:1035.0,958.0] || -> product(g1,a,a,c)*.
% 0.40/0.61 1050[5:Res:1039.0,121.0] || -> equal(c,a)**.
% 0.40/0.61 1054[5:MRR:1050.0,956.0] || -> .
% 0.40/0.61 1055[1:Spt:1054.0,56.0,64.0] || equal(d3,c)** -> .
% 0.40/0.61 1056[1:Spt:1054.0,56.1,56.2] || -> equal(d3,b)** equal(d3,a).
% 0.40/0.61 1057[2:Spt:1056.0] || -> equal(d3,b)**.
% 0.40/0.61 1059[2:Rew:1057.0,1055.0] || equal(c,b)** -> .
% 0.40/0.61 1060[2:Rew:1057.0,33.0] || -> product(g1,d1,d2,b)*.
% 0.40/0.61 1061[2:Rew:1057.0,34.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b))* -> .
% 0.40/0.61 1064[2:Rew:28.0,1061.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),g)* -> .
% 0.40/0.61 1073[3:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 1075[3:Rew:1073.0,1060.0] || -> product(g1,c,d2,b)*.
% 0.40/0.61 1076[3:Rew:1073.0,1064.0] || product(g2,an_isomorphism(c),an_isomorphism(d2),g)* -> .
% 0.40/0.61 1082[3:Rew:29.0,1076.0] || product(g2,h,an_isomorphism(d2),g)* -> .
% 0.40/0.61 1089[4:Spt:57.0] || -> equal(d2,c)**.
% 0.40/0.61 1092[4:Rew:1089.0,1082.0] || product(g2,h,an_isomorphism(c),g)* -> .
% 0.40/0.61 1098[4:Rew:29.0,1092.0] || product(g2,h,h,g)* -> .
% 0.40/0.61 1099[4:MRR:1098.0,26.0] || -> .
% 0.40/0.61 1104[4:Spt:1099.0,57.0,1089.0] || equal(d2,c)** -> .
% 0.40/0.61 1105[4:Spt:1099.0,57.1,57.2] || -> equal(d2,b)** equal(d2,a).
% 0.40/0.61 1106[5:Spt:1105.0] || -> equal(d2,b)**.
% 0.40/0.61 1109[5:Rew:1106.0,1075.0] || -> product(g1,c,b,b)*.
% 0.40/0.61 1124[5:Res:1109.0,119.0] || -> equal(b,a)**.
% 0.40/0.61 1125[0:Res:41.2,119.0] || group_member(b,g1) group_member(c,g1) -> equal(multiply(g1,c,b),a)**.
% 0.40/0.61 1144[5:Rew:1124.0,1059.0] || equal(c,a)** -> .
% 0.40/0.61 1239[5:Rew:1124.0,1125.2,1124.0,1125.0] || group_member(a,g1) group_member(c,g1) -> equal(multiply(g1,c,a),a)**.
% 0.40/0.61 1240[5:Rew:734.0,1239.2] || group_member(a,g1) group_member(c,g1)* -> equal(c,a).
% 0.40/0.61 1241[5:MRR:1240.0,1240.1,1.0,3.0] || -> equal(c,a)**.
% 0.40/0.61 1242[5:MRR:1241.0,1144.0] || -> .
% 0.40/0.61 1269[5:Spt:1242.0,1105.0,1106.0] || equal(d2,b)** -> .
% 0.40/0.61 1270[5:Spt:1242.0,1105.1] || -> equal(d2,a)**.
% 0.40/0.61 1274[5:Rew:1270.0,1075.0] || -> product(g1,c,a,b)*.
% 0.40/0.61 1361[5:Res:1274.0,126.0] || -> equal(c,b)**.
% 0.40/0.61 1363[5:MRR:1361.0,1059.0] || -> .
% 0.40/0.61 1364[3:Spt:1363.0,58.0,1073.0] || equal(d1,c)** -> .
% 0.40/0.61 1365[3:Spt:1363.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 1366[4:Spt:1365.0] || -> equal(d1,b)**.
% 0.40/0.61 1369[4:Rew:1366.0,1060.0] || -> product(g1,b,d2,b)*.
% 0.40/0.61 1370[4:Rew:1366.0,1064.0] || product(g2,an_isomorphism(b),an_isomorphism(d2),g)* -> .
% 0.40/0.61 1376[4:Rew:28.0,1370.0] || product(g2,g,an_isomorphism(d2),g)* -> .
% 0.40/0.61 1384[5:Spt:57.0] || -> equal(d2,c)**.
% 0.40/0.61 1386[5:Rew:1384.0,1369.0] || -> product(g1,b,c,b)*.
% 0.40/0.61 1426[5:Res:1386.0,120.0] || -> equal(b,a)**.
% 0.40/0.61 1428[0:Res:41.2,120.0] || group_member(c,g1) group_member(b,g1) -> equal(multiply(g1,b,c),a)**.
% 0.40/0.61 1431[5:Rew:1426.0,1059.0] || equal(c,a)** -> .
% 0.40/0.61 1542[5:Rew:1426.0,1428.2,1426.0,1428.1] || group_member(c,g1) group_member(a,g1) -> equal(multiply(g1,a,c),a)**.
% 0.40/0.61 1543[5:Rew:740.0,1542.2] || group_member(c,g1)* group_member(a,g1) -> equal(c,a).
% 0.40/0.61 1544[5:MRR:1543.0,1543.1,3.0,1.0] || -> equal(c,a)**.
% 0.40/0.61 1545[5:MRR:1544.0,1431.0] || -> .
% 0.40/0.61 1572[5:Spt:1545.0,57.0,1384.0] || equal(d2,c)** -> .
% 0.40/0.61 1573[5:Spt:1545.0,57.1,57.2] || -> equal(d2,b)** equal(d2,a).
% 0.40/0.61 1574[6:Spt:1573.0] || -> equal(d2,b)**.
% 0.40/0.61 1577[6:Rew:1574.0,1369.0] || -> product(g1,b,b,b)*.
% 0.40/0.61 1679[6:Res:1577.0,125.0] || -> equal(c,b)**.
% 0.40/0.61 1681[6:MRR:1679.0,1059.0] || -> .
% 0.40/0.61 1683[6:Spt:1681.0,1573.0,1574.0] || equal(d2,b)** -> .
% 0.40/0.61 1684[6:Spt:1681.0,1573.1] || -> equal(d2,a)**.
% 0.40/0.61 1689[6:Rew:1684.0,1376.0] || product(g2,g,an_isomorphism(a),g)* -> .
% 0.40/0.61 1690[6:Rew:27.0,1689.0] || product(g2,g,f,g)* -> .
% 0.40/0.61 1691[6:MRR:1690.0,20.0] || -> .
% 0.40/0.61 1701[4:Spt:1691.0,1365.0,1366.0] || equal(d1,b)** -> .
% 0.40/0.61 1702[4:Spt:1691.0,1365.1] || -> equal(d1,a)**.
% 0.40/0.61 1705[4:Rew:1702.0,1701.0] || equal(b,a)** -> .
% 0.40/0.61 1706[4:Rew:1702.0,1060.0] || -> product(g1,a,d2,b)*.
% 0.40/0.61 1707[4:Rew:1702.0,1064.0] || product(g2,an_isomorphism(a),an_isomorphism(d2),g)* -> .
% 0.40/0.61 1708[4:Rew:27.0,1707.0] || product(g2,f,an_isomorphism(d2),g)* -> .
% 0.40/0.61 1721[5:Spt:57.0] || -> equal(d2,c)**.
% 0.40/0.61 1723[5:Rew:1721.0,1706.0] || -> product(g1,a,c,b)*.
% 0.40/0.61 1734[5:Res:1723.0,127.0] || -> equal(c,b)**.
% 0.40/0.61 1738[5:MRR:1734.0,1059.0] || -> .
% 0.40/0.61 1739[5:Spt:1738.0,57.0,1721.0] || equal(d2,c)** -> .
% 0.40/0.61 1740[5:Spt:1738.0,57.1,57.2] || -> equal(d2,b)** equal(d2,a).
% 0.40/0.61 1741[6:Spt:1740.0] || -> equal(d2,b)**.
% 0.40/0.61 1745[6:Rew:1741.0,1708.0] || product(g2,f,an_isomorphism(b),g)* -> .
% 0.40/0.61 1751[6:Rew:28.0,1745.0] || product(g2,f,g,g)* -> .
% 0.40/0.61 1752[6:MRR:1751.0,19.0] || -> .
% 0.40/0.61 1757[6:Spt:1752.0,1740.0,1741.0] || equal(d2,b)** -> .
% 0.40/0.61 1758[6:Spt:1752.0,1740.1] || -> equal(d2,a)**.
% 0.40/0.61 1762[6:Rew:1758.0,1706.0] || -> product(g1,a,a,b)*.
% 0.40/0.61 1773[6:Res:1762.0,121.0] || -> equal(b,a)**.
% 0.40/0.61 1777[6:MRR:1773.0,1705.0] || -> .
% 0.40/0.61 1778[2:Spt:1777.0,1056.0,1057.0] || equal(d3,b)** -> .
% 0.40/0.61 1779[2:Spt:1777.0,1056.1] || -> equal(d3,a)**.
% 0.40/0.61 1781[2:Rew:1779.0,1055.0] || equal(c,a)** -> .
% 0.40/0.61 1782[2:Rew:1779.0,1778.0] || equal(b,a)** -> .
% 0.40/0.61 1783[2:Rew:1779.0,33.0] || -> product(g1,d1,d2,a)*.
% 0.40/0.61 1784[2:Rew:1779.0,34.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))* -> .
% 0.40/0.61 1785[2:Rew:27.0,1784.0] || product(g2,an_isomorphism(d1),an_isomorphism(d2),f)* -> .
% 0.40/0.61 1796[3:Spt:57.0] || -> equal(d2,c)**.
% 0.40/0.61 1798[3:Rew:1796.0,1783.0] || -> product(g1,d1,c,a)*.
% 0.40/0.61 1799[3:Rew:1796.0,1785.0] || product(g2,an_isomorphism(d1),an_isomorphism(c),f)* -> .
% 0.40/0.61 1805[3:Rew:29.0,1799.0] || product(g2,an_isomorphism(d1),h,f)* -> .
% 0.40/0.61 1812[4:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 1814[4:Rew:1812.0,1798.0] || -> product(g1,c,c,a)*.
% 0.40/0.61 1829[4:Res:1814.0,122.0] || -> equal(b,a)**.
% 0.40/0.61 1831[4:MRR:1829.0,1782.0] || -> .
% 0.40/0.61 1833[4:Spt:1831.0,58.0,1812.0] || equal(d1,c)** -> .
% 0.40/0.61 1834[4:Spt:1831.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 1835[5:Spt:1834.0] || -> equal(d1,b)**.
% 0.40/0.61 1839[5:Rew:1835.0,1805.0] || product(g2,an_isomorphism(b),h,f)* -> .
% 0.40/0.61 1845[5:Rew:28.0,1839.0] || product(g2,g,h,f)* -> .
% 0.40/0.61 1846[5:MRR:1845.0,24.0] || -> .
% 0.40/0.61 1851[5:Spt:1846.0,1834.0,1835.0] || equal(d1,b)** -> .
% 0.40/0.61 1852[5:Spt:1846.0,1834.1] || -> equal(d1,a)**.
% 0.40/0.61 1856[5:Rew:1852.0,1798.0] || -> product(g1,a,c,a)*.
% 0.40/0.61 1867[5:Res:1856.0,127.0] || -> equal(c,a)**.
% 0.40/0.61 1871[5:MRR:1867.0,1781.0] || -> .
% 0.40/0.61 1872[3:Spt:1871.0,57.0,1796.0] || equal(d2,c)** -> .
% 0.40/0.61 1873[3:Spt:1871.0,57.1,57.2] || -> equal(d2,b)** equal(d2,a).
% 0.40/0.61 1874[4:Spt:1873.0] || -> equal(d2,b)**.
% 0.40/0.61 1877[4:Rew:1874.0,1783.0] || -> product(g1,d1,b,a)*.
% 0.40/0.61 1878[4:Rew:1874.0,1785.0] || product(g2,an_isomorphism(d1),an_isomorphism(b),f)* -> .
% 0.40/0.61 1884[4:Rew:28.0,1878.0] || product(g2,an_isomorphism(d1),g,f)* -> .
% 0.40/0.61 1892[5:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 1895[5:Rew:1892.0,1884.0] || product(g2,an_isomorphism(c),g,f)* -> .
% 0.40/0.61 1901[5:Rew:29.0,1895.0] || product(g2,h,g,f)* -> .
% 0.40/0.61 1902[5:MRR:1901.0,25.0] || -> .
% 0.40/0.61 1907[5:Spt:1902.0,58.0,1892.0] || equal(d1,c)** -> .
% 0.40/0.61 1908[5:Spt:1902.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 1909[6:Spt:1908.0] || -> equal(d1,b)**.
% 0.40/0.61 1912[6:Rew:1909.0,1877.0] || -> product(g1,b,b,a)*.
% 0.40/0.61 1923[6:Res:1912.0,125.0] || -> equal(c,a)**.
% 0.40/0.61 1927[6:MRR:1923.0,1781.0] || -> .
% 0.40/0.61 1928[6:Spt:1927.0,1908.0,1909.0] || equal(d1,b)** -> .
% 0.40/0.61 1929[6:Spt:1927.0,1908.1] || -> equal(d1,a)**.
% 0.40/0.61 1933[6:Rew:1929.0,1877.0] || -> product(g1,a,b,a)*.
% 0.40/0.61 1944[6:Res:1933.0,124.0] || -> equal(b,a)**.
% 0.40/0.61 1948[6:MRR:1944.0,1782.0] || -> .
% 0.40/0.61 1949[4:Spt:1948.0,1873.0,1874.0] || equal(d2,b)** -> .
% 0.40/0.61 1950[4:Spt:1948.0,1873.1] || -> equal(d2,a)**.
% 0.40/0.61 1954[4:Rew:1950.0,1783.0] || -> product(g1,d1,a,a)*.
% 0.40/0.61 1955[4:Rew:1950.0,1785.0] || product(g2,an_isomorphism(d1),an_isomorphism(a),f)* -> .
% 0.40/0.61 1956[4:Rew:27.0,1955.0] || product(g2,an_isomorphism(d1),f,f)* -> .
% 0.40/0.61 1969[5:Spt:58.0] || -> equal(d1,c)**.
% 0.40/0.61 1971[5:Rew:1969.0,1954.0] || -> product(g1,c,a,a)*.
% 0.40/0.61 1982[5:Res:1971.0,126.0] || -> equal(c,a)**.
% 0.40/0.61 1986[5:MRR:1982.0,1781.0] || -> .
% 0.40/0.61 1987[5:Spt:1986.0,58.0,1969.0] || equal(d1,c)** -> .
% 0.40/0.61 1988[5:Spt:1986.0,58.1,58.2] || -> equal(d1,b)** equal(d1,a).
% 0.40/0.61 1989[6:Spt:1988.0] || -> equal(d1,b)**.
% 0.40/0.61 1992[6:Rew:1989.0,1954.0] || -> product(g1,b,a,a)*.
% 0.40/0.61 2003[6:Res:1992.0,123.0] || -> equal(b,a)**.
% 0.40/0.61 2007[6:MRR:2003.0,1782.0] || -> .
% 0.40/0.61 2008[6:Spt:2007.0,1988.0,1989.0] || equal(d1,b)** -> .
% 0.40/0.61 2009[6:Spt:2007.0,1988.1] || -> equal(d1,a)**.
% 0.40/0.61 2014[6:Rew:2009.0,1956.0] || product(g2,an_isomorphism(a),f,f)* -> .
% 0.40/0.61 2015[6:Rew:27.0,2014.0] || product(g2,f,f,f)* -> .
% 0.40/0.61 2016[6:MRR:2015.0,18.0] || -> .
% 0.40/0.61 % SZS output end Refutation
% 0.40/0.61 Formulae used in the proof : a_in_group1 b_in_group1 c_in_group1 all_of_group1 a_times_a_is_a a_times_b_is_b b_times_a_is_b a_times_c_is_c c_times_a_is_c b_times_b_is_c b_times_c_is_a c_times_b_is_a c_times_c_is_b f_times_f_is_f f_times_g_is_g g_times_f_is_g f_times_h_is_h h_times_f_is_h g_times_g_is_h g_times_h_is_f h_times_g_is_f h_times_h_is_g a_maps_to_f b_maps_to_g c_maps_to_h d1_in_group1 d2_in_group1 d3_in_group1 d1_times_d2_is_d3 prove_product_holds_in_group2 total_function1_1 total_function2
% 0.40/0.61
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