%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD028-3 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n028.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 02:28:22 EDT 2022 % Result : Unsatisfiable 26.66s 26.90s % Output : Refutation 27.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : FLD028-3 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.13/0.14 % Command : run_spass %d %s % 0.14/0.36 % Computer : n028.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Mon Jun 6 16:21:44 EDT 2022 % 0.14/0.36 % CPUTime : % 26.66/26.90 % 26.66/26.90 SPASS V 3.9 % 26.66/26.90 SPASS beiseite: Proof found. % 26.66/26.90 % SZS status Theorem % 26.66/26.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 26.66/26.90 SPASS derived 17749 clauses, backtracked 581 clauses, performed 8 splits and kept 11880 clauses. % 26.66/26.90 SPASS allocated 91728 KBytes. % 26.66/26.90 SPASS spent 0:0:26.51 on the problem. % 26.66/26.90 0:00:00.03 for the input. % 26.66/26.90 0:00:00.00 for the FLOTTER CNF translation. % 26.66/26.90 0:00:00.18 for inferences. % 26.66/26.90 0:00:01.53 for the backtracking. % 26.66/26.90 0:0:24.48 for the reduction. % 26.66/26.90 % 26.66/26.90 % 26.66/26.90 Here is a proof with depth 18, length 158 : % 26.66/26.90 % SZS output start Refutation % 26.66/26.90 1[0:Inp] || -> defined(a)*. % 26.66/26.90 2[0:Inp] || -> defined(b)*. % 26.66/26.90 3[0:Inp] || -> defined(u__dfg)*. % 26.66/26.90 4[0:Inp] || -> defined(v__dfg)*. % 26.66/26.90 5[0:Inp] || sum__dfg(additive_identity,a,additive_identity)* -> . % 26.66/26.90 6[0:Inp] || -> product(a,u__dfg,b)*. % 26.66/26.90 7[0:Inp] || -> product(a,v__dfg,b)*. % 26.66/26.90 8[0:Inp] || product(multiplicative_identity,u__dfg,v__dfg)* -> . % 26.66/26.90 9[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,v,y)* sum__dfg(z,x,u)* -> sum__dfg(z,y,w)*. % 26.66/26.90 10[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*. % 26.66/26.90 11[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*. % 26.66/26.90 12[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*. % 26.66/26.90 13[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 26.66/26.90 14[0:Inp] || product(u,v,w)*+ product(x,v,y)* product(z,x,u)* -> product(z,y,w)*. % 26.66/26.90 15[0:Inp] || product(u,v,w)*+ product(x,y,v)* product(u,x,z)* -> product(z,y,w)*. % 26.66/26.90 16[0:Inp] defined(u) || -> product(multiplicative_identity,u,u)*. % 26.66/26.90 17[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,additive_identity) product(multiplicative_inverse(u),u,multiplicative_identity)*. % 26.66/26.90 18[0:Inp] || product(u,v,w)*+ -> product(v,u,w)*. % 26.66/26.90 20[0:Inp] || sum__dfg(u,v,w)*+ product(x,y,v)* product(z,y,u)* sum__dfg(z,x,x1)* -> product(x1,y,w)*. % 26.66/26.90 22[0:Inp] || -> defined(additive_identity)*. % 26.66/26.90 23[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 26.66/26.90 25[0:Inp] || -> defined(multiplicative_identity)*. % 26.66/26.90 26[0:Inp] defined(u) || -> defined(multiplicative_inverse(u)) sum__dfg(additive_identity,u,additive_identity)*. % 26.66/26.90 34[0:Inp] || sum__dfg(additive_identity,additive_identity,multiplicative_identity)* -> . % 26.66/26.90 37[0:Res:7.0,15.0] || product(a,u,v)*+ product(v__dfg,w,u)* -> product(b,w,v)*. % 26.66/26.90 38[0:Res:7.0,18.0] || -> product(v__dfg,a,b)*. % 26.66/26.90 40[0:Res:7.0,14.1] || product(u,v__dfg,v)*+ product(w,a,u)* -> product(w,b,v)*. % 26.66/26.90 50[0:Res:6.0,15.0] || product(a,u,v)*+ product(u__dfg,w,u)* -> product(b,w,v)*. % 26.66/26.90 51[0:Res:6.0,18.0] || -> product(u__dfg,a,b)*. % 26.66/26.90 53[0:Res:6.0,14.1] || product(u,u__dfg,v)*+ product(w,a,u)* -> product(w,b,v)*. % 26.66/26.90 62[0:Res:14.3,8.0] || product(u,v,v__dfg)*+ product(w,v,u__dfg)* product(multiplicative_identity,w,u)* -> . % 26.66/26.90 63[0:Res:15.3,8.0] || product(u,v,v__dfg)*+ product(u,w,multiplicative_identity)* product(w,u__dfg,v)* -> . % 26.66/26.90 65[0:Res:17.2,5.0] defined(a) || -> product(multiplicative_inverse(a),a,multiplicative_identity)*. % 26.66/26.90 73[0:MRR:65.0,1.0] || -> product(multiplicative_inverse(a),a,multiplicative_identity)*. % 26.66/26.90 85[0:Res:11.1,13.0] defined(u) || -> sum__dfg(u,additive_identity,u)*. % 26.66/26.90 94[0:Res:16.1,18.0] defined(u) || -> product(u,multiplicative_identity,u)*. % 26.66/26.90 101[0:Res:17.2,18.0] defined(u) || -> sum__dfg(additive_identity,u,additive_identity) product(u,multiplicative_inverse(u),multiplicative_identity)*. % 26.66/26.90 108[0:Res:6.0,50.0] || product(u__dfg,u,u__dfg) -> product(b,u,b)*. % 26.66/26.90 111[0:Res:94.1,50.0] defined(a) || product(u__dfg,u,multiplicative_identity) -> product(b,u,a)*. % 26.66/26.90 114[0:SSi:111.0,1.0] || product(u__dfg,u,multiplicative_identity) -> product(b,u,a)*. % 26.66/26.90 119[0:Res:12.1,10.0] defined(u) || sum__dfg(v,w,u)* sum__dfg(additive_inverse(u),v,x)*+ -> sum__dfg(x,w,additive_identity)*. % 26.66/26.90 126[0:Res:108.1,18.0] || product(u__dfg,u,u__dfg)*+ -> product(u,b,b)*. % 26.66/26.90 127[0:Res:114.1,18.0] || product(u__dfg,u,multiplicative_identity)*+ -> product(u,b,a)*. % 26.66/26.90 128[0:Res:94.1,126.0] defined(u__dfg) || -> product(multiplicative_identity,b,b)*. % 26.66/26.90 129[0:SSi:128.0,3.0] || -> product(multiplicative_identity,b,b)*. % 26.66/26.90 130[0:Res:11.1,9.0] defined(u) || sum__dfg(v,u,w)*+ sum__dfg(x,v,additive_identity)* -> sum__dfg(x,w,u)*. % 26.66/26.90 140[0:Res:101.2,127.0] defined(u__dfg) || -> sum__dfg(additive_identity,u__dfg,additive_identity) product(multiplicative_inverse(u__dfg),b,a)*. % 26.66/26.90 141[0:SSi:140.0,3.0] || -> sum__dfg(additive_identity,u__dfg,additive_identity) product(multiplicative_inverse(u__dfg),b,a)*. % 26.66/26.90 142[0:Res:141.1,18.0] || -> sum__dfg(additive_identity,u__dfg,additive_identity) product(b,multiplicative_inverse(u__dfg),a)*. % 26.66/26.90 152[0:Res:17.2,15.0] defined(u) || product(v,w,u)* product(multiplicative_inverse(u),v,x)*+ -> sum__dfg(additive_identity,u,additive_identity) product(x,w,multiplicative_identity)*. % 26.66/26.90 155[0:Res:16.1,15.0] defined(u) || product(v,w,u)*+ product(multiplicative_identity,v,x)* -> product(x,w,u)*. % 26.66/26.90 161[1:Spt:142.0] || -> sum__dfg(additive_identity,u__dfg,additive_identity)*. % 26.66/26.90 164[1:Res:161.0,13.0] || -> sum__dfg(u__dfg,additive_identity,additive_identity)*. % 26.66/26.90 182[0:Res:16.1,14.0] defined(u) || product(v,u,w)*+ product(x,v,multiplicative_identity)* -> product(x,w,u)*. % 26.66/26.90 300[0:Res:12.1,20.0] defined(u) || product(v,w,u)* product(x,w,additive_inverse(u))*+ sum__dfg(x,v,y)* -> product(y,w,additive_identity)*. % 26.66/26.90 347[0:Res:94.1,37.0] defined(a) || product(v__dfg,u,multiplicative_identity) -> product(b,u,a)*. % 26.66/26.90 357[0:SSi:347.0,1.0] || product(v__dfg,u,multiplicative_identity) -> product(b,u,a)*. % 26.66/26.90 405[0:Res:357.1,18.0] || product(v__dfg,u,multiplicative_identity)*+ -> product(u,b,a)*. % 26.66/26.90 429[0:Res:101.2,405.0] defined(v__dfg) || -> sum__dfg(additive_identity,v__dfg,additive_identity) product(multiplicative_inverse(v__dfg),b,a)*. % 26.66/26.90 430[0:SSi:429.0,4.0] || -> sum__dfg(additive_identity,v__dfg,additive_identity) product(multiplicative_inverse(v__dfg),b,a)*. % 26.66/26.90 434[0:Res:430.1,18.0] || -> sum__dfg(additive_identity,v__dfg,additive_identity) product(b,multiplicative_inverse(v__dfg),a)*. % 26.66/26.90 436[2:Spt:434.0] || -> sum__dfg(additive_identity,v__dfg,additive_identity)*. % 26.66/26.90 499[0:Res:16.1,53.0] defined(u__dfg) || product(u,a,multiplicative_identity)* -> product(u,b,u__dfg). % 26.66/26.90 510[0:SSi:499.0,3.0] || product(u,a,multiplicative_identity)* -> product(u,b,u__dfg). % 26.66/26.90 583[0:Res:16.1,40.0] defined(v__dfg) || product(u,a,multiplicative_identity)* -> product(u,b,v__dfg). % 26.66/26.90 594[0:SSi:583.0,4.0] || product(u,a,multiplicative_identity)* -> product(u,b,v__dfg). % 26.66/26.90 615[0:Res:73.0,510.0] || -> product(multiplicative_inverse(a),b,u__dfg)*. % 26.66/26.90 670[0:Res:73.0,594.0] || -> product(multiplicative_inverse(a),b,v__dfg)*. % 26.66/26.90 787[0:Res:94.1,62.0] defined(v__dfg) || product(u,multiplicative_identity,u__dfg)* product(multiplicative_identity,u,v__dfg)* -> . % 26.66/26.90 790[0:SSi:787.0,4.0] || product(u,multiplicative_identity,u__dfg)*+ product(multiplicative_identity,u,v__dfg)* -> . % 26.66/26.90 852[0:Res:94.1,63.0] defined(v__dfg) || product(v__dfg,u,multiplicative_identity)* product(u,u__dfg,multiplicative_identity)* -> . % 26.66/26.90 855[0:SSi:852.0,4.0] || product(v__dfg,u,multiplicative_identity)*+ product(u,u__dfg,multiplicative_identity)* -> . % 26.66/26.90 949[1:Res:164.0,130.1] defined(additive_identity) || sum__dfg(u,u__dfg,additive_identity)* -> sum__dfg(u,additive_identity,additive_identity). % 26.66/26.90 955[1:Res:161.0,130.1] defined(u__dfg) || sum__dfg(u,additive_identity,additive_identity) -> sum__dfg(u,additive_identity,u__dfg)*. % 26.66/26.90 956[2:Res:436.0,130.1] defined(v__dfg) || sum__dfg(u,additive_identity,additive_identity) -> sum__dfg(u,additive_identity,v__dfg)*. % 26.66/26.90 960[1:SSi:949.0,22.0] || sum__dfg(u,u__dfg,additive_identity)* -> sum__dfg(u,additive_identity,additive_identity). % 26.66/26.90 962[1:SSi:955.0,3.0] || sum__dfg(u,additive_identity,additive_identity) -> sum__dfg(u,additive_identity,u__dfg)*. % 26.66/26.90 963[2:SSi:956.0,4.0] || sum__dfg(u,additive_identity,additive_identity) -> sum__dfg(u,additive_identity,v__dfg)*. % 26.66/26.90 1059[0:Res:94.1,155.1] defined(u) defined(u) || product(multiplicative_identity,u,v)* -> product(v,multiplicative_identity,u)*. % 26.66/26.90 1120[0:Obv:1059.0] defined(u) || product(multiplicative_identity,u,v)*+ -> product(v,multiplicative_identity,u)*. % 26.66/26.90 1193[0:Res:51.0,182.1] defined(a) || product(u,u__dfg,multiplicative_identity) -> product(u,b,a)*. % 26.66/26.90 1194[0:Res:38.0,182.1] defined(a) || product(u,v__dfg,multiplicative_identity) -> product(u,b,a)*. % 26.66/26.90 1208[0:Res:129.0,182.1] defined(b) || product(u,multiplicative_identity,multiplicative_identity) -> product(u,b,b)*. % 26.66/26.90 1264[0:SSi:1193.0,1.0] || product(u,u__dfg,multiplicative_identity) -> product(u,b,a)*. % 26.66/26.90 1265[0:SSi:1194.0,1.0] || product(u,v__dfg,multiplicative_identity) -> product(u,b,a)*. % 26.66/26.90 1266[0:SSi:1208.0,2.0] || product(u,multiplicative_identity,multiplicative_identity) -> product(u,b,b)*. % 26.66/26.90 1496[1:Res:12.1,960.0] defined(u__dfg) || -> sum__dfg(additive_inverse(u__dfg),additive_identity,additive_identity)*. % 26.66/26.90 1500[1:SSi:1496.0,3.0] || -> sum__dfg(additive_inverse(u__dfg),additive_identity,additive_identity)*. % 26.66/26.90 1514[1:Res:1500.0,119.2] defined(u__dfg) || sum__dfg(additive_identity,u,u__dfg)* -> sum__dfg(additive_identity,u,additive_identity). % 26.66/26.90 1515[1:SSi:1514.0,3.0] || sum__dfg(additive_identity,u,u__dfg)* -> sum__dfg(additive_identity,u,additive_identity). % 26.66/26.90 1609[1:Res:962.1,13.0] || sum__dfg(u,additive_identity,additive_identity)*+ -> sum__dfg(additive_identity,u,u__dfg)*. % 26.66/26.90 1683[2:Res:963.1,13.0] || sum__dfg(u,additive_identity,additive_identity)*+ -> sum__dfg(additive_identity,u,v__dfg)*. % 26.66/26.90 1865[0:Res:1264.1,18.0] || product(u,u__dfg,multiplicative_identity)*+ -> product(b,u,a)*. % 26.66/26.90 1883[0:Res:1265.1,18.0] || product(u,v__dfg,multiplicative_identity)*+ -> product(b,u,a)*. % 26.66/26.90 1929[0:Res:1266.1,18.0] || product(u,multiplicative_identity,multiplicative_identity)*+ -> product(b,u,b)*. % 26.66/26.90 1957[1:Res:12.1,1609.0] defined(additive_identity) || -> sum__dfg(additive_identity,additive_inverse(additive_identity),u__dfg)*. % 26.66/26.90 1963[1:SSi:1957.0,22.0] || -> sum__dfg(additive_identity,additive_inverse(additive_identity),u__dfg)*. % 26.66/26.90 2048[1:Res:1963.0,1515.0] || -> sum__dfg(additive_identity,additive_inverse(additive_identity),additive_identity)*. % 26.66/26.90 2052[1:Res:1963.0,13.0] || -> sum__dfg(additive_inverse(additive_identity),additive_identity,u__dfg)*. % 26.66/26.90 2085[1:Res:2048.0,13.0] || -> sum__dfg(additive_inverse(additive_identity),additive_identity,additive_identity)*. % 26.66/26.90 2616[0:Res:615.0,152.2] defined(a) || product(b,u,a)* -> sum__dfg(additive_identity,a,additive_identity) product(u__dfg,u,multiplicative_identity). % 26.66/26.90 2617[0:Res:670.0,152.2] defined(a) || product(b,u,a)* -> sum__dfg(additive_identity,a,additive_identity) product(v__dfg,u,multiplicative_identity). % 26.66/26.90 2620[0:SSi:2616.0,1.0] || product(b,u,a)* -> sum__dfg(additive_identity,a,additive_identity) product(u__dfg,u,multiplicative_identity). % 26.66/26.90 2621[0:MRR:2620.1,5.0] || product(b,u,a)* -> product(u__dfg,u,multiplicative_identity). % 26.66/26.90 2622[0:SSi:2617.0,1.0] || product(b,u,a)* -> sum__dfg(additive_identity,a,additive_identity) product(v__dfg,u,multiplicative_identity). % 26.66/26.90 2623[0:MRR:2622.1,5.0] || product(b,u,a)* -> product(v__dfg,u,multiplicative_identity). % 26.66/26.90 3592[2:Res:2085.0,1683.0] || -> sum__dfg(additive_identity,additive_inverse(additive_identity),v__dfg)*. % 26.66/26.90 3771[2:Res:3592.0,13.0] || -> sum__dfg(additive_inverse(additive_identity),additive_identity,v__dfg)*. % 26.66/26.90 4060[0:Res:94.1,300.2] defined(additive_inverse(u)) defined(u) || product(v,multiplicative_identity,u) sum__dfg(additive_inverse(u),v,w)* -> product(w,multiplicative_identity,additive_identity). % 26.66/26.90 4061[0:SSi:4060.0,23.1] defined(u) || product(v,multiplicative_identity,u) sum__dfg(additive_inverse(u),v,w)* -> product(w,multiplicative_identity,additive_identity). % 26.66/26.90 4080[0:Res:17.2,1865.0] defined(u__dfg) || -> sum__dfg(additive_identity,u__dfg,additive_identity) product(b,multiplicative_inverse(u__dfg),a)*. % 26.66/26.90 4081[0:Res:17.2,1883.0] defined(v__dfg) || -> sum__dfg(additive_identity,v__dfg,additive_identity) product(b,multiplicative_inverse(v__dfg),a)*. % 26.66/26.90 4082[0:Res:17.2,1929.0] defined(multiplicative_identity) || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity) product(b,multiplicative_inverse(multiplicative_identity),b)*. % 26.66/26.90 4085[0:SSi:4082.0,25.0] || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity) product(b,multiplicative_inverse(multiplicative_identity),b)*. % 26.66/26.90 4250[0:Res:4085.1,18.0] || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity) product(multiplicative_inverse(multiplicative_identity),b,b)*. % 26.66/26.90 4262[3:Spt:4250.0] || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity)*. % 26.66/26.90 4269[3:Res:4262.0,130.1] defined(multiplicative_identity) || sum__dfg(u,additive_identity,additive_identity)* -> sum__dfg(u,additive_identity,multiplicative_identity). % 26.66/26.90 4276[3:SSi:4269.0,25.0] || sum__dfg(u,additive_identity,additive_identity)* -> sum__dfg(u,additive_identity,multiplicative_identity). % 26.66/26.90 5261[0:Res:357.1,2621.0] || product(v__dfg,u,multiplicative_identity) -> product(u__dfg,u,multiplicative_identity)*. % 26.66/26.90 5813[3:Res:85.1,4276.0] defined(additive_identity) || -> sum__dfg(additive_identity,additive_identity,multiplicative_identity)*. % 26.66/26.90 5819[3:SSi:5813.0,22.0] || -> sum__dfg(additive_identity,additive_identity,multiplicative_identity)*. % 26.66/26.90 5820[3:MRR:5819.0,34.0] || -> . % 26.66/26.90 5825[3:Spt:5820.0,4250.0,4262.0] || sum__dfg(additive_identity,multiplicative_identity,additive_identity)* -> . % 26.66/26.90 5826[3:Spt:5820.0,4250.1] || -> product(multiplicative_inverse(multiplicative_identity),b,b)*. % 26.66/26.90 5867[3:Res:26.2,5825.0] defined(multiplicative_identity) || -> defined(multiplicative_inverse(multiplicative_identity))*. % 26.66/26.90 5868[3:SSi:5867.0,25.0] || -> defined(multiplicative_inverse(multiplicative_identity))*. % 26.66/26.90 18431[0:Res:5261.1,18.0] || product(v__dfg,u,multiplicative_identity)* -> product(u,u__dfg,multiplicative_identity)*. % 26.66/26.90 18466[0:MRR:18431.1,855.1] || product(v__dfg,u,multiplicative_identity)* -> . % 26.66/26.90 18467[0:MRR:2623.1,18466.0] || product(b,u,a)* -> . % 26.66/26.90 21771[0:Res:12.1,4061.2] defined(u) defined(u) || product(u,multiplicative_identity,u)* -> product(additive_identity,multiplicative_identity,additive_identity)*. % 26.66/26.90 21817[1:Res:2052.0,4061.2] defined(additive_identity) || product(additive_identity,multiplicative_identity,additive_identity) -> product(u__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 21820[2:Res:3771.0,4061.2] defined(additive_identity) || product(additive_identity,multiplicative_identity,additive_identity) -> product(v__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 21899[1:SSi:21817.0,22.0] || product(additive_identity,multiplicative_identity,additive_identity) -> product(u__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 21902[2:SSi:21820.0,22.0] || product(additive_identity,multiplicative_identity,additive_identity) -> product(v__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 21954[0:Obv:21771.0] defined(u) || product(u,multiplicative_identity,u)* -> product(additive_identity,multiplicative_identity,additive_identity)*. % 26.66/26.90 21955[0:MRR:21954.1,94.1] defined(u) || -> product(additive_identity,multiplicative_identity,additive_identity)*. % 26.66/26.90 23384[3:EmS:21955.0,5868.0] || -> product(additive_identity,multiplicative_identity,additive_identity)*. % 26.66/26.90 23393[3:MRR:21899.0,23384.0] || -> product(u__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 23394[3:MRR:21902.0,23384.0] || -> product(v__dfg,multiplicative_identity,additive_identity)*. % 26.66/26.90 23437[3:Res:23393.0,18.0] || -> product(multiplicative_identity,u__dfg,additive_identity)*. % 26.66/26.90 23472[3:Res:23394.0,18.0] || -> product(multiplicative_identity,v__dfg,additive_identity)*. % 26.66/26.90 23606[3:Res:23437.0,1120.1] defined(u__dfg) || -> product(additive_identity,multiplicative_identity,u__dfg)*. % 26.66/26.90 23613[3:SSi:23606.0,3.0] || -> product(additive_identity,multiplicative_identity,u__dfg)*. % 26.66/26.90 23635[3:Res:23472.0,1120.1] defined(v__dfg) || -> product(additive_identity,multiplicative_identity,v__dfg)*. % 26.66/26.90 23649[3:SSi:23635.0,4.0] || -> product(additive_identity,multiplicative_identity,v__dfg)*. % 26.66/26.90 23698[3:Res:23613.0,790.0] || product(multiplicative_identity,additive_identity,v__dfg)* -> . % 26.66/26.90 23768[3:Res:23649.0,18.0] || -> product(multiplicative_identity,additive_identity,v__dfg)*. % 26.66/26.90 23782[3:MRR:23768.0,23698.0] || -> . % 26.66/26.90 23791[2:Spt:23782.0,434.0,436.0] || sum__dfg(additive_identity,v__dfg,additive_identity)* -> . % 26.66/26.90 23792[2:Spt:23782.0,434.1] || -> product(b,multiplicative_inverse(v__dfg),a)*. % 26.66/26.90 23802[0:SSi:4081.0,4.0] || -> sum__dfg(additive_identity,v__dfg,additive_identity) product(b,multiplicative_inverse(v__dfg),a)*. % 26.66/26.90 23803[0:MRR:23802.1,18467.0] || -> sum__dfg(additive_identity,v__dfg,additive_identity)*. % 26.66/26.90 23804[2:MRR:23803.0,23791.0] || -> . % 26.66/26.90 23844[1:Spt:23804.0,142.0,161.0] || sum__dfg(additive_identity,u__dfg,additive_identity)* -> . % 27.32/27.55 23845[1:Spt:23804.0,142.1] || -> product(b,multiplicative_inverse(u__dfg),a)*. % 27.32/27.55 23857[0:SSi:4080.0,3.0] || -> sum__dfg(additive_identity,u__dfg,additive_identity) product(b,multiplicative_inverse(u__dfg),a)*. % 27.32/27.55 23858[0:MRR:23857.1,18467.0] || -> sum__dfg(additive_identity,u__dfg,additive_identity)*. % 27.32/27.55 23859[1:MRR:23858.0,23844.0] || -> . % 27.32/27.55 % SZS output end Refutation % 27.32/27.55 Formulae used in the proof : a_is_defined b_is_defined u_is_defined v_is_defined not_sum_5 product_6 product_7 not_product_8 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_2 well_definedness_of_additive_identity well_definedness_of_additive_inverse well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse different_identities % 27.32/27.55 %------------------------------------------------------------------------------