TSTP Solution File: FLD043-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD043-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 02:28:28 EDT 2022
% Result : Unsatisfiable 1.37s 1.60s
% Output : Refutation 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD043-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 6 21:59:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.37/1.60
% 1.37/1.60 SPASS V 3.9
% 1.37/1.60 SPASS beiseite: Proof found.
% 1.37/1.60 % SZS status Theorem
% 1.37/1.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.60 SPASS derived 2992 clauses, backtracked 224 clauses, performed 7 splits and kept 2359 clauses.
% 1.37/1.60 SPASS allocated 78917 KBytes.
% 1.37/1.60 SPASS spent 0:00:01.25 on the problem.
% 1.37/1.60 0:00:00.04 for the input.
% 1.37/1.60 0:00:00.00 for the FLOTTER CNF translation.
% 1.37/1.60 0:00:00.03 for inferences.
% 1.37/1.60 0:00:00.04 for the backtracking.
% 1.37/1.60 0:00:01.10 for the reduction.
% 1.37/1.60
% 1.37/1.60
% 1.37/1.60 Here is a proof with depth 15, length 115 :
% 1.37/1.60 % SZS output start Refutation
% 1.37/1.60 1[0:Inp] || -> defined(a)*.
% 1.37/1.60 2[0:Inp] || -> defined(b)*.
% 1.37/1.60 3[0:Inp] || -> product(additive_identity,a,b)*.
% 1.37/1.60 4[0:Inp] || sum__dfg(additive_identity,b,additive_identity)* -> .
% 1.37/1.60 5[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,v,y)* sum__dfg(z,x,u)* -> sum__dfg(z,y,w)*.
% 1.37/1.60 6[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*.
% 1.37/1.60 7[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*.
% 1.37/1.60 8[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*.
% 1.37/1.60 9[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*.
% 1.37/1.60 10[0:Inp] || product(u,v,w)*+ product(x,v,y)* product(z,x,u)* -> product(z,y,w)*.
% 1.37/1.60 11[0:Inp] || product(u,v,w)*+ product(x,y,v)* product(u,x,z)* -> product(z,y,w)*.
% 1.37/1.60 12[0:Inp] defined(u) || -> product(multiplicative_identity,u,u)*.
% 1.37/1.60 13[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,additive_identity) product(multiplicative_inverse(u),u,multiplicative_identity)*.
% 1.37/1.60 14[0:Inp] || product(u,v,w)*+ -> product(v,u,w)*.
% 1.37/1.60 15[0:Inp] || product(u,v,w)*+ product(x,v,y)* product(z,v,x1)* sum__dfg(x,u,z)* -> sum__dfg(y,w,x1)*.
% 1.37/1.60 16[0:Inp] || sum__dfg(u,v,w)*+ product(x,y,v)* product(z,y,u)* sum__dfg(z,x,x1)* -> product(x1,y,w)*.
% 1.37/1.60 17[0:Inp] defined(u) defined(v) || -> defined(add(v,u))*.
% 1.37/1.60 18[0:Inp] || -> defined(additive_identity)*.
% 1.37/1.60 21[0:Inp] || -> defined(multiplicative_identity)*.
% 1.37/1.60 22[0:Inp] defined(u) || -> defined(multiplicative_inverse(u)) sum__dfg(additive_identity,u,additive_identity)*.
% 1.37/1.60 23[0:Inp] defined(u) defined(v) || -> sum__dfg(v,u,add(v,u))*.
% 1.37/1.60 30[0:Inp] || sum__dfg(additive_identity,additive_identity,multiplicative_identity)* -> .
% 1.37/1.60 35[0:Res:3.0,11.2] || product(u,v,a)*+ product(additive_identity,u,w)* -> product(w,v,b)*.
% 1.37/1.60 38[0:Res:3.0,15.3] || product(u,a,v)*+ product(w,a,x)* sum__dfg(u,additive_identity,w)* -> sum__dfg(v,b,x)*.
% 1.37/1.60 42[0:Res:3.0,15.2] || product(u,a,v)*+ product(w,a,x)* sum__dfg(additive_identity,u,w)* -> sum__dfg(b,v,x)*.
% 1.37/1.60 43[0:Res:3.0,16.1] || product(u,a,v)*+ sum__dfg(b,v,w)* sum__dfg(additive_identity,u,x)* -> product(x,a,w)*.
% 1.37/1.60 47[0:Res:9.1,4.0] || sum__dfg(b,additive_identity,additive_identity)* -> .
% 1.37/1.60 53[0:Res:3.0,35.0] || product(a,u,a)* -> product(b,u,b).
% 1.37/1.60 55[0:Res:3.0,42.1] || product(u,a,v)*+ sum__dfg(additive_identity,u,additive_identity)* -> sum__dfg(b,v,b)*.
% 1.37/1.60 56[0:Res:3.0,38.1] || product(u,a,v)*+ sum__dfg(u,additive_identity,additive_identity)* -> sum__dfg(v,b,b)*.
% 1.37/1.60 59[0:Res:3.0,42.2] || product(u,a,v)*+ sum__dfg(additive_identity,additive_identity,u)* -> sum__dfg(b,b,v)*.
% 1.37/1.60 61[0:Res:3.0,43.1] || sum__dfg(b,b,u)*+ sum__dfg(additive_identity,additive_identity,v)* -> product(v,a,u)*.
% 1.37/1.60 75[0:Res:7.1,9.0] defined(u) || -> sum__dfg(u,additive_identity,u)*.
% 1.37/1.60 82[0:Res:12.1,14.0] defined(u) || -> product(u,multiplicative_identity,u)*.
% 1.37/1.60 84[0:Res:82.1,53.0] defined(a) || -> product(b,multiplicative_identity,b)*.
% 1.37/1.60 86[0:SSi:84.0,1.0] || -> product(b,multiplicative_identity,b)*.
% 1.37/1.60 87[0:Res:86.0,14.0] || -> product(multiplicative_identity,b,b)*.
% 1.37/1.60 90[0:Res:22.2,9.0] defined(u) || -> defined(multiplicative_inverse(u)) sum__dfg(u,additive_identity,additive_identity)*.
% 1.37/1.60 97[0:Res:23.2,9.0] defined(u) defined(v) || -> sum__dfg(u,v,add(v,u))*.
% 1.37/1.60 99[0:Res:7.1,6.0] defined(u) || sum__dfg(v,w,u)*+ sum__dfg(additive_identity,v,x)* -> sum__dfg(x,w,u)*.
% 1.37/1.60 100[0:Res:8.1,6.0] defined(u) || sum__dfg(v,w,u)* sum__dfg(additive_inverse(u),v,x)*+ -> sum__dfg(x,w,additive_identity)*.
% 1.37/1.60 109[0:Res:3.0,59.0] || sum__dfg(additive_identity,additive_identity,additive_identity) -> sum__dfg(b,b,b)*.
% 1.37/1.60 119[0:Res:7.1,5.0] defined(u) || sum__dfg(v,u,w)*+ sum__dfg(x,v,additive_identity)* -> sum__dfg(x,w,u)*.
% 1.37/1.60 173[0:Res:12.1,10.0] defined(u) || product(v,u,w)*+ product(x,v,multiplicative_identity)* -> product(x,w,u)*.
% 1.37/1.60 191[0:Res:13.2,56.0] defined(a) || sum__dfg(multiplicative_inverse(a),additive_identity,additive_identity)* -> sum__dfg(additive_identity,a,additive_identity) sum__dfg(multiplicative_identity,b,b).
% 1.37/1.60 195[0:SSi:191.0,1.0] || sum__dfg(multiplicative_inverse(a),additive_identity,additive_identity)* -> sum__dfg(additive_identity,a,additive_identity) sum__dfg(multiplicative_identity,b,b).
% 1.37/1.60 225[1:Spt:195.1] || -> sum__dfg(additive_identity,a,additive_identity)*.
% 1.37/1.60 228[1:Res:225.0,9.0] || -> sum__dfg(a,additive_identity,additive_identity)*.
% 1.37/1.60 264[0:Res:109.1,61.0] || sum__dfg(additive_identity,additive_identity,additive_identity)*+ sum__dfg(additive_identity,additive_identity,u)* -> product(u,a,b).
% 1.37/1.60 327[0:Res:7.1,264.0] defined(additive_identity) || sum__dfg(additive_identity,additive_identity,u)* -> product(u,a,b).
% 1.37/1.60 332[0:SSi:327.0,18.0] || sum__dfg(additive_identity,additive_identity,u)* -> product(u,a,b).
% 1.37/1.60 338[0:Res:97.2,332.0] defined(additive_identity) defined(additive_identity) || -> product(add(additive_identity,additive_identity),a,b)*.
% 1.37/1.60 341[0:Obv:338.0] defined(additive_identity) || -> product(add(additive_identity,additive_identity),a,b)*.
% 1.37/1.60 342[0:SSi:341.0,18.0] || -> product(add(additive_identity,additive_identity),a,b)*.
% 1.37/1.60 355[0:Res:342.0,56.0] || sum__dfg(add(additive_identity,additive_identity),additive_identity,additive_identity)* -> sum__dfg(b,b,b).
% 1.37/1.60 356[0:Res:342.0,55.0] || sum__dfg(additive_identity,add(additive_identity,additive_identity),additive_identity)* -> sum__dfg(b,b,b).
% 1.37/1.60 362[0:Res:90.2,355.0] defined(add(additive_identity,additive_identity)) || -> defined(multiplicative_inverse(add(additive_identity,additive_identity)))* sum__dfg(b,b,b).
% 1.37/1.60 363[0:SSi:362.0,17.0,18.0,18.2] || -> defined(multiplicative_inverse(add(additive_identity,additive_identity)))* sum__dfg(b,b,b).
% 1.37/1.60 364[2:Spt:363.1] || -> sum__dfg(b,b,b)*.
% 1.37/1.60 637[1:Res:225.0,99.1] defined(additive_identity) || sum__dfg(additive_identity,additive_identity,u)* -> sum__dfg(u,a,additive_identity)*.
% 1.37/1.60 659[1:SSi:637.0,18.0] || sum__dfg(additive_identity,additive_identity,u)*+ -> sum__dfg(u,a,additive_identity)*.
% 1.37/1.60 712[1:Res:228.0,119.1] defined(additive_identity) || sum__dfg(u,a,additive_identity)* -> sum__dfg(u,additive_identity,additive_identity).
% 1.37/1.60 737[2:Res:364.0,119.1] defined(b) || sum__dfg(u,b,additive_identity) -> sum__dfg(u,b,b)*.
% 1.37/1.60 738[1:SSi:712.0,18.0] || sum__dfg(u,a,additive_identity)* -> sum__dfg(u,additive_identity,additive_identity).
% 1.37/1.60 740[2:SSi:737.0,2.0] || sum__dfg(u,b,additive_identity) -> sum__dfg(u,b,b)*.
% 1.37/1.60 925[0:Res:87.0,173.1] defined(b) || product(u,multiplicative_identity,multiplicative_identity) -> product(u,b,b)*.
% 1.37/1.60 961[0:SSi:925.0,2.0] || product(u,multiplicative_identity,multiplicative_identity) -> product(u,b,b)*.
% 1.37/1.60 1014[1:Res:97.2,659.0] defined(additive_identity) defined(additive_identity) || -> sum__dfg(add(additive_identity,additive_identity),a,additive_identity)*.
% 1.37/1.60 1017[1:Obv:1014.0] defined(additive_identity) || -> sum__dfg(add(additive_identity,additive_identity),a,additive_identity)*.
% 1.37/1.60 1018[1:SSi:1017.0,18.0] || -> sum__dfg(add(additive_identity,additive_identity),a,additive_identity)*.
% 1.37/1.60 1092[1:Res:1018.0,738.0] || -> sum__dfg(add(additive_identity,additive_identity),additive_identity,additive_identity)*.
% 1.37/1.60 1132[1:Res:1092.0,9.0] || -> sum__dfg(additive_identity,add(additive_identity,additive_identity),additive_identity)*.
% 1.37/1.60 1251[2:Res:740.1,9.0] || sum__dfg(u,b,additive_identity)*+ -> sum__dfg(b,u,b)*.
% 1.37/1.60 1427[0:Res:961.1,14.0] || product(u,multiplicative_identity,multiplicative_identity)*+ -> product(b,u,b)*.
% 1.37/1.60 2139[2:Res:8.1,1251.0] defined(b) || -> sum__dfg(b,additive_inverse(b),b)*.
% 1.37/1.60 2142[2:SSi:2139.0,2.0] || -> sum__dfg(b,additive_inverse(b),b)*.
% 1.37/1.60 2147[2:Res:2142.0,9.0] || -> sum__dfg(additive_inverse(b),b,b)*.
% 1.37/1.60 2164[2:Res:2147.0,100.2] defined(b) || sum__dfg(b,u,b)* -> sum__dfg(b,u,additive_identity).
% 1.37/1.60 2169[2:SSi:2164.0,2.0] || sum__dfg(b,u,b)* -> sum__dfg(b,u,additive_identity).
% 1.37/1.60 2174[0:Res:13.2,1427.0] defined(multiplicative_identity) || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity) product(b,multiplicative_inverse(multiplicative_identity),b)*.
% 1.37/1.62 2176[0:SSi:2174.0,21.0] || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity) product(b,multiplicative_inverse(multiplicative_identity),b)*.
% 1.37/1.62 3056[2:Res:75.1,2169.0] defined(b) || -> sum__dfg(b,additive_identity,additive_identity)*.
% 1.37/1.62 3068[2:SSi:3056.0,2.0] || -> sum__dfg(b,additive_identity,additive_identity)*.
% 1.37/1.62 3069[2:MRR:3068.0,47.0] || -> .
% 1.37/1.62 3072[2:Spt:3069.0,363.1,364.0] || sum__dfg(b,b,b)* -> .
% 1.37/1.62 3073[2:Spt:3069.0,363.0] || -> defined(multiplicative_inverse(add(additive_identity,additive_identity)))*.
% 1.37/1.62 3084[1:MRR:356.0,1132.0] || -> sum__dfg(b,b,b)*.
% 1.37/1.62 3085[2:MRR:3084.0,3072.0] || -> .
% 1.37/1.62 3106[1:Spt:3085.0,195.1,225.0] || sum__dfg(additive_identity,a,additive_identity)* -> .
% 1.37/1.62 3107[1:Spt:3085.0,195.0,195.2] || sum__dfg(multiplicative_inverse(a),additive_identity,additive_identity)* -> sum__dfg(multiplicative_identity,b,b).
% 1.37/1.62 3230[2:Spt:2176.0] || -> sum__dfg(additive_identity,multiplicative_identity,additive_identity)*.
% 1.37/1.62 3256[2:Res:3230.0,119.1] defined(multiplicative_identity) || sum__dfg(u,additive_identity,additive_identity)* -> sum__dfg(u,additive_identity,multiplicative_identity).
% 1.37/1.62 3264[2:SSi:3256.0,21.0] || sum__dfg(u,additive_identity,additive_identity)* -> sum__dfg(u,additive_identity,multiplicative_identity).
% 1.37/1.62 3864[2:Res:75.1,3264.0] defined(additive_identity) || -> sum__dfg(additive_identity,additive_identity,multiplicative_identity)*.
% 1.37/1.62 3870[2:SSi:3864.0,18.0] || -> sum__dfg(additive_identity,additive_identity,multiplicative_identity)*.
% 1.37/1.62 3871[2:MRR:3870.0,30.0] || -> .
% 1.37/1.62 3878[2:Spt:3871.0,2176.0,3230.0] || sum__dfg(additive_identity,multiplicative_identity,additive_identity)* -> .
% 1.37/1.62 3879[2:Spt:3871.0,2176.1] || -> product(b,multiplicative_inverse(multiplicative_identity),b)*.
% 1.37/1.62 4005[3:Spt:363.1] || -> sum__dfg(b,b,b)*.
% 1.37/1.62 4012[3:Res:4005.0,119.1] defined(b) || sum__dfg(u,b,additive_identity) -> sum__dfg(u,b,b)*.
% 1.37/1.62 4019[3:SSi:4012.0,2.0] || sum__dfg(u,b,additive_identity) -> sum__dfg(u,b,b)*.
% 1.37/1.62 4052[3:Res:4019.1,9.0] || sum__dfg(u,b,additive_identity)*+ -> sum__dfg(b,u,b)*.
% 1.37/1.62 4157[3:Res:8.1,4052.0] defined(b) || -> sum__dfg(b,additive_inverse(b),b)*.
% 1.37/1.62 4160[3:SSi:4157.0,2.0] || -> sum__dfg(b,additive_inverse(b),b)*.
% 1.37/1.62 4165[3:Res:4160.0,9.0] || -> sum__dfg(additive_inverse(b),b,b)*.
% 1.37/1.62 4185[3:Res:4165.0,100.2] defined(b) || sum__dfg(b,u,b)* -> sum__dfg(b,u,additive_identity).
% 1.37/1.62 4190[3:SSi:4185.0,2.0] || sum__dfg(b,u,b)* -> sum__dfg(b,u,additive_identity).
% 1.37/1.62 4202[3:Res:75.1,4190.0] defined(b) || -> sum__dfg(b,additive_identity,additive_identity)*.
% 1.37/1.62 4214[3:SSi:4202.0,2.0] || -> sum__dfg(b,additive_identity,additive_identity)*.
% 1.37/1.62 4215[3:MRR:4214.0,47.0] || -> .
% 1.37/1.62 4218[3:Spt:4215.0,363.1,4005.0] || sum__dfg(b,b,b)* -> .
% 1.37/1.62 4219[3:Spt:4215.0,363.0] || -> defined(multiplicative_inverse(add(additive_identity,additive_identity)))*.
% 1.37/1.62 4220[3:MRR:109.1,4218.0] || sum__dfg(additive_identity,additive_identity,additive_identity)* -> .
% 1.37/1.62 4234[3:Res:75.1,4220.0] defined(additive_identity) || -> .
% 1.37/1.62 4238[3:SSi:4234.0,18.0] || -> .
% 1.37/1.62 % SZS output end Refutation
% 1.37/1.62 Formulae used in the proof : a_is_defined b_is_defined product_3 not_sum_4 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_1 distributivity_2 well_definedness_of_addition well_definedness_of_additive_identity well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse totality_of_addition different_identities
% 1.37/1.62
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