%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG040-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 155.20s 155.39s
% Output   : Refutation 156.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG040-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n024.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 13:01:06 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 155.20/155.39  
% 155.20/155.39  SPASS V 3.9 
% 155.20/155.39  SPASS beiseite: Proof found.
% 155.20/155.39  % SZS status Theorem
% 155.20/155.39  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 155.20/155.39  SPASS derived 112924 clauses, backtracked 32309 clauses, performed 21 splits and kept 73002 clauses.
% 155.20/155.39  SPASS allocated 142466 KBytes.
% 155.20/155.39  SPASS spent	0:2:34.91 on the problem.
% 155.20/155.39  		0:00:00.04 for the input.
% 155.20/155.39  		0:00:00.00 for the FLOTTER CNF translation.
% 155.20/155.39  		0:00:00.88 for inferences.
% 155.20/155.39  		0:00:09.18 for the backtracking.
% 155.20/155.39  		0:2:23.77 for the reduction.
% 155.20/155.39  
% 155.20/155.39  
% 155.20/155.39  Here is a proof with depth 11, length 284 :
% 155.20/155.39  % SZS output start Refutation
% 155.20/155.39  1[0:Inp] ||  -> product(u,multiplicative_identity,u)*.
% 155.20/155.39  2[0:Inp] ||  -> product(multiplicative_identity,u,u)*.
% 155.20/155.39  3[0:Inp] ||  -> equal(u,additive_identity) product(u,h(u),multiplicative_identity)*.
% 155.20/155.39  4[0:Inp] ||  -> equal(u,additive_identity) product(h(u),u,multiplicative_identity)*.
% 155.20/155.39  5[0:Inp] || product(u,v,w)*+ -> product(v,u,w)*.
% 155.20/155.39  6[0:Inp] ||  -> sum__dfg(b,c,d)*.
% 155.20/155.39  7[0:Inp] ||  -> product(d,a,additive_identity)*.
% 155.20/155.39  8[0:Inp] ||  -> product(b,a,l)*.
% 155.20/155.39  9[0:Inp] ||  -> product(c,a,n)*.
% 155.20/155.39  10[0:Inp] || sum__dfg(l,n,additive_identity)* -> .
% 155.20/155.39  11[0:Inp] ||  -> sum__dfg(additive_identity,u,u)*.
% 155.20/155.39  12[0:Inp] ||  -> sum__dfg(u,additive_identity,u)*.
% 155.20/155.39  13[0:Inp] ||  -> product(u,v,multiply(u,v))*.
% 155.20/155.39  14[0:Inp] ||  -> sum__dfg(u,v,add(u,v))*.
% 155.20/155.39  15[0:Inp] ||  -> sum__dfg(additive_inverse(u),u,additive_identity)*.
% 155.20/155.39  16[0:Inp] ||  -> sum__dfg(u,additive_inverse(u),additive_identity)*.
% 155.20/155.39  17[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,v,y)* sum__dfg(z,x,u)* -> sum__dfg(z,y,w)*.
% 155.20/155.39  18[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*.
% 155.20/155.39  19[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*.
% 155.20/155.39  20[0:Inp] || product(u,v,w)*+ product(x,v,y)* product(z,x,u)* -> product(z,y,w)*.
% 155.20/155.39  21[0:Inp] || product(u,v,w)*+ product(x,y,v)* product(u,x,z)* -> product(z,y,w)*.
% 155.20/155.39  24[0:Inp] || product(u,v,w)*+ sum__dfg(x,y,u)* product(y,v,z)* product(x,v,x1)* -> sum__dfg(x1,z,w)*.
% 155.20/155.39  26[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(u,v,x)* -> equal(x,w)*.
% 155.20/155.39  27[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equal(x,w)*.
% 155.20/155.39  32[0:Res:9.0,20.0] || product(n,u,v)*+ product(a,u,w)* -> product(c,w,v)*.
% 155.20/155.39  33[0:Res:9.0,21.0] || product(c,u,v)*+ product(a,w,u)* -> product(n,w,v)*.
% 155.20/155.39  34[0:Res:9.0,27.0] || product(c,a,u)* -> equal(n,u).
% 155.20/155.39  37[0:Res:9.0,21.2] || product(u,v,a)*+ product(c,u,w)* -> product(w,v,n)*.
% 155.20/155.39  41[0:Res:9.0,20.1] || product(u,a,v)*+ product(w,c,u)* -> product(w,n,v)*.
% 155.20/155.39  48[0:Res:8.0,24.0] || product(u,a,v)*+ product(w,a,x)* sum__dfg(b,w,u)* -> sum__dfg(l,x,v)*.
% 155.20/155.39  52[0:Res:8.0,21.0] || product(b,u,v)*+ product(a,w,u)* -> product(l,w,v)*.
% 155.20/155.39  53[0:Res:8.0,27.0] || product(b,a,u)* -> equal(l,u).
% 155.20/155.39  54[0:Res:8.0,5.0] ||  -> product(a,b,l)*.
% 155.20/155.39  60[0:Res:8.0,20.1] || product(u,a,v)*+ product(w,b,u)* -> product(w,l,v)*.
% 155.20/155.39  65[0:Res:8.0,24.3] || sum__dfg(u,v,b)*+ product(v,a,w)* product(u,a,x)* -> sum__dfg(x,w,l)*.
% 155.20/155.39  67[0:Res:13.0,53.0] ||  -> equal(multiply(b,a),l)**.
% 155.20/155.39  71[0:Res:13.0,34.0] ||  -> equal(multiply(c,a),n)**.
% 155.20/155.39  79[0:Res:14.0,19.0] ||  -> sum__dfg(u,v,add(v,u))*.
% 155.20/155.39  84[0:Res:7.0,5.0] ||  -> product(a,d,additive_identity)*.
% 155.20/155.39  89[0:Res:13.0,5.0] ||  -> product(u,v,multiply(v,u))*.
% 155.20/155.39  104[0:Res:6.0,26.0] || sum__dfg(b,c,u)* -> equal(u,d).
% 155.20/155.39  106[0:Res:11.0,26.0] || sum__dfg(additive_identity,u,v)* -> equal(v,u).
% 155.20/155.39  107[0:Res:12.0,26.0] || sum__dfg(u,additive_identity,v)* -> equal(v,u).
% 155.20/155.39  108[0:Res:15.0,26.0] || sum__dfg(additive_inverse(u),u,v)* -> equal(v,additive_identity).
% 155.20/155.39  109[0:Res:16.0,26.0] || sum__dfg(u,additive_inverse(u),v)* -> equal(v,additive_identity).
% 155.20/155.39  110[0:Res:14.0,26.0] || sum__dfg(u,v,w)* -> equal(w,add(u,v)).
% 155.20/155.39  113[0:Res:14.0,104.0] ||  -> equal(add(b,c),d)**.
% 155.20/155.39  126[0:Res:7.0,27.0] || product(d,a,u)* -> equal(u,additive_identity).
% 155.20/155.39  130[0:Res:2.0,27.0] || product(multiplicative_identity,u,v)* -> equal(v,u).
% 155.20/155.39  132[0:Res:13.0,27.0] || product(u,v,w)* -> equal(w,multiply(u,v)).
% 155.20/155.39  133[0:Res:89.0,27.0] || product(u,v,w)* -> equal(w,multiply(v,u)).
% 155.20/155.39  134[0:Res:4.1,27.0] || product(h(u),u,v)* -> equal(u,additive_identity) equal(v,multiplicative_identity).
% 155.20/155.39  137[0:Res:13.0,126.0] ||  -> equal(multiply(d,a),additive_identity)**.
% 155.20/155.39  138[0:Res:89.0,126.0] ||  -> equal(multiply(a,d),additive_identity)**.
% 155.20/155.39  151[0:Res:12.0,18.0] || sum__dfg(u,v,additive_identity)*+ sum__dfg(w,u,x)* -> sum__dfg(x,v,w)*.
% 155.20/155.39  152[0:Res:15.0,18.0] || sum__dfg(u,v,w)* sum__dfg(additive_inverse(w),u,x)*+ -> sum__dfg(x,v,additive_identity)*.
% 155.20/155.39  164[0:Res:16.0,106.0] ||  -> equal(additive_inverse(additive_identity),additive_identity)**.
% 155.20/155.39  165[0:Res:14.0,106.0] ||  -> equal(add(additive_identity,u),u)**.
% 155.20/155.39  172[0:Res:11.0,17.0] || sum__dfg(u,v,w)*+ sum__dfg(x,u,additive_identity)* -> sum__dfg(x,w,v)*.
% 155.20/155.39  192[0:Res:13.0,130.0] ||  -> equal(multiply(multiplicative_identity,u),u)**.
% 155.20/155.39  194[0:Res:3.1,130.0] ||  -> equal(additive_identity,multiplicative_identity) equal(h(multiplicative_identity),multiplicative_identity)**.
% 155.20/155.39  203[0:Res:13.0,21.0] || product(u,v,w)*+ product(x,u,y)* -> product(y,v,multiply(x,w))*.
% 155.20/155.39  205[0:Res:4.1,21.0] || product(u,v,w)* product(h(w),u,x)*+ -> equal(w,additive_identity) product(x,v,multiplicative_identity)*.
% 155.20/155.39  214[1:Spt:194.0] ||  -> equal(additive_identity,multiplicative_identity)**.
% 155.20/155.39  217[1:Rew:214.0,12.0] ||  -> sum__dfg(u,multiplicative_identity,u)*.
% 155.20/155.39  218[1:Rew:214.0,10.0] || sum__dfg(l,n,multiplicative_identity)* -> .
% 155.20/155.39  219[1:Rew:214.0,15.0] ||  -> sum__dfg(additive_inverse(u),u,multiplicative_identity)*.
% 155.20/155.39  220[1:Rew:214.0,16.0] ||  -> sum__dfg(u,additive_inverse(u),multiplicative_identity)*.
% 155.20/155.39  223[1:Rew:214.0,3.0] ||  -> equal(u,multiplicative_identity) product(u,h(u),multiplicative_identity)*.
% 155.20/155.39  226[1:Rew:214.0,137.0] ||  -> equal(multiply(d,a),multiplicative_identity)**.
% 155.20/155.39  232[1:Rew:214.0,107.0] || sum__dfg(u,multiplicative_identity,v)* -> equal(v,u).
% 155.20/155.39  234[1:Rew:214.0,109.1] || sum__dfg(u,additive_inverse(u),v)* -> equal(v,multiplicative_identity).
% 155.20/155.39  239[1:Rew:214.0,151.0] || sum__dfg(u,v,multiplicative_identity)*+ sum__dfg(w,u,x)* -> sum__dfg(x,v,w)*.
% 155.20/155.39  242[1:Rew:214.0,172.1] || sum__dfg(u,v,w)*+ sum__dfg(x,u,multiplicative_identity)* -> sum__dfg(x,w,v)*.
% 155.20/155.39  307[0:Res:2.0,20.0] || product(u,v,w)*+ product(x,u,multiplicative_identity)* -> product(x,w,v)*.
% 155.20/155.39  364[0:Res:79.0,110.0] ||  -> equal(add(u,v),add(v,u))*.
% 155.20/155.39  413[0:Res:89.0,132.0] ||  -> equal(multiply(u,v),multiply(v,u))*.
% 155.20/155.39  478[0:Res:8.0,52.0] || product(a,u,a) -> product(l,u,l)*.
% 155.20/155.39  479[0:Res:1.0,52.0] || product(a,u,multiplicative_identity) -> product(l,u,b)*.
% 155.20/155.39  490[0:Res:478.1,5.0] || product(a,u,a)*+ -> product(u,l,l)*.
% 155.20/155.39  501[0:Res:479.1,5.0] || product(a,u,multiplicative_identity)*+ -> product(u,l,b)*.
% 155.20/155.39  512[1:Res:223.1,501.0] ||  -> equal(a,multiplicative_identity) product(h(a),l,b)*.
% 155.20/155.39  522[0:Res:9.0,33.0] || product(a,u,a) -> product(n,u,n)*.
% 155.20/155.39  523[0:Res:1.0,33.0] || product(a,u,multiplicative_identity) -> product(n,u,c)*.
% 155.20/155.39  540[2:Spt:512.0] ||  -> equal(a,multiplicative_identity)**.
% 155.20/155.39  546[2:Rew:540.0,67.0] ||  -> equal(multiply(b,multiplicative_identity),l)**.
% 155.20/155.39  548[2:Rew:540.0,71.0] ||  -> equal(multiply(c,multiplicative_identity),n)**.
% 155.20/155.39  553[2:Rew:540.0,226.0] ||  -> equal(multiply(d,multiplicative_identity),multiplicative_identity)**.
% 155.20/155.39  640[2:Rew:192.0,546.0,413.0,546.0] ||  -> equal(l,b)**.
% 155.20/155.39  641[2:Rew:640.0,218.0] || sum__dfg(b,n,multiplicative_identity)* -> .
% 155.20/155.39  657[2:Rew:192.0,548.0,413.0,548.0] ||  -> equal(n,c)**.
% 155.20/155.39  660[2:Rew:192.0,553.0,413.0,553.0] ||  -> equal(d,multiplicative_identity)**.
% 155.20/155.39  661[2:Rew:660.0,6.0] ||  -> sum__dfg(b,c,multiplicative_identity)*.
% 155.20/155.39  678[2:Rew:657.0,641.0] || sum__dfg(b,c,multiplicative_identity)* -> .
% 155.20/155.39  679[2:MRR:678.0,661.0] ||  -> .
% 155.20/155.39  781[2:Spt:679.0,512.0,540.0] || equal(a,multiplicative_identity)** -> .
% 155.20/155.39  782[2:Spt:679.0,512.1] ||  -> product(h(a),l,b)*.
% 155.20/155.39  1005[0:Res:523.1,5.0] || product(a,u,multiplicative_identity)*+ -> product(u,n,c)*.
% 155.20/155.39  1014[0:Res:522.1,132.0] || product(a,u,a)* -> equal(multiply(n,u),n).
% 155.20/155.39  1029[0:Res:13.0,32.0] || product(a,u,v) -> product(c,v,multiply(n,u))*.
% 155.20/155.39  1174[0:Res:2.0,60.0] || product(u,b,multiplicative_identity) -> product(u,l,a)*.
% 155.20/155.39  1213[0:Res:2.0,41.0] || product(u,c,multiplicative_identity) -> product(u,n,a)*.
% 155.20/155.39  1283[0:Res:1174.1,5.0] || product(u,b,multiplicative_identity)*+ -> product(l,u,a)*.
% 155.20/155.39  1498[0:Res:1213.1,5.0] || product(u,c,multiplicative_identity)*+ -> product(n,u,a)*.
% 155.20/155.39  1587[1:Res:220.0,239.0] || sum__dfg(u,v,w) -> sum__dfg(w,additive_inverse(v),u)*.
% 155.20/155.39  1630[1:Res:219.0,242.0] || sum__dfg(u,additive_inverse(v),multiplicative_identity)* -> sum__dfg(u,multiplicative_identity,v).
% 155.20/155.39  1654[0:Res:13.0,307.0] || product(u,v,multiplicative_identity) -> product(u,multiply(v,w),w)*.
% 155.20/155.39  1655[0:Res:89.0,307.0] || product(u,v,multiplicative_identity) -> product(u,multiply(w,v),w)*.
% 155.20/155.39  1676[0:Res:54.0,307.0] || product(u,a,multiplicative_identity) -> product(u,l,b)*.
% 155.20/155.39  3751[0:Res:89.0,203.0] || product(u,v,w) -> product(w,x,multiply(u,multiply(x,v)))*.
% 155.20/155.39  4232[1:Res:219.0,1630.0] ||  -> sum__dfg(additive_inverse(additive_inverse(u)),multiplicative_identity,u)*.
% 155.20/155.39  4249[1:Res:4232.0,232.0] ||  -> equal(additive_inverse(additive_inverse(u)),u)**.
% 155.20/155.39  8637[1:Res:1587.1,19.0] || sum__dfg(u,v,w) -> sum__dfg(additive_inverse(v),w,u)*.
% 155.20/155.39  8640[1:Res:1587.1,234.0] || sum__dfg(u,v,v)* -> equal(u,multiplicative_identity).
% 155.20/155.39  8871[1:Res:8637.1,8640.0] || sum__dfg(u,v,u)* -> equal(additive_inverse(v),multiplicative_identity).
% 155.20/155.39  8945[1:Res:1587.1,8871.0] || sum__dfg(u,v,u)* -> equal(additive_inverse(additive_inverse(v)),multiplicative_identity).
% 155.20/155.39  8969[1:Rew:4249.0,8945.1] || sum__dfg(u,v,u)* -> equal(v,multiplicative_identity).
% 155.20/155.39  22631[0:Res:2.0,48.0] || product(u,a,v)*+ sum__dfg(b,u,multiplicative_identity)* -> sum__dfg(l,v,a)*.
% 155.20/155.39  22647[0:Res:8.0,48.0] || product(u,a,v)*+ sum__dfg(b,u,b)* -> sum__dfg(l,v,l)*.
% 155.20/155.39  35411[0:Res:1676.1,133.0] || product(u,a,multiplicative_identity)* -> equal(multiply(l,u),b).
% 155.20/155.39  63401[0:Res:2.0,22631.0] || sum__dfg(b,multiplicative_identity,multiplicative_identity) -> sum__dfg(l,a,a)*.
% 155.20/155.39  63434[0:Res:9.0,22631.0] || sum__dfg(b,c,multiplicative_identity) -> sum__dfg(l,n,a)*.
% 155.20/155.39  63560[0:Res:2.0,22647.0] || sum__dfg(b,multiplicative_identity,b) -> sum__dfg(l,a,l)*.
% 155.20/155.39  63590[0:Res:8.0,22647.0] || sum__dfg(b,b,b) -> sum__dfg(l,l,l)*.
% 155.20/155.39  63593[0:Res:9.0,22647.0] || sum__dfg(b,c,b) -> sum__dfg(l,n,l)*.
% 155.20/155.39  63610[1:MRR:63560.0,217.0] ||  -> sum__dfg(l,a,l)*.
% 155.20/155.39  63647[1:Res:63610.0,8969.0] ||  -> equal(a,multiplicative_identity)**.
% 155.20/155.39  63654[2:MRR:63647.0,781.0] ||  -> .
% 155.20/155.39  63675[1:Spt:63654.0,194.0,214.0] || equal(additive_identity,multiplicative_identity)** -> .
% 155.20/155.39  63676[1:Spt:63654.0,194.1] ||  -> equal(h(multiplicative_identity),multiplicative_identity)**.
% 155.20/155.39  63677[0:Rew:413.0,138.0] ||  -> equal(multiply(d,a),additive_identity)**.
% 155.20/155.39  63721[0:Res:84.0,307.0] || product(u,a,multiplicative_identity)* -> product(u,additive_identity,d).
% 155.20/155.39  63734[0:Res:7.0,307.0] || product(u,d,multiplicative_identity)* -> product(u,additive_identity,a).
% 155.20/155.39  63751[0:Res:7.0,48.0] || product(u,a,v)* sum__dfg(b,u,d)* -> sum__dfg(l,v,additive_identity)*.
% 155.20/155.39  63779[0:Res:12.0,65.0] || product(additive_identity,a,u) product(b,a,v) -> sum__dfg(v,u,l)*.
% 155.20/155.39  63952[0:Res:4.1,1498.0] ||  -> equal(c,additive_identity) product(n,h(c),a)*.
% 155.20/155.39  63955[0:Res:4.1,1283.0] ||  -> equal(b,additive_identity) product(l,h(b),a)*.
% 155.20/155.39  63982[0:Res:3.1,20.0] || product(u,h(v),w)*+ product(x,u,v)* -> equal(v,additive_identity) product(x,w,multiplicative_identity)*.
% 155.20/155.39  63998[0:Res:3.1,1005.0] ||  -> equal(a,additive_identity) product(h(a),n,c)*.
% 155.20/155.39  63999[0:Res:3.1,501.0] ||  -> equal(a,additive_identity) product(h(a),l,b)*.
% 155.20/155.39  64058[2:Spt:63952.0] ||  -> equal(c,additive_identity)**.
% 155.20/155.39  64064[2:Rew:64058.0,113.0] ||  -> equal(add(b,additive_identity),d)**.
% 155.20/155.39  64922[2:Rew:64058.0,63593.0] || sum__dfg(b,additive_identity,b) -> sum__dfg(l,n,l)*.
% 155.20/155.39  65020[2:Rew:165.0,64064.0,364.0,64064.0] ||  -> equal(d,b)**.
% 155.20/155.39  65023[2:Rew:65020.0,63677.0] ||  -> equal(multiply(b,a),additive_identity)**.
% 155.20/155.39  65066[2:Rew:67.0,65023.0] ||  -> equal(l,additive_identity)**.
% 155.20/155.39  65125[2:Rew:65066.0,10.0] || sum__dfg(additive_identity,n,additive_identity)* -> .
% 155.20/155.39  65643[2:Rew:65066.0,64922.1] || sum__dfg(b,additive_identity,b)* -> sum__dfg(additive_identity,n,additive_identity).
% 155.20/155.39  65644[2:MRR:65643.0,12.0] ||  -> sum__dfg(additive_identity,n,additive_identity)*.
% 155.20/155.39  65645[2:MRR:65644.0,65125.0] ||  -> .
% 155.20/155.39  66413[2:Spt:65645.0,63952.0,64058.0] || equal(c,additive_identity)** -> .
% 155.20/155.39  66414[2:Spt:65645.0,63952.1] ||  -> product(n,h(c),a)*.
% 155.20/155.39  66428[2:Res:66414.0,5.0] ||  -> product(h(c),n,a)*.
% 155.20/155.39  66654[3:Spt:63998.0] ||  -> equal(a,additive_identity)**.
% 155.20/155.39  66657[3:Rew:66654.0,66414.0] ||  -> product(n,h(c),additive_identity)*.
% 155.20/155.39  66659[3:Rew:66654.0,9.0] ||  -> product(c,additive_identity,n)*.
% 155.20/155.39  66661[3:Rew:66654.0,84.0] ||  -> product(additive_identity,d,additive_identity)*.
% 155.20/155.39  66664[3:Rew:66654.0,71.0] ||  -> equal(multiply(c,additive_identity),n)**.
% 155.20/155.39  66665[3:Rew:66654.0,63677.0] ||  -> equal(multiply(d,additive_identity),additive_identity)**.
% 155.20/155.39  66667[3:Rew:66654.0,66428.0] ||  -> product(h(c),n,additive_identity)*.
% 155.20/155.39  66706[3:Rew:66654.0,1005.0] || product(additive_identity,u,multiplicative_identity)*+ -> product(u,n,c)*.
% 155.20/155.39  66831[3:Rew:66654.0,490.0] || product(additive_identity,u,additive_identity)*+ -> product(u,l,l)*.
% 155.20/155.39  66867[3:Rew:66654.0,35411.0] || product(u,additive_identity,multiplicative_identity)* -> equal(multiply(l,u),b).
% 155.20/155.39  67308[3:Rew:66654.0,63955.1] ||  -> equal(b,additive_identity) product(l,h(b),additive_identity)*.
% 155.20/155.39  67343[3:Rew:66654.0,63434.1] || sum__dfg(b,c,multiplicative_identity) -> sum__dfg(l,n,additive_identity)*.
% 155.20/155.39  67385[3:Rew:66654.0,63734.1] || product(u,d,multiplicative_identity)* -> product(u,additive_identity,additive_identity).
% 155.20/155.39  67415[3:Rew:66654.0,63401.1] || sum__dfg(b,multiplicative_identity,multiplicative_identity) -> sum__dfg(l,additive_identity,additive_identity)*.
% 155.20/155.39  67463[3:Rew:66654.0,37.0] || product(u,v,additive_identity)*+ product(c,u,w)* -> product(w,v,n)*.
% 155.20/155.39  67953[3:Rew:413.0,66664.0] ||  -> equal(multiply(additive_identity,c),n)**.
% 155.20/155.39  67954[3:Rew:413.0,66665.0] ||  -> equal(multiply(additive_identity,d),additive_identity)**.
% 155.20/155.39  67960[3:MRR:67343.1,10.0] || sum__dfg(b,c,multiplicative_identity)* -> .
% 155.20/155.39  68503[4:Spt:67308.0] ||  -> equal(b,additive_identity)**.
% 155.20/155.39  68506[4:Rew:68503.0,113.0] ||  -> equal(add(additive_identity,c),d)**.
% 155.20/155.39  69118[4:Rew:68503.0,67415.0] || sum__dfg(additive_identity,multiplicative_identity,multiplicative_identity) -> sum__dfg(l,additive_identity,additive_identity)*.
% 155.20/155.39  69504[4:Rew:165.0,68506.0] ||  -> equal(d,c)**.
% 155.20/155.39  69508[4:Rew:69504.0,67954.0] ||  -> equal(multiply(additive_identity,c),additive_identity)**.
% 155.20/155.39  69552[4:Rew:67953.0,69508.0] ||  -> equal(n,additive_identity)**.
% 155.20/155.39  69553[4:Rew:69552.0,10.0] || sum__dfg(l,additive_identity,additive_identity)* -> .
% 155.20/155.39  70114[4:MRR:69118.0,11.0] ||  -> sum__dfg(l,additive_identity,additive_identity)*.
% 155.20/155.39  70115[4:MRR:70114.0,69553.0] ||  -> .
% 155.20/155.39  70818[4:Spt:70115.0,67308.0,68503.0] || equal(b,additive_identity)** -> .
% 155.20/155.39  70819[4:Spt:70115.0,67308.1] ||  -> product(l,h(b),additive_identity)*.
% 155.20/155.39  71568[3:Res:66661.0,66831.0] ||  -> product(d,l,l)*.
% 155.20/155.39  71574[3:Res:71568.0,307.0] || product(u,d,multiplicative_identity) -> product(u,l,l)*.
% 155.20/155.39  71583[3:Res:71568.0,5.0] ||  -> product(l,d,l)*.
% 155.20/155.39  71587[3:Res:71583.0,307.0] || product(u,l,multiplicative_identity) -> product(u,l,d)*.
% 155.20/155.39  72116[3:Res:66661.0,67463.0] || product(c,additive_identity,u)*+ -> product(u,d,n)*.
% 155.20/155.39  72398[0:Res:16.0,172.0] || sum__dfg(u,v,additive_identity) -> sum__dfg(u,additive_identity,additive_inverse(v))*.
% 155.20/155.39  72400[0:Res:15.0,172.0] || sum__dfg(u,additive_inverse(v),additive_identity)* -> sum__dfg(u,additive_identity,v).
% 155.20/155.39  72409[0:Res:63590.1,172.0] || sum__dfg(b,b,b)* sum__dfg(u,l,additive_identity) -> sum__dfg(u,l,l)*.
% 155.20/155.39  72665[3:Res:4.1,67385.0] ||  -> equal(d,additive_identity) product(h(d),additive_identity,additive_identity)*.
% 155.20/155.39  72666[5:Spt:72665.0] ||  -> equal(d,additive_identity)**.
% 155.20/155.39  72749[5:Rew:72666.0,71574.0] || product(u,additive_identity,multiplicative_identity) -> product(u,l,l)*.
% 155.20/155.39  73109[5:Rew:72666.0,71587.1] || product(u,l,multiplicative_identity) -> product(u,l,additive_identity)*.
% 155.20/155.39  73711[0:Res:15.0,152.1] || sum__dfg(u,v,u)*+ -> sum__dfg(additive_identity,v,additive_identity)*.
% 155.20/155.39  73862[3:Res:66667.0,205.1] || product(n,u,c)* -> equal(c,additive_identity) product(additive_identity,u,multiplicative_identity).
% 155.20/155.39  73870[3:MRR:73862.1,66413.0] || product(n,u,c)* -> product(additive_identity,u,multiplicative_identity).
% 155.20/155.39  74069[3:Res:66657.0,63982.0] || product(u,n,c)* -> equal(c,additive_identity) product(u,additive_identity,multiplicative_identity).
% 155.20/155.39  74075[3:MRR:74069.1,66413.0] || product(u,n,c)* -> product(u,additive_identity,multiplicative_identity).
% 155.20/155.39  75224[5:Res:72749.1,133.0] || product(u,additive_identity,multiplicative_identity)* -> equal(multiply(l,u),l).
% 156.78/157.06  75242[5:Rew:66867.1,75224.1] || product(u,additive_identity,multiplicative_identity)* -> equal(l,b).
% 156.78/157.06  75912[5:Res:73109.1,134.0] || product(h(l),l,multiplicative_identity)* -> equal(l,additive_identity) equal(additive_identity,multiplicative_identity).
% 156.78/157.06  75935[5:MRR:75912.0,75912.2,4.1,63675.0] ||  -> equal(l,additive_identity)**.
% 156.78/157.06  75940[5:Rew:75935.0,10.0] || sum__dfg(additive_identity,n,additive_identity)* -> .
% 156.78/157.06  75944[5:Rew:75935.0,75242.1] || product(u,additive_identity,multiplicative_identity)* -> equal(b,additive_identity).
% 156.78/157.06  77068[5:MRR:75944.1,70818.0] || product(u,additive_identity,multiplicative_identity)* -> .
% 156.78/157.06  77070[5:MRR:74075.1,77068.0] || product(u,n,c)* -> .
% 156.78/157.06  77071[5:MRR:66706.1,77070.0] || product(additive_identity,u,multiplicative_identity)* -> .
% 156.78/157.06  77073[5:MRR:73870.1,77071.0] || product(n,u,c)* -> .
% 156.78/157.06  77616[5:Res:1654.1,77073.0] || product(n,u,multiplicative_identity)* -> .
% 156.78/157.06  77645[5:Res:3.1,77616.0] ||  -> equal(n,additive_identity)**.
% 156.78/157.06  77705[5:Rew:77645.0,75940.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 156.78/157.06  78461[5:MRR:77705.0,11.0] ||  -> .
% 156.78/157.06  78628[5:Spt:78461.0,72665.0,72666.0] || equal(d,additive_identity)** -> .
% 156.78/157.06  78629[5:Spt:78461.0,72665.1] ||  -> product(h(d),additive_identity,additive_identity)*.
% 156.78/157.06  80222[3:Res:66659.0,72116.0] ||  -> product(n,d,n)*.
% 156.78/157.06  80254[3:Res:80222.0,307.0] || product(u,n,multiplicative_identity) -> product(u,n,d)*.
% 156.78/157.06  80550[3:Res:71587.1,134.0] || product(h(l),l,multiplicative_identity)* -> equal(l,additive_identity) equal(d,multiplicative_identity).
% 156.78/157.06  80557[3:MRR:80550.0,4.1] ||  -> equal(l,additive_identity)** equal(d,multiplicative_identity).
% 156.78/157.06  80594[6:Spt:80557.1] ||  -> equal(d,multiplicative_identity)**.
% 156.78/157.06  80601[6:Rew:80594.0,6.0] ||  -> sum__dfg(b,c,multiplicative_identity)*.
% 156.78/157.06  81491[6:MRR:80601.0,67960.0] ||  -> .
% 156.78/157.06  81826[6:Spt:81491.0,80557.1,80594.0] || equal(d,multiplicative_identity)** -> .
% 156.78/157.06  81827[6:Spt:81491.0,80557.0] ||  -> equal(l,additive_identity)**.
% 156.78/157.06  81830[6:Rew:81827.0,10.0] || sum__dfg(additive_identity,n,additive_identity)* -> .
% 156.78/157.06  85417[3:Res:80254.1,134.0] || product(h(n),n,multiplicative_identity)* -> equal(n,additive_identity) equal(d,multiplicative_identity).
% 156.78/157.06  85426[6:MRR:85417.0,85417.2,4.1,81826.0] ||  -> equal(n,additive_identity)**.
% 156.78/157.06  85455[6:Rew:85426.0,81830.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 156.78/157.06  86549[6:MRR:85455.0,11.0] ||  -> .
% 156.78/157.06  86949[3:Spt:86549.0,63998.0,66654.0] || equal(a,additive_identity)** -> .
% 156.78/157.06  86950[3:Spt:86549.0,63998.1] ||  -> product(h(a),n,c)*.
% 156.78/157.06  86951[3:MRR:63999.0,86949.0] ||  -> product(h(a),l,b)*.
% 156.78/157.06  86973[3:Res:86950.0,27.0] || product(h(a),n,u)* -> equal(u,c).
% 156.78/157.06  86974[3:Res:86950.0,5.0] ||  -> product(n,h(a),c)*.
% 156.78/157.06  87068[2:Res:66428.0,205.1] || product(n,u,c)* -> equal(c,additive_identity) product(a,u,multiplicative_identity).
% 156.78/157.06  87070[2:MRR:87068.1,66413.0] || product(n,u,c)* -> product(a,u,multiplicative_identity).
% 156.78/157.06  87154[3:Res:86951.0,27.0] || product(h(a),l,u)* -> equal(u,b).
% 156.78/157.06  87269[4:Spt:63955.0] ||  -> equal(b,additive_identity)**.
% 156.78/157.06  87277[4:Rew:87269.0,113.0] ||  -> equal(add(additive_identity,c),d)**.
% 156.78/157.06  87665[4:Rew:87269.0,87154.1] || product(h(a),l,u)* -> equal(u,additive_identity).
% 156.78/157.06  88065[4:Rew:87269.0,72409.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* sum__dfg(u,l,additive_identity) -> sum__dfg(u,l,l)*.
% 156.78/157.06  88578[4:Rew:165.0,87277.0] ||  -> equal(d,c)**.
% 156.78/157.06  88581[4:Rew:88578.0,63677.0] ||  -> equal(multiply(c,a),additive_identity)**.
% 156.78/157.06  88625[4:Rew:71.0,88581.0] ||  -> equal(n,additive_identity)**.
% 156.78/157.06  89195[4:Rew:88625.0,86973.0] || product(h(a),additive_identity,u)* -> equal(u,c).
% 156.78/157.06  89427[4:MRR:88065.0,11.0] || sum__dfg(u,l,additive_identity) -> sum__dfg(u,l,l)*.
% 156.78/157.06  91076[4:Res:3751.1,87665.0] || product(u,v,h(a)) -> equal(multiply(u,multiply(l,v)),additive_identity)**.
% 156.78/157.06  92227[4:Res:3751.1,89195.0] || product(u,v,h(a)) -> equal(multiply(u,multiply(additive_identity,v)),c)**.
% 156.78/157.06  92319[4:Res:89427.1,108.0] || sum__dfg(additive_inverse(l),l,additive_identity)* -> equal(l,additive_identity).
% 156.78/157.06  92325[4:MRR:92319.0,15.0] ||  -> equal(l,additive_identity)**.
% 156.78/157.06  93097[4:Rew:92325.0,91076.1] || product(u,v,h(a)) -> equal(multiply(u,multiply(additive_identity,v)),additive_identity)**.
% 156.78/157.06  93389[4:Rew:92227.1,93097.1] || product(u,v,h(a))* -> equal(c,additive_identity).
% 156.78/157.06  93390[4:MRR:93389.1,66413.0] || product(u,v,h(a))* -> .
% 156.78/157.06  93391[4:UnC:93390.0,1.0] ||  -> .
% 156.78/157.06  93557[4:Spt:93391.0,63955.0,87269.0] || equal(b,additive_identity)** -> .
% 156.78/157.06  93558[4:Spt:93391.0,63955.1] ||  -> product(l,h(b),a)*.
% 156.78/157.06  95743[0:Res:4.1,63734.0] ||  -> equal(d,additive_identity) product(h(d),additive_identity,a)*.
% 156.78/157.06  95744[5:Spt:95743.0] ||  -> equal(d,additive_identity)**.
% 156.78/157.06  95745[5:Rew:95744.0,6.0] ||  -> sum__dfg(b,c,additive_identity)*.
% 156.78/157.06  96020[5:Rew:95744.0,63751.1] || product(u,a,v)*+ sum__dfg(b,u,additive_identity)* -> sum__dfg(l,v,additive_identity)*.
% 156.78/157.06  96874[3:Res:86974.0,87070.0] ||  -> product(a,h(a),multiplicative_identity)*.
% 156.78/157.06  96888[3:Res:96874.0,5.0] ||  -> product(h(a),a,multiplicative_identity)*.
% 156.78/157.06  99395[0:Res:72398.1,107.0] || sum__dfg(u,v,additive_identity)* -> equal(additive_inverse(v),u).
% 156.78/157.06  99474[0:Res:15.0,72400.0] ||  -> sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u)*.
% 156.78/157.06  99506[0:Res:99474.0,107.0] ||  -> equal(additive_inverse(additive_inverse(u)),u)**.
% 156.78/157.06  132680[0:Res:63779.2,73711.0] || product(additive_identity,a,u) product(b,a,l) -> sum__dfg(additive_identity,u,additive_identity)*.
% 156.78/157.06  132713[0:MRR:132680.1,8.0] || product(additive_identity,a,u) -> sum__dfg(additive_identity,u,additive_identity)*.
% 156.78/157.06  133690[0:Res:132713.1,99395.0] || product(additive_identity,a,u)* -> equal(additive_inverse(u),additive_identity).
% 156.78/157.06  134430[0:Res:13.0,133690.0] ||  -> equal(additive_inverse(multiply(additive_identity,a)),additive_identity)**.
% 156.78/157.06  134900[5:Res:1029.1,96020.0] || product(a,u,a) sum__dfg(b,c,additive_identity) -> sum__dfg(l,multiply(n,u),additive_identity)*.
% 156.78/157.06  134946[5:Rew:1014.1,134900.2] || product(a,u,a)* sum__dfg(b,c,additive_identity) -> sum__dfg(l,n,additive_identity)*.
% 156.78/157.06  134947[5:MRR:134946.1,134946.2,95745.0,10.0] || product(a,u,a)* -> .
% 156.78/157.06  134948[5:UnC:134947.0,1.0] ||  -> .
% 156.78/157.06  134949[5:Spt:134948.0,95743.0,95744.0] || equal(d,additive_identity)** -> .
% 156.78/157.06  134950[5:Spt:134948.0,95743.1] ||  -> product(h(d),additive_identity,a)*.
% 156.78/157.06  135397[0:SpR:134430.0,99506.0] ||  -> equal(multiply(additive_identity,a),additive_inverse(additive_identity))**.
% 156.78/157.06  135440[0:Rew:164.0,135397.0] ||  -> equal(multiply(additive_identity,a),additive_identity)**.
% 156.78/157.06  135518[0:SpR:135440.0,1655.1] || product(u,a,multiplicative_identity)* -> product(u,additive_identity,additive_identity).
% 156.78/157.06  136941[3:Res:96888.0,63721.0] ||  -> product(h(a),additive_identity,d)*.
% 156.78/157.06  136948[3:Res:136941.0,133.0] ||  -> equal(multiply(additive_identity,h(a)),d)**.
% 156.78/157.06  147313[3:Res:96888.0,135518.0] ||  -> product(h(a),additive_identity,additive_identity)*.
% 156.78/157.06  147338[3:Res:147313.0,132.0] ||  -> equal(multiply(h(a),additive_identity),additive_identity)**.
% 156.78/157.06  147350[3:Rew:136948.0,147338.0,413.0,147338.0] ||  -> equal(d,additive_identity)**.
% 156.78/157.06  147351[5:MRR:147350.0,134949.0] ||  -> .
% 156.78/157.06  % SZS output end Refutation
% 156.78/157.06  Formulae used in the proof : right_multiplicative_identity left_multiplicative_identity clause30 clause31 product_symmetry b_plus_c d_plus_a b_plus_a c_plus_a prove_equation additive_identity1 additive_identity2 closure_of_multiplication closure_of_addition left_inverse right_inverse associativity_of_addition1 associativity_of_addition2 commutativity_of_addition associativity_of_multiplication1 associativity_of_multiplication2 distributivity3 addition_is_well_defined multiplication_is_well_defined
% 156.78/157.06  
%------------------------------------------------------------------------------