TSTP Solution File: RNG040-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG040-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:41:18 EDT 2022
% Result : Unsatisfiable 185.57s 185.83s
% Output : Refutation 188.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG040-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 May 30 07:02:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 185.57/185.83
% 185.57/185.83 SPASS V 3.9
% 185.57/185.83 SPASS beiseite: Proof found.
% 185.57/185.83 % SZS status Theorem
% 185.57/185.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 185.57/185.83 SPASS derived 149084 clauses, backtracked 38404 clauses, performed 26 splits and kept 78804 clauses.
% 185.57/185.83 SPASS allocated 161335 KBytes.
% 185.57/185.83 SPASS spent 0:03:05.27 on the problem.
% 185.57/185.83 0:00:00.03 for the input.
% 185.57/185.83 0:00:00.00 for the FLOTTER CNF translation.
% 185.57/185.83 0:00:01.31 for inferences.
% 185.57/185.83 0:0:13.55 for the backtracking.
% 185.57/185.83 0:2:48.74 for the reduction.
% 185.57/185.83
% 185.57/185.83
% 185.57/185.83 Here is a proof with depth 12, length 400 :
% 185.57/185.83 % SZS output start Refutation
% 185.57/185.83 1[0:Inp] || -> sum__dfg(additive_identity,u,u)*.
% 185.57/185.83 2[0:Inp] || -> sum__dfg(u,additive_identity,u)*.
% 185.57/185.83 3[0:Inp] || -> product(u,v,multiply(u,v))*.
% 185.57/185.83 4[0:Inp] || -> sum__dfg(u,v,add(u,v))*.
% 185.57/185.83 5[0:Inp] || -> sum__dfg(additive_inverse(u),u,additive_identity)*.
% 185.57/185.83 6[0:Inp] || -> sum__dfg(u,additive_inverse(u),additive_identity)*.
% 185.57/185.83 7[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,v,y)* sum__dfg(z,x,u)* -> sum__dfg(z,y,w)*.
% 185.57/185.83 8[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*.
% 185.57/185.83 9[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*.
% 185.57/185.83 10[0:Inp] || product(u,v,w)*+ product(x,v,y)* product(z,x,u)* -> product(z,y,w)*.
% 185.57/185.83 11[0:Inp] || product(u,v,w)*+ product(x,y,v)* product(u,x,z)* -> product(z,y,w)*.
% 185.57/185.83 12[0:Inp] || product(u,v,w)*+ sum__dfg(x,y,v)* product(u,y,z)* product(u,x,x1)* -> sum__dfg(x1,z,w)*.
% 185.57/185.83 14[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(u,v,x)* -> equal(x,w)*.
% 185.57/185.83 15[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equal(x,w)*.
% 185.57/185.83 16[0:Inp] || -> product(u,multiplicative_identity,u)*.
% 185.57/185.83 17[0:Inp] || -> product(multiplicative_identity,u,u)*.
% 185.57/185.83 18[0:Inp] || -> equal(u,additive_identity) product(u,h(u),multiplicative_identity)*.
% 185.57/185.83 19[0:Inp] || -> equal(u,additive_identity) product(h(u),u,multiplicative_identity)*.
% 185.57/185.83 20[0:Inp] || product(u,v,w)*+ -> product(v,u,w)*.
% 185.57/185.83 21[0:Inp] || -> sum__dfg(b,c,d)*.
% 185.57/185.83 22[0:Inp] || -> product(d,a,additive_identity)*.
% 185.57/185.83 23[0:Inp] || -> product(b,a,l)*.
% 185.57/185.83 24[0:Inp] || -> product(c,a,n)*.
% 185.57/185.83 25[0:Inp] || sum__dfg(l,n,additive_identity)* -> .
% 185.57/185.83 27[0:Res:24.0,12.0] || product(c,u,v)*+ sum__dfg(a,w,u)* product(c,w,x)* -> sum__dfg(n,x,v)*.
% 185.57/185.83 29[0:Res:24.0,11.0] || product(c,u,v)*+ product(a,w,u)* -> product(n,w,v)*.
% 185.57/185.83 30[0:Res:24.0,15.0] || product(c,a,u)* -> equal(n,u).
% 185.57/185.83 31[0:Res:24.0,20.0] || -> product(a,c,n)*.
% 185.57/185.83 37[0:Res:24.0,10.1] || product(u,a,v)*+ product(w,c,u)* -> product(w,n,v)*.
% 185.57/185.83 39[0:Res:24.0,10.2] || product(u,v,c)*+ product(v,a,w)* -> product(u,w,n)*.
% 185.57/185.83 41[0:Res:23.0,12.0] || product(b,u,v)*+ sum__dfg(a,w,u)* product(b,w,x)* -> sum__dfg(l,x,v)*.
% 185.57/185.83 43[0:Res:23.0,11.0] || product(b,u,v)*+ product(a,w,u)* -> product(l,w,v)*.
% 185.57/185.83 44[0:Res:23.0,15.0] || product(b,a,u)* -> equal(l,u).
% 185.57/185.83 45[0:Res:23.0,20.0] || -> product(a,b,l)*.
% 185.57/185.83 51[0:Res:23.0,10.1] || product(u,a,v)*+ product(w,b,u)* -> product(w,l,v)*.
% 185.57/185.83 52[0:Res:23.0,11.1] || product(u,l,v)*+ product(u,b,w)* -> product(w,a,v)*.
% 185.57/185.83 53[0:Res:23.0,10.2] || product(u,v,b)*+ product(v,a,w)* -> product(u,w,l)*.
% 185.57/185.83 55[0:Res:3.0,44.0] || -> equal(multiply(b,a),l)**.
% 185.57/185.83 59[0:Res:3.0,30.0] || -> equal(multiply(c,a),n)**.
% 185.57/185.83 62[0:Res:21.0,9.0] || -> sum__dfg(c,b,d)*.
% 185.57/185.83 67[0:Res:4.0,9.0] || -> sum__dfg(u,v,add(v,u))*.
% 185.57/185.83 72[0:Res:22.0,20.0] || -> product(a,d,additive_identity)*.
% 185.57/185.83 77[0:Res:3.0,20.0] || -> product(u,v,multiply(v,u))*.
% 185.57/185.83 92[0:Res:21.0,14.0] || sum__dfg(b,c,u)* -> equal(u,d).
% 185.57/185.83 94[0:Res:1.0,14.0] || sum__dfg(additive_identity,u,v)* -> equal(v,u).
% 185.57/185.83 95[0:Res:2.0,14.0] || sum__dfg(u,additive_identity,v)* -> equal(v,u).
% 185.57/185.83 96[0:Res:5.0,14.0] || sum__dfg(additive_inverse(u),u,v)* -> equal(v,additive_identity).
% 185.57/185.83 97[0:Res:6.0,14.0] || sum__dfg(u,additive_inverse(u),v)* -> equal(v,additive_identity).
% 185.57/185.83 98[0:Res:4.0,14.0] || sum__dfg(u,v,w)* -> equal(w,add(u,v)).
% 185.57/185.83 99[0:Res:67.0,14.0] || sum__dfg(u,v,w)* -> equal(w,add(v,u)).
% 185.57/185.83 101[0:Res:4.0,92.0] || -> equal(add(b,c),d)**.
% 185.57/185.83 114[0:Res:22.0,15.0] || product(d,a,u)* -> equal(u,additive_identity).
% 185.57/185.83 115[0:Res:45.0,15.0] || product(a,b,u)* -> equal(u,l).
% 185.57/185.83 118[0:Res:17.0,15.0] || product(multiplicative_identity,u,v)* -> equal(v,u).
% 185.57/185.83 119[0:Res:16.0,15.0] || product(u,multiplicative_identity,v)* -> equal(v,u).
% 185.57/185.83 120[0:Res:3.0,15.0] || product(u,v,w)* -> equal(w,multiply(u,v)).
% 185.57/185.83 122[0:Res:19.1,15.0] || product(h(u),u,v)* -> equal(u,additive_identity) equal(v,multiplicative_identity).
% 185.57/185.83 125[0:Res:3.0,114.0] || -> equal(multiply(d,a),additive_identity)**.
% 185.57/185.83 138[0:Res:1.0,8.0] || sum__dfg(u,v,w)*+ sum__dfg(additive_identity,u,x)* -> sum__dfg(x,v,w)*.
% 185.57/185.83 139[0:Res:2.0,8.0] || sum__dfg(u,v,additive_identity)*+ sum__dfg(w,u,x)* -> sum__dfg(x,v,w)*.
% 185.57/185.83 141[0:Res:6.0,8.0] || sum__dfg(u,v,additive_inverse(w))*+ sum__dfg(w,u,x)* -> sum__dfg(x,v,additive_identity)*.
% 185.57/185.83 142[0:Res:4.0,8.0] || sum__dfg(u,v,w)*+ sum__dfg(x,u,y)* -> sum__dfg(y,v,add(x,w))*.
% 185.57/185.83 153[0:Res:4.0,94.0] || -> equal(add(additive_identity,u),u)**.
% 185.57/185.83 160[0:Res:1.0,7.0] || sum__dfg(u,v,w)*+ sum__dfg(x,u,additive_identity)* -> sum__dfg(x,w,v)*.
% 185.57/185.83 164[0:Res:4.0,7.0] || sum__dfg(u,v,w)*+ sum__dfg(x,u,y)* -> sum__dfg(x,w,add(y,v))*.
% 185.57/185.83 180[0:Res:3.0,118.0] || -> equal(multiply(multiplicative_identity,u),u)**.
% 185.57/185.83 181[0:Res:77.0,118.0] || -> equal(multiply(u,multiplicative_identity),u)**.
% 185.57/185.83 182[0:Res:18.1,118.0] || -> equal(multiplicative_identity,additive_identity) equal(h(multiplicative_identity),multiplicative_identity)**.
% 185.57/185.84 185[0:Res:22.0,11.0] || product(u,v,a)*+ product(d,u,w)* -> product(w,v,additive_identity)*.
% 185.57/185.84 191[0:Res:3.0,11.0] || product(u,v,w)*+ product(x,u,y)* -> product(y,v,multiply(x,w))*.
% 185.57/185.84 193[0:Res:19.1,11.0] || product(u,v,w)* product(h(w),u,x)*+ -> equal(w,additive_identity) product(x,v,multiplicative_identity)*.
% 185.57/185.84 202[1:Spt:182.0] || -> equal(multiplicative_identity,additive_identity)**.
% 185.57/185.84 203[1:Rew:202.0,17.0] || -> product(additive_identity,u,u)*.
% 185.57/185.84 204[1:Rew:202.0,16.0] || -> product(u,additive_identity,u)*.
% 185.57/185.84 205[1:Rew:202.0,19.1] || -> equal(u,additive_identity) product(h(u),u,additive_identity)*.
% 185.57/185.84 206[1:Rew:202.0,18.1] || -> equal(u,additive_identity) product(u,h(u),additive_identity)*.
% 185.57/185.84 208[1:Rew:202.0,180.0] || -> equal(multiply(additive_identity,u),u)**.
% 185.57/185.84 209[1:Rew:202.0,181.0] || -> equal(multiply(u,additive_identity),u)**.
% 185.57/185.84 244[0:Res:3.0,10.0] || product(u,v,w)*+ product(x,u,y)* -> product(x,w,multiply(y,v))*.
% 185.57/185.84 263[0:Res:67.0,96.0] || -> equal(add(u,additive_inverse(u)),additive_identity)**.
% 185.57/185.84 271[0:Res:22.0,12.0] || sum__dfg(u,v,a)*+ product(d,v,w)* product(d,u,x)* -> sum__dfg(x,w,additive_identity)*.
% 185.57/185.84 276[0:Res:3.0,12.0] || sum__dfg(u,v,w)*+ product(x,v,y)* product(x,u,z)* -> sum__dfg(z,y,multiply(x,w))*.
% 185.57/185.84 298[0:Res:67.0,98.0] || -> equal(add(u,v),add(v,u))*.
% 185.57/185.84 339[0:Res:77.0,120.0] || -> equal(multiply(u,v),multiply(v,u))*.
% 185.57/185.84 392[1:Res:204.0,43.0] || product(a,u,additive_identity) -> product(l,u,b)*.
% 185.57/185.84 415[1:Res:392.1,20.0] || product(a,u,additive_identity)*+ -> product(u,l,b)*.
% 185.57/185.84 420[0:Res:24.0,29.0] || product(a,u,a) -> product(n,u,n)*.
% 185.57/185.84 431[1:Res:206.1,415.0] || -> equal(a,additive_identity) product(h(a),l,b)*.
% 185.57/185.84 456[2:Spt:431.0] || -> equal(a,additive_identity)**.
% 185.57/185.84 463[2:Rew:456.0,55.0] || -> equal(multiply(b,additive_identity),l)**.
% 185.57/185.84 465[2:Rew:456.0,59.0] || -> equal(multiply(c,additive_identity),n)**.
% 185.57/185.84 468[2:Rew:456.0,125.0] || -> equal(multiply(d,additive_identity),additive_identity)**.
% 185.57/185.84 544[2:Rew:208.0,463.0,339.0,463.0] || -> equal(l,b)**.
% 185.57/185.84 545[2:Rew:544.0,25.0] || sum__dfg(b,n,additive_identity)* -> .
% 185.57/185.84 559[2:Rew:208.0,465.0,339.0,465.0] || -> equal(n,c)**.
% 185.57/185.84 562[2:Rew:208.0,468.0,339.0,468.0] || -> equal(d,additive_identity)**.
% 185.57/185.84 563[2:Rew:562.0,21.0] || -> sum__dfg(b,c,additive_identity)*.
% 185.57/185.84 578[2:Rew:559.0,545.0] || sum__dfg(b,c,additive_identity)* -> .
% 185.57/185.84 579[2:MRR:578.0,563.0] || -> .
% 185.57/185.84 667[2:Spt:579.0,431.0,456.0] || equal(a,additive_identity)** -> .
% 185.57/185.84 668[2:Spt:579.0,431.1] || -> product(h(a),l,b)*.
% 185.57/185.84 895[0:Res:420.1,20.0] || product(a,u,a)*+ -> product(u,n,n)*.
% 185.57/185.84 990[1:Res:203.0,51.0] || product(u,b,additive_identity) -> product(u,l,a)*.
% 185.57/185.84 998[0:Res:22.0,51.0] || product(u,b,d) -> product(u,l,additive_identity)*.
% 185.57/185.84 999[0:Res:23.0,51.0] || product(u,b,b) -> product(u,l,l)*.
% 185.57/185.84 1000[0:Res:24.0,51.0] || product(u,b,c) -> product(u,l,n)*.
% 185.57/185.84 1026[0:Res:23.0,37.0] || product(u,c,b) -> product(u,n,l)*.
% 185.57/185.84 1047[1:Res:990.1,120.0] || product(u,b,additive_identity)* -> equal(multiply(u,l),a).
% 185.57/185.84 1052[1:Res:990.1,20.0] || product(u,b,additive_identity)*+ -> product(l,u,a)*.
% 185.57/185.84 1119[0:Res:998.1,120.0] || product(u,b,d)* -> equal(multiply(u,l),additive_identity).
% 185.57/185.84 1190[0:Res:999.1,20.0] || product(u,b,b)*+ -> product(l,u,l)*.
% 185.57/185.84 1216[0:Res:1000.1,20.0] || product(u,b,c)*+ -> product(l,u,n)*.
% 185.57/185.84 1272[0:Res:1.0,138.0] || sum__dfg(additive_identity,additive_identity,u)*+ -> sum__dfg(u,v,v)*.
% 185.57/185.84 1310[0:Res:5.0,139.0] || sum__dfg(u,additive_inverse(v),w)* -> sum__dfg(w,v,u).
% 185.57/185.84 1311[0:Res:6.0,139.0] || sum__dfg(u,v,w) -> sum__dfg(w,additive_inverse(v),u)*.
% 185.57/185.84 1335[0:Res:5.0,160.0] || sum__dfg(u,additive_inverse(v),additive_identity)* -> sum__dfg(u,additive_identity,v).
% 185.57/185.84 1336[0:Res:6.0,160.0] || sum__dfg(u,v,additive_identity) -> sum__dfg(u,additive_identity,additive_inverse(v))*.
% 185.57/185.84 1355[0:Res:1026.1,120.0] || product(u,c,b)* -> equal(multiply(u,n),l).
% 185.57/185.84 1437[1:Res:205.1,1052.0] || -> equal(b,additive_identity) product(l,h(b),a)*.
% 185.57/185.84 1438[3:Spt:1437.0] || -> equal(b,additive_identity)**.
% 185.57/185.84 1446[3:Rew:1438.0,55.0] || -> equal(multiply(additive_identity,a),l)**.
% 185.57/185.84 1448[3:Rew:1438.0,101.0] || -> equal(add(additive_identity,c),d)**.
% 185.57/185.84 1587[3:Rew:1438.0,1047.0] || product(u,additive_identity,additive_identity)* -> equal(multiply(u,l),a).
% 185.57/185.84 1642[3:Rew:1438.0,1119.0] || product(u,additive_identity,d)* -> equal(multiply(u,l),additive_identity).
% 185.57/185.84 1712[3:Rew:1438.0,1355.0] || product(u,c,additive_identity)* -> equal(multiply(u,n),l).
% 185.57/185.84 1723[3:Rew:208.0,1446.0] || -> equal(l,a)**.
% 185.57/185.84 1766[3:Rew:153.0,1448.0] || -> equal(d,c)**.
% 185.57/185.84 1768[3:Rew:1766.0,22.0] || -> product(c,a,additive_identity)*.
% 185.57/185.84 1769[3:Rew:1766.0,125.0] || -> equal(multiply(c,a),additive_identity)**.
% 185.57/185.84 1848[3:Rew:59.0,1769.0] || -> equal(n,additive_identity)**.
% 185.57/185.84 1897[3:Rew:1848.0,27.3] || product(c,u,v)*+ sum__dfg(a,w,u)* product(c,w,x)* -> sum__dfg(additive_identity,x,v)*.
% 185.57/185.84 2063[3:Rew:1723.0,1587.1] || product(u,additive_identity,additive_identity)* -> equal(multiply(u,a),a).
% 185.57/185.84 2068[3:Rew:1723.0,1642.1,1766.0,1642.0] || product(u,additive_identity,c)* -> equal(multiply(u,a),additive_identity).
% 185.57/185.84 2078[3:Rew:1848.0,1712.1,1723.0,1712.1] || product(u,c,additive_identity)* -> equal(multiply(u,additive_identity),a).
% 185.57/185.84 2079[3:Rew:209.0,2078.1] || product(u,c,additive_identity)* -> equal(u,a).
% 185.57/185.84 2404[3:Res:205.1,2079.0] || -> equal(c,additive_identity) equal(h(c),a)**.
% 185.57/185.84 2407[4:Spt:2404.0] || -> equal(c,additive_identity)**.
% 185.57/185.84 2452[4:Rew:2407.0,2068.0] || product(u,additive_identity,additive_identity)* -> equal(multiply(u,a),additive_identity).
% 185.57/185.84 2522[4:Rew:2063.1,2452.1] || product(u,additive_identity,additive_identity)* -> equal(a,additive_identity).
% 185.57/185.84 2523[4:MRR:2522.1,667.0] || product(u,additive_identity,additive_identity)* -> .
% 185.57/185.84 2524[4:UnC:2523.0,204.0] || -> .
% 185.57/185.84 2546[4:Spt:2524.0,2404.0,2407.0] || equal(c,additive_identity)** -> .
% 185.57/185.84 2547[4:Spt:2524.0,2404.1] || -> equal(h(c),a)**.
% 185.57/185.84 2871[0:Res:1.0,141.0] || sum__dfg(u,additive_identity,v) -> sum__dfg(v,additive_inverse(u),additive_identity)*.
% 185.57/185.84 3114[0:Res:4.0,142.0] || sum__dfg(u,v,w) -> sum__dfg(w,x,add(u,add(v,x)))*.
% 185.57/185.84 3166[0:Res:5.0,164.0] || sum__dfg(u,additive_inverse(v),w) -> sum__dfg(u,additive_identity,add(w,v))*.
% 185.57/185.84 3189[0:Res:3.0,191.0] || product(u,v,w) -> product(w,x,multiply(u,multiply(v,x)))*.
% 185.57/185.84 3278[0:Res:5.0,1335.0] || -> sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u)*.
% 185.57/185.84 3296[0:Res:3278.0,95.0] || -> equal(additive_inverse(additive_inverse(u)),u)**.
% 185.57/185.84 3339[0:Res:1336.1,1272.0] || sum__dfg(additive_identity,u,additive_identity) -> sum__dfg(additive_inverse(u),v,v)*.
% 185.57/185.84 3727[0:Res:3339.1,9.0] || sum__dfg(additive_identity,u,additive_identity) -> sum__dfg(v,additive_inverse(u),v)*.
% 185.57/185.84 4107[3:Res:1768.0,1897.0] || sum__dfg(a,u,a) product(c,u,v)* -> sum__dfg(additive_identity,v,additive_identity).
% 185.57/185.84 4118[0:SpR:3296.0,3727.1] || sum__dfg(additive_identity,additive_inverse(u),additive_identity)*+ -> sum__dfg(v,u,v)*.
% 185.57/185.84 4353[0:Res:2871.1,4118.0] || sum__dfg(u,additive_identity,additive_identity)*+ -> sum__dfg(v,u,v)*.
% 185.57/185.84 4506[0:Res:4.0,1310.0] || -> sum__dfg(add(u,additive_inverse(v)),v,u)*.
% 185.57/185.84 4507[0:Res:67.0,1310.0] || -> sum__dfg(add(additive_inverse(u),v),u,v)*.
% 185.57/185.84 4521[0:SpR:3296.0,4506.0] || -> sum__dfg(add(u,v),additive_inverse(v),u)*.
% 185.57/185.84 4533[0:Res:4506.0,99.0] || -> equal(add(u,add(v,additive_inverse(u))),v)**.
% 185.57/185.84 4603[0:SpR:3296.0,4507.0] || -> sum__dfg(add(u,v),additive_inverse(u),v)*.
% 185.57/185.84 4615[0:Res:4507.0,99.0] || -> equal(add(u,add(additive_inverse(u),v)),v)**.
% 185.57/185.84 4683[0:Res:4521.0,99.0] || -> equal(add(additive_inverse(u),add(v,u)),v)**.
% 185.57/185.84 4779[0:Res:4603.0,99.0] || -> equal(add(additive_inverse(u),add(u,v)),v)**.
% 185.57/185.84 5037[0:SpR:4683.0,4521.0] || -> sum__dfg(u,additive_inverse(add(u,v)),additive_inverse(v))*.
% 185.57/185.84 5043[0:SpR:4683.0,4683.0] || -> equal(add(additive_inverse(add(u,v)),u),additive_inverse(v))**.
% 185.57/185.84 5063[0:Rew:298.0,5043.0] || -> equal(add(u,additive_inverse(add(u,v))),additive_inverse(v))**.
% 185.57/185.84 5461[0:SpR:4683.0,5037.0] || -> sum__dfg(additive_inverse(u),additive_inverse(v),additive_inverse(add(v,u)))*.
% 185.57/185.84 5761[0:SpR:5063.0,4615.0] || -> equal(additive_inverse(add(additive_inverse(u),v)),add(u,additive_inverse(v)))**.
% 185.57/185.84 6073[0:Res:1311.1,9.0] || sum__dfg(u,v,w) -> sum__dfg(additive_inverse(v),w,u)*.
% 185.57/185.84 6081[0:Res:1311.1,97.0] || sum__dfg(u,v,v)* -> equal(u,additive_identity).
% 185.57/185.84 7858[0:Res:6073.1,6081.0] || sum__dfg(u,v,u)* -> equal(additive_inverse(v),additive_identity).
% 185.57/185.84 7979[0:Res:1311.1,7858.0] || sum__dfg(u,v,u)* -> equal(additive_inverse(additive_inverse(v)),additive_identity).
% 185.57/185.84 8002[0:Rew:3296.0,7979.1] || sum__dfg(u,v,u)* -> equal(v,additive_identity).
% 185.57/185.84 12989[0:SpR:4533.0,3114.1] || sum__dfg(u,v,w) -> sum__dfg(w,additive_inverse(u),v)*.
% 185.57/185.84 15977[3:Res:204.0,4107.1] || sum__dfg(a,additive_identity,a)* -> sum__dfg(additive_identity,c,additive_identity).
% 185.57/185.84 16013[3:MRR:15977.0,2.0] || -> sum__dfg(additive_identity,c,additive_identity)*.
% 185.57/185.84 16035[3:Res:16013.0,98.0] || -> equal(add(additive_identity,c),additive_identity)**.
% 185.57/185.84 16062[3:Rew:153.0,16035.0] || -> equal(c,additive_identity)**.
% 185.57/185.84 16063[4:MRR:16062.0,2546.0] || -> .
% 185.57/185.84 16068[3:Spt:16063.0,1437.0,1438.0] || equal(b,additive_identity)** -> .
% 185.57/185.84 16069[3:Spt:16063.0,1437.1] || -> product(l,h(b),a)*.
% 185.57/185.84 16095[0:Res:62.0,142.0] || sum__dfg(u,c,v) -> sum__dfg(v,b,add(u,d))*.
% 185.57/185.84 16119[0:Res:21.0,276.0] || product(u,c,v) product(u,b,w) -> sum__dfg(w,v,multiply(u,d))*.
% 185.57/185.84 16124[0:Res:21.0,142.0] || sum__dfg(u,b,v) -> sum__dfg(v,c,add(u,d))*.
% 185.57/185.84 16195[0:Res:22.0,244.0] || product(u,d,v) -> product(u,additive_identity,multiply(v,a))*.
% 185.57/185.84 16196[0:Res:22.0,191.0] || product(u,d,v) -> product(v,a,multiply(u,additive_identity))*.
% 185.57/185.84 16209[0:Res:72.0,244.0] || product(u,a,v) -> product(u,additive_identity,multiply(v,d))*.
% 185.57/185.84 16266[0:SpR:101.0,4779.0] || -> equal(add(additive_inverse(b),d),c)**.
% 185.57/185.84 16284[0:SpR:101.0,4683.0] || -> equal(add(additive_inverse(c),d),b)**.
% 185.57/185.84 16313[0:Rew:298.0,16266.0] || -> equal(add(d,additive_inverse(b)),c)**.
% 185.57/185.84 16316[0:Rew:298.0,16284.0] || -> equal(add(d,additive_inverse(c)),b)**.
% 185.57/185.84 17893[0:Res:23.0,41.0] || sum__dfg(a,u,a) product(b,u,v)* -> sum__dfg(l,v,l).
% 185.57/185.84 17904[0:Res:1.0,271.0] || product(d,a,u)*+ product(d,additive_identity,v)* -> sum__dfg(v,u,additive_identity)*.
% 185.57/185.84 55726[0:Res:16095.1,8002.0] || sum__dfg(u,c,add(u,d))* -> equal(b,additive_identity).
% 185.57/185.84 55736[3:MRR:55726.1,16068.0] || sum__dfg(u,c,add(u,d))* -> .
% 185.57/185.84 55815[3:Res:16124.1,55736.0] || sum__dfg(u,b,u)* -> .
% 185.57/185.84 56101[1:Res:204.0,17893.1] || sum__dfg(a,additive_identity,a) -> sum__dfg(l,b,l)*.
% 185.57/185.84 56139[0:Res:23.0,17893.1] || sum__dfg(a,a,a) -> sum__dfg(l,l,l)*.
% 185.57/185.84 56164[3:MRR:56101.0,56101.1,2.0,55815.0] || -> .
% 185.57/185.84 56179[1:Spt:56164.0,182.0,202.0] || equal(multiplicative_identity,additive_identity)** -> .
% 185.57/185.84 56180[1:Spt:56164.0,182.1] || -> equal(h(multiplicative_identity),multiplicative_identity)**.
% 185.57/185.84 56318[0:Res:16.0,27.0] || sum__dfg(a,u,multiplicative_identity) product(c,u,v)* -> sum__dfg(n,v,c).
% 185.57/185.84 56320[0:Res:16.0,39.0] || product(multiplicative_identity,a,u) -> product(c,u,n)*.
% 185.57/185.84 56326[0:Res:16.0,53.0] || product(multiplicative_identity,a,u) -> product(b,u,l)*.
% 185.57/185.84 56329[0:Res:17.0,191.0] || product(u,multiplicative_identity,v) -> product(v,w,multiply(u,w))*.
% 185.57/185.84 56333[0:Res:17.0,10.0] || product(u,v,w)*+ product(x,u,multiplicative_identity)* -> product(x,w,v)*.
% 185.57/185.84 56340[0:Res:17.0,37.0] || product(u,c,multiplicative_identity) -> product(u,n,a)*.
% 185.57/185.84 56341[0:Res:17.0,51.0] || product(u,b,multiplicative_identity) -> product(u,l,a)*.
% 185.57/185.84 56345[0:Res:17.0,185.0] || product(d,multiplicative_identity,u)*+ -> product(u,a,additive_identity)*.
% 185.57/185.84 56377[0:Res:18.1,191.0] || product(u,v,w) -> equal(v,additive_identity) product(w,h(v),multiply(u,multiplicative_identity))*.
% 185.57/185.84 56381[0:Res:18.1,10.0] || product(u,h(v),w)*+ product(x,u,v)* -> equal(v,additive_identity) product(x,w,multiplicative_identity)*.
% 185.57/185.84 56393[0:Rew:181.0,56377.2] || product(u,v,w) -> equal(v,additive_identity) product(w,h(v),u)*.
% 185.57/185.84 56416[0:SpR:180.0,16209.1] || product(u,a,multiplicative_identity)* -> product(u,additive_identity,d).
% 185.57/185.84 56422[0:SpR:180.0,16195.1] || product(u,d,multiplicative_identity)* -> product(u,additive_identity,a).
% 185.57/185.84 56438[0:Res:19.1,52.0] || product(h(l),b,u)* -> equal(l,additive_identity) product(u,a,multiplicative_identity).
% 185.57/185.84 56514[0:Res:56139.1,6081.0] || sum__dfg(a,a,a)* -> equal(l,additive_identity).
% 185.57/185.84 56975[0:Res:19.1,193.1] || product(u,v,u)* -> equal(u,additive_identity) equal(u,additive_identity) product(multiplicative_identity,v,multiplicative_identity)*.
% 185.57/185.84 57004[0:Obv:56975.1] || product(u,v,u)*+ -> equal(u,additive_identity) product(multiplicative_identity,v,multiplicative_identity)*.
% 185.57/185.84 57099[0:Res:18.1,56381.0] || product(u,v,v)* -> equal(v,additive_identity) equal(v,additive_identity) product(u,multiplicative_identity,multiplicative_identity)*.
% 185.57/185.84 57115[0:Obv:57099.1] || product(u,v,v)*+ -> equal(v,additive_identity) product(u,multiplicative_identity,multiplicative_identity)*.
% 185.57/185.84 57308[0:Res:56320.1,119.0] || product(multiplicative_identity,a,multiplicative_identity)* -> equal(n,c).
% 185.57/185.84 57412[0:Res:56326.1,119.0] || product(multiplicative_identity,a,multiplicative_identity)* -> equal(l,b).
% 185.57/185.84 57523[0:Res:56340.1,20.0] || product(u,c,multiplicative_identity)*+ -> product(n,u,a)*.
% 185.57/185.84 57534[0:Res:56340.1,118.0] || product(multiplicative_identity,c,multiplicative_identity)* -> equal(n,a).
% 185.57/185.84 57551[0:Res:56341.1,20.0] || product(u,b,multiplicative_identity)*+ -> product(l,u,a)*.
% 185.57/185.84 57872[0:Res:19.1,56416.0] || -> equal(a,additive_identity) product(h(a),additive_identity,d)*.
% 185.57/185.84 57884[2:Spt:57872.0] || -> equal(a,additive_identity)**.
% 185.57/185.84 57915[2:Rew:57884.0,45.0] || -> product(additive_identity,b,l)*.
% 185.57/185.84 57922[2:Rew:57884.0,895.0] || product(additive_identity,u,additive_identity)* -> product(u,n,n)*.
% 185.57/185.84 57928[2:Rew:57884.0,72.0] || -> product(additive_identity,d,additive_identity)*.
% 185.57/185.84 57930[2:Rew:57884.0,59.0] || -> equal(multiply(c,additive_identity),n)**.
% 185.57/185.84 57936[2:Rew:57884.0,125.0] || -> equal(multiply(d,additive_identity),additive_identity)**.
% 185.57/185.84 57959[2:Rew:57884.0,56514.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> equal(l,additive_identity).
% 185.57/185.84 57993[2:Rew:57884.0,56341.1] || product(u,b,multiplicative_identity) -> product(u,l,additive_identity)*.
% 185.57/185.84 58954[2:Rew:57884.0,56318.0] || sum__dfg(additive_identity,u,multiplicative_identity) product(c,u,v)* -> sum__dfg(n,v,c).
% 185.57/185.84 59178[2:Rew:339.0,57930.0] || -> equal(multiply(additive_identity,c),n)**.
% 185.57/185.84 59179[2:Rew:339.0,57936.0] || -> equal(multiply(additive_identity,d),additive_identity)**.
% 185.57/185.84 59180[2:MRR:57959.0,2.0] || -> equal(l,additive_identity)**.
% 185.57/185.84 59184[2:Rew:59180.0,25.0] || sum__dfg(additive_identity,n,additive_identity)* -> .
% 185.57/185.84 59255[2:Rew:59180.0,57915.0] || -> product(additive_identity,b,additive_identity)*.
% 185.57/185.84 59281[2:Rew:59180.0,57993.1] || product(u,b,multiplicative_identity)* -> product(u,additive_identity,additive_identity).
% 185.57/185.84 60367[2:Res:57928.0,57922.0] || -> product(d,n,n)*.
% 185.57/185.84 60368[2:Res:59255.0,57922.0] || -> product(b,n,n)*.
% 185.57/185.84 60379[2:Res:60367.0,20.0] || -> product(n,d,n)*.
% 185.57/185.84 60391[2:Res:60368.0,20.0] || -> product(n,b,n)*.
% 185.57/185.84 60400[2:Res:60379.0,56333.0] || product(u,n,multiplicative_identity) -> product(u,n,d)*.
% 185.57/185.84 60412[2:Res:60391.0,56333.0] || product(u,n,multiplicative_identity) -> product(u,n,b)*.
% 185.57/185.84 61122[2:Res:19.1,59281.0] || -> equal(b,additive_identity) product(h(b),additive_identity,additive_identity)*.
% 185.57/185.84 61123[3:Spt:61122.0] || -> equal(b,additive_identity)**.
% 185.57/185.84 61133[3:Rew:61123.0,101.0] || -> equal(add(additive_identity,c),d)**.
% 185.57/185.84 62454[3:Rew:153.0,61133.0] || -> equal(d,c)**.
% 185.57/185.84 62464[3:Rew:62454.0,59179.0] || -> equal(multiply(additive_identity,c),additive_identity)**.
% 185.57/185.84 62716[3:Rew:59178.0,62464.0] || -> equal(n,additive_identity)**.
% 185.57/185.84 62725[3:Rew:62716.0,59184.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 185.57/185.84 63124[3:MRR:62725.0,2.0] || -> .
% 185.57/185.84 64613[3:Spt:63124.0,61122.0,61123.0] || equal(b,additive_identity)** -> .
% 185.57/185.84 64614[3:Spt:63124.0,61122.1] || -> product(h(b),additive_identity,additive_identity)*.
% 185.57/185.84 67631[2:Res:60412.1,122.0] || product(h(n),n,multiplicative_identity)* -> equal(n,additive_identity) equal(b,multiplicative_identity).
% 185.57/185.84 67639[2:MRR:67631.0,19.1] || -> equal(n,additive_identity)** equal(b,multiplicative_identity).
% 185.57/185.84 67647[4:Spt:67639.1] || -> equal(b,multiplicative_identity)**.
% 185.57/185.84 67668[4:Rew:67647.0,16313.0] || -> equal(add(d,additive_inverse(multiplicative_identity)),c)**.
% 185.57/185.84 70831[2:Res:60400.1,122.0] || product(h(n),n,multiplicative_identity)* -> equal(n,additive_identity) equal(d,multiplicative_identity).
% 185.57/185.84 70838[2:MRR:70831.0,19.1] || -> equal(n,additive_identity)** equal(d,multiplicative_identity).
% 185.57/185.84 70850[5:Spt:70838.1] || -> equal(d,multiplicative_identity)**.
% 185.57/185.84 70929[5:Rew:70850.0,67668.0] || -> equal(add(multiplicative_identity,additive_inverse(multiplicative_identity)),c)**.
% 185.57/185.84 71983[5:Rew:263.0,70929.0] || -> equal(c,additive_identity)**.
% 185.57/185.84 72245[5:Rew:71983.0,58954.1] || sum__dfg(additive_identity,u,multiplicative_identity) product(additive_identity,u,v)* -> sum__dfg(n,v,c).
% 185.57/185.84 73224[5:Rew:71983.0,72245.2] || sum__dfg(additive_identity,u,multiplicative_identity) product(additive_identity,u,v)* -> sum__dfg(n,v,additive_identity).
% 185.57/185.84 82612[5:Res:16.0,73224.1] || sum__dfg(additive_identity,multiplicative_identity,multiplicative_identity) -> sum__dfg(n,additive_identity,additive_identity)*.
% 185.57/185.84 82637[5:MRR:82612.0,1.0] || -> sum__dfg(n,additive_identity,additive_identity)*.
% 185.57/185.84 82678[5:Res:82637.0,4353.0] || -> sum__dfg(u,n,u)*.
% 185.57/185.84 82692[5:UnC:82678.0,59184.0] || -> .
% 185.57/185.84 82710[5:Spt:82692.0,70838.1,70850.0] || equal(d,multiplicative_identity)** -> .
% 185.57/185.84 82711[5:Spt:82692.0,70838.0] || -> equal(n,additive_identity)**.
% 185.57/185.84 82712[5:Rew:82711.0,59184.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 185.57/185.84 82741[5:MRR:82712.0,2.0] || -> .
% 185.57/185.84 83425[4:Spt:82741.0,67639.1,67647.0] || equal(b,multiplicative_identity)** -> .
% 185.57/185.84 83426[4:Spt:82741.0,67639.0] || -> equal(n,additive_identity)**.
% 185.57/185.84 83433[4:Rew:83426.0,59184.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 185.57/185.84 83434[4:MRR:83433.0,2.0] || -> .
% 185.57/185.84 84238[2:Spt:83434.0,57872.0,57884.0] || equal(a,additive_identity)** -> .
% 185.57/185.84 84239[2:Spt:83434.0,57872.1] || -> product(h(a),additive_identity,d)*.
% 185.57/185.84 84268[2:Res:84239.0,20.0] || -> product(additive_identity,h(a),d)*.
% 185.57/185.84 84582[2:Res:84268.0,15.0] || product(additive_identity,h(a),u)* -> equal(u,d).
% 185.57/185.84 85321[0:Res:56329.1,115.0] || product(u,multiplicative_identity,a)* -> equal(multiply(u,b),l).
% 185.57/185.84 87090[0:Res:19.1,57551.0] || -> equal(b,additive_identity) product(l,h(b),a)*.
% 185.57/185.84 87092[3:Spt:87090.0] || -> equal(b,additive_identity)**.
% 185.57/185.84 87097[3:Rew:87092.0,101.0] || -> equal(add(additive_identity,c),d)**.
% 185.57/185.84 87115[3:Rew:87092.0,55.0] || -> equal(multiply(additive_identity,a),l)**.
% 185.57/185.84 87507[3:Rew:87092.0,999.0] || product(u,additive_identity,additive_identity) -> product(u,l,l)*.
% 185.57/185.84 87508[3:Rew:87092.0,1190.0] || product(u,additive_identity,additive_identity)*+ -> product(l,u,l)*.
% 185.57/185.84 87534[3:Rew:87092.0,1216.0] || product(u,additive_identity,c)* -> product(l,u,n)*.
% 185.57/185.84 88218[3:Rew:87092.0,56438.0] || product(h(l),additive_identity,u)* -> equal(l,additive_identity) product(u,a,multiplicative_identity).
% 185.57/185.84 88560[3:Rew:153.0,87097.0] || -> equal(d,c)**.
% 185.57/185.84 88561[3:Rew:88560.0,84239.0] || -> product(h(a),additive_identity,c)*.
% 185.57/185.84 88562[3:Rew:88560.0,22.0] || -> product(c,a,additive_identity)*.
% 185.57/185.84 88563[3:Rew:88560.0,72.0] || -> product(a,c,additive_identity)*.
% 185.57/185.84 88564[3:Rew:88560.0,125.0] || -> equal(multiply(c,a),additive_identity)**.
% 185.57/185.84 88588[3:Rew:88560.0,56345.0] || product(c,multiplicative_identity,u)*+ -> product(u,a,additive_identity)*.
% 185.57/185.84 88687[3:Rew:88560.0,84582.1] || product(additive_identity,h(a),u)* -> equal(u,c).
% 185.57/185.84 88692[3:Rew:88560.0,17904.0] || product(c,a,u)* product(d,additive_identity,v)* -> sum__dfg(v,u,additive_identity)*.
% 185.57/185.84 88718[3:Rew:88560.0,56422.0] || product(u,c,multiplicative_identity)* -> product(u,additive_identity,a).
% 185.57/185.84 88800[3:Rew:59.0,88564.0] || -> equal(n,additive_identity)**.
% 185.57/185.84 88803[3:Rew:88800.0,25.0] || sum__dfg(l,additive_identity,additive_identity)* -> .
% 185.57/185.84 88804[3:Rew:88800.0,59.0] || -> equal(multiply(c,a),additive_identity)**.
% 185.57/185.84 88806[3:Rew:88800.0,57534.1] || product(multiplicative_identity,c,multiplicative_identity)* -> equal(a,additive_identity).
% 185.57/185.84 88834[3:Rew:88800.0,56320.1] || product(multiplicative_identity,a,u) -> product(c,u,additive_identity)*.
% 185.57/185.84 89319[3:MRR:88806.1,84238.0] || product(multiplicative_identity,c,multiplicative_identity)* -> .
% 185.57/185.84 89395[3:Rew:88800.0,87534.1] || product(u,additive_identity,c)*+ -> product(l,u,additive_identity)*.
% 185.57/185.84 89924[3:Rew:88560.0,88692.1] || product(c,a,u)*+ product(c,additive_identity,v)* -> sum__dfg(v,u,additive_identity)*.
% 185.57/185.84 91429[3:Res:87507.1,57115.0] || product(u,additive_identity,additive_identity) -> equal(l,additive_identity) product(u,multiplicative_identity,multiplicative_identity)*.
% 185.57/185.84 91471[3:Res:88561.0,89395.0] || -> product(l,h(a),additive_identity)*.
% 185.57/185.84 91510[3:Res:91471.0,15.0] || product(l,h(a),u)* -> equal(u,additive_identity).
% 185.57/185.84 91852[3:Res:3189.1,88687.0] || product(u,v,additive_identity) -> equal(multiply(u,multiply(v,h(a))),c)**.
% 185.57/185.84 91986[3:Res:19.1,88718.0] || -> equal(c,additive_identity) product(h(c),additive_identity,a)*.
% 185.57/185.84 91989[4:Spt:91986.0] || -> equal(c,additive_identity)**.
% 185.57/185.84 91996[4:Rew:91989.0,88804.0] || -> equal(multiply(additive_identity,a),additive_identity)**.
% 185.57/185.84 92793[4:Rew:87115.0,91996.0] || -> equal(l,additive_identity)**.
% 185.57/185.84 92800[4:Rew:92793.0,88803.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 185.57/185.84 93343[4:MRR:92800.0,2.0] || -> .
% 185.57/185.84 93815[4:Spt:93343.0,91986.0,91989.0] || equal(c,additive_identity)** -> .
% 185.57/185.84 93816[4:Spt:93343.0,91986.1] || -> product(h(c),additive_identity,a)*.
% 185.57/185.84 95465[3:Res:88834.1,87508.0] || product(multiplicative_identity,a,additive_identity) -> product(l,c,l)*.
% 185.57/185.84 95477[3:Res:95465.1,57004.0] || product(multiplicative_identity,a,additive_identity)* -> equal(l,additive_identity) product(multiplicative_identity,c,multiplicative_identity).
% 185.57/185.84 95480[3:MRR:95477.2,89319.0] || product(multiplicative_identity,a,additive_identity)* -> equal(l,additive_identity).
% 185.57/185.84 95523[3:Res:3189.1,91510.0] || product(u,v,l) -> equal(multiply(u,multiply(v,h(a))),additive_identity)**.
% 185.57/185.84 97366[5:Spt:88218.1] || -> equal(l,additive_identity)**.
% 185.57/185.84 97773[5:Rew:97366.0,95523.0] || product(u,v,additive_identity) -> equal(multiply(u,multiply(v,h(a))),additive_identity)**.
% 185.57/185.84 98734[5:Rew:91852.1,97773.1] || product(u,v,additive_identity)* -> equal(c,additive_identity).
% 185.57/185.84 98735[5:MRR:98734.1,93815.0] || product(u,v,additive_identity)* -> .
% 185.57/185.84 98736[5:UnC:98735.0,88563.0] || -> .
% 185.57/185.84 99072[5:Spt:98736.0,88218.1,97366.0] || equal(l,additive_identity)** -> .
% 185.57/185.84 99073[5:Spt:98736.0,88218.0,88218.2] || product(h(l),additive_identity,u)* -> product(u,a,multiplicative_identity).
% 185.57/185.84 99079[5:MRR:95480.1,99072.0] || product(multiplicative_identity,a,additive_identity)* -> .
% 185.57/185.84 99095[5:MRR:91429.1,99072.0] || product(u,additive_identity,additive_identity) -> product(u,multiplicative_identity,multiplicative_identity)*.
% 185.57/185.84 100594[5:Res:99095.1,88588.0] || product(c,additive_identity,additive_identity)* -> product(multiplicative_identity,a,additive_identity).
% 185.57/185.84 100639[5:MRR:100594.1,99079.0] || product(c,additive_identity,additive_identity)* -> .
% 185.57/185.84 103694[3:Res:88562.0,89924.0] || product(c,additive_identity,u)* -> sum__dfg(u,additive_identity,additive_identity).
% 185.57/185.84 103928[3:Res:3.0,103694.0] || -> sum__dfg(multiply(c,additive_identity),additive_identity,additive_identity)*.
% 185.57/185.84 103942[3:Rew:339.0,103928.0] || -> sum__dfg(multiply(additive_identity,c),additive_identity,additive_identity)*.
% 185.57/185.84 104001[3:Res:103942.0,95.0] || -> equal(multiply(additive_identity,c),additive_identity)**.
% 185.57/185.84 104046[3:SpR:104001.0,77.0] || -> product(c,additive_identity,additive_identity)*.
% 185.57/185.84 104067[5:MRR:104046.0,100639.0] || -> .
% 185.57/185.84 104068[3:Spt:104067.0,87090.0,87092.0] || equal(b,additive_identity)** -> .
% 185.57/185.84 104069[3:Spt:104067.0,87090.1] || -> product(l,h(b),a)*.
% 185.57/185.84 104077[3:MRR:55726.1,104068.0] || sum__dfg(u,c,add(u,d))* -> .
% 185.57/185.84 105075[3:SpL:298.0,104077.0] || sum__dfg(u,c,add(d,u))* -> .
% 185.57/185.84 105097[3:Res:3114.1,105075.0] || sum__dfg(d,u,add(u,c))* -> .
% 185.57/185.84 105141[3:Res:1311.1,105097.0] || sum__dfg(add(additive_inverse(u),c),u,d)* -> .
% 185.57/185.84 105151[3:Rew:298.0,105141.0] || sum__dfg(add(c,additive_inverse(u)),u,d)* -> .
% 185.57/185.84 105491[3:Res:12989.1,105151.0] || sum__dfg(u,d,add(c,additive_inverse(additive_inverse(u))))* -> .
% 185.57/185.84 105494[3:Rew:3296.0,105491.0] || sum__dfg(u,d,add(c,u))* -> .
% 185.57/185.84 105495[3:SpL:298.0,105494.0] || sum__dfg(u,d,add(u,c))* -> .
% 185.57/185.84 107643[0:Res:19.1,56422.0] || -> equal(d,additive_identity) product(h(d),additive_identity,a)*.
% 185.57/185.84 107646[4:Spt:107643.0] || -> equal(d,additive_identity)**.
% 185.57/185.84 107647[4:Rew:107646.0,21.0] || -> sum__dfg(b,c,additive_identity)*.
% 185.57/185.84 107686[4:Rew:107646.0,16316.0] || -> equal(add(additive_identity,additive_inverse(c)),b)**.
% 185.57/185.84 107738[4:Rew:107646.0,105495.0] || sum__dfg(u,additive_identity,add(u,c))* -> .
% 185.57/185.84 108199[4:Rew:107646.0,16119.2] || product(u,c,v) product(u,b,w) -> sum__dfg(w,v,multiply(u,additive_identity))*.
% 185.57/185.84 108316[4:Rew:107646.0,16196.0] || product(u,additive_identity,v) -> product(v,a,multiply(u,additive_identity))*.
% 185.57/185.84 108813[4:Rew:153.0,107686.0] || -> equal(additive_inverse(c),b)**.
% 185.57/185.84 109517[4:SpR:108813.0,5461.0] || -> sum__dfg(additive_inverse(u),b,additive_inverse(add(c,u)))*.
% 185.57/185.84 110471[4:Res:3166.1,107738.0] || sum__dfg(u,additive_inverse(c),u)* -> .
% 185.57/185.84 110472[4:Rew:108813.0,110471.0] || sum__dfg(u,b,u)* -> .
% 185.57/185.84 112872[4:SpR:5761.0,109517.0] || -> sum__dfg(add(u,additive_inverse(v)),b,additive_inverse(add(c,add(additive_inverse(u),v))))*.
% 185.57/185.84 113991[0:Res:19.1,57523.0] || -> equal(c,additive_identity) product(n,h(c),a)*.
% 185.57/185.84 113993[5:Spt:113991.0] || -> equal(c,additive_identity)**.
% 185.57/185.84 115384[5:Rew:113993.0,112872.0] || -> sum__dfg(add(u,additive_inverse(v)),b,additive_inverse(add(additive_identity,add(additive_inverse(u),v))))*.
% 185.57/185.84 116525[5:Rew:5761.0,115384.0,153.0,115384.0] || -> sum__dfg(add(u,additive_inverse(v)),b,add(u,additive_inverse(v)))*.
% 185.57/185.84 116526[5:MRR:116525.0,110472.0] || -> .
% 185.57/185.84 117641[5:Spt:116526.0,113991.0,113993.0] || equal(c,additive_identity)** -> .
% 185.57/185.84 117642[5:Spt:116526.0,113991.1] || -> product(n,h(c),a)*.
% 185.57/185.84 124025[4:Res:108316.1,57004.0] || product(u,additive_identity,multiply(u,additive_identity))* -> equal(multiply(u,additive_identity),additive_identity) product(multiplicative_identity,a,multiplicative_identity).
% 185.57/185.84 124052[4:MRR:124025.0,3.0] || -> equal(multiply(u,additive_identity),additive_identity)** product(multiplicative_identity,a,multiplicative_identity)*.
% 185.57/185.84 124057[6:Spt:124052.1] || -> product(multiplicative_identity,a,multiplicative_identity)*.
% 185.57/185.84 124058[6:MRR:57412.0,124057.0] || -> equal(l,b)**.
% 185.57/185.84 124061[6:MRR:57308.0,124057.0] || -> equal(n,c)**.
% 185.57/185.84 124168[6:Rew:124058.0,25.0] || sum__dfg(b,n,additive_identity)* -> .
% 185.57/185.84 125700[6:Rew:124061.0,124168.0] || sum__dfg(b,c,additive_identity)* -> .
% 185.57/185.84 125701[6:MRR:125700.0,107647.0] || -> .
% 185.57/185.84 127913[6:Spt:125701.0,124052.1,124057.0] || product(multiplicative_identity,a,multiplicative_identity)* -> .
% 185.57/185.84 127914[6:Spt:125701.0,124052.0] || -> equal(multiply(u,additive_identity),additive_identity)**.
% 185.57/185.84 127937[6:Rew:127914.0,108199.2] || product(u,c,v)*+ product(u,b,w)* -> sum__dfg(w,v,additive_identity)*.
% 185.57/185.84 145341[6:Res:31.0,127937.0] || product(a,b,u)* -> sum__dfg(u,n,additive_identity).
% 185.57/185.84 145380[6:Res:56329.1,145341.0] || product(u,multiplicative_identity,a) -> sum__dfg(multiply(u,b),n,additive_identity)*.
% 185.57/185.84 145393[6:Rew:85321.1,145380.1] || product(u,multiplicative_identity,a)* -> sum__dfg(l,n,additive_identity).
% 185.57/185.84 145394[6:MRR:145393.1,25.0] || product(u,multiplicative_identity,a)* -> .
% 185.57/185.84 145395[6:UnC:145394.0,16.0] || -> .
% 185.57/185.84 145402[4:Spt:145395.0,107643.0,107646.0] || equal(d,additive_identity)** -> .
% 185.57/185.84 145403[4:Spt:145395.0,107643.1] || -> product(h(d),additive_identity,a)*.
% 185.57/185.84 145521[4:Res:145403.0,20.0] || -> product(additive_identity,h(d),a)*.
% 185.57/185.84 145883[4:Res:145521.0,15.0] || product(additive_identity,h(d),u)* -> equal(u,a).
% 188.37/188.60 181578[0:Res:22.0,17904.0] || product(d,additive_identity,u)* -> sum__dfg(u,additive_identity,additive_identity).
% 188.37/188.60 198486[4:Res:56393.2,145883.0] || product(u,d,additive_identity)* -> equal(d,additive_identity) equal(u,a).
% 188.37/188.60 198497[4:MRR:198486.1,145402.0] || product(u,d,additive_identity)* -> equal(u,a).
% 188.37/188.60 198510[0:Res:3.0,181578.0] || -> sum__dfg(multiply(d,additive_identity),additive_identity,additive_identity)*.
% 188.37/188.60 198519[0:Rew:339.0,198510.0] || -> sum__dfg(multiply(additive_identity,d),additive_identity,additive_identity)*.
% 188.37/188.60 198561[0:Res:198519.0,95.0] || -> equal(multiply(additive_identity,d),additive_identity)**.
% 188.37/188.60 198602[0:SpR:198561.0,3.0] || -> product(additive_identity,d,additive_identity)*.
% 188.37/188.60 198628[4:Res:198602.0,198497.0] || -> equal(a,additive_identity)**.
% 188.37/188.60 198629[4:MRR:198628.0,84238.0] || -> .
% 188.37/188.60 % SZS output end Refutation
% 188.37/188.60 Formulae used in the proof : additive_identity1 additive_identity2 closure_of_multiplication closure_of_addition additive_inverse1 additive_inverse2 associativity_of_addition1 associativity_of_addition2 commutativity_of_addition associativity_of_multiplication1 associativity_of_multiplication2 distributivity1 addition_is_well_defined multiplication_is_well_defined right_multiplicative_identity left_multiplicative_identity clause30 clause31 product_symmetry b_plus_c d_plus_a b_plus_a c_plus_a prove_equation
% 188.37/188.60
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