TSTP Solution File: NUM461+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 14:26:26 EDT 2022
% Result : Theorem 38.45s 38.63s
% Output : Refutation 46.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 18:50:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 38.45/38.63
% 38.45/38.63 SPASS V 3.9
% 38.45/38.63 SPASS beiseite: Proof found.
% 38.45/38.63 % SZS status Theorem
% 38.45/38.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.45/38.63 SPASS derived 17251 clauses, backtracked 654 clauses, performed 12 splits and kept 5603 clauses.
% 38.45/38.63 SPASS allocated 131610 KBytes.
% 38.45/38.63 SPASS spent 0:0:38.27 on the problem.
% 38.45/38.63 0:00:00.04 for the input.
% 38.45/38.63 0:00:00.03 for the FLOTTER CNF translation.
% 38.45/38.63 0:00:00.18 for inferences.
% 38.45/38.63 0:00:00.20 for the backtracking.
% 38.45/38.63 0:0:37.74 for the reduction.
% 38.45/38.63
% 38.45/38.63
% 38.45/38.63 Here is a proof with depth 8, length 228 :
% 38.45/38.63 % SZS output start Refutation
% 38.45/38.63 1[0:Inp] || -> aNaturalNumber0(sz00)*.
% 38.45/38.63 3[0:Inp] || -> aNaturalNumber0(xl)*.
% 38.45/38.63 4[0:Inp] || -> aNaturalNumber0(xn)*.
% 38.45/38.63 5[0:Inp] || -> aNaturalNumber0(skc1)*.
% 38.45/38.63 6[0:Inp] || -> aNaturalNumber0(xm)*.
% 38.45/38.63 7[0:Inp] || -> sdtlseqdt0(xl,xn)*.
% 38.45/38.63 9[0:Inp] || -> aNaturalNumber0(skf1(u,v))*.
% 38.45/38.63 10[0:Inp] || equal(xn,xl)** -> .
% 38.45/38.63 11[0:Inp] || -> equal(sdtpldt0(xl,skc1),xn)**.
% 38.45/38.63 12[0:Inp] aNaturalNumber0(u) || -> sdtlseqdt0(u,u)*.
% 38.45/38.63 13[0:Inp] aNaturalNumber0(u) || -> equal(sdtpldt0(u,sz00),u)**.
% 38.45/38.63 14[0:Inp] aNaturalNumber0(u) || -> equal(sdtpldt0(sz00,u),u)**.
% 38.45/38.63 20[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtpldt0(v,u))*.
% 38.45/38.63 22[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(v,u)* sdtlseqdt0(u,v)*.
% 38.45/38.63 23[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtpldt0(v,u),sdtpldt0(u,v))*.
% 38.45/38.63 26[0:Inp] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xm,xl),u),sdtpldt0(xm,xn))** -> SkC0.
% 38.45/38.63 28[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(sdtpldt0(v,u),sz00)** -> equal(u,sz00).
% 38.45/38.63 29[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) -> equal(sdtpldt0(v,skf1(u,v)),u)**.
% 38.45/38.63 30[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 38.45/38.63 32[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> sdtlseqdt0(v,u)*.
% 38.45/38.63 33[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) equal(w,sdtmndt0(u,v))*+ -> aNaturalNumber0(w)*.
% 38.45/38.63 35[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),sdtpldt0(u,w))* -> equal(v,u).
% 38.45/38.63 38[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || -> equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u)))**.
% 38.45/38.63 39[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) equal(w,sdtmndt0(u,v))*+ -> equal(sdtpldt0(v,w),u)*.
% 38.45/38.63 44[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,w) equal(sdtpldt0(v,u),w)* -> equal(u,sdtmndt0(w,v))*.
% 38.45/38.63 45[0:Inp] || SkC0 sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl))**.
% 38.45/38.63 46[0:Inp] aNaturalNumber0(u) || SkC0 equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl)).
% 38.45/38.63 47[0:MRR:44.3,32.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> equal(w,sdtmndt0(u,v))*.
% 38.45/38.63 62[1:Spt:26.0,26.1] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xm,xl),u),sdtpldt0(xm,xn))** -> .
% 38.45/38.63 163[1:SpL:23.2,62.1] aNaturalNumber0(xl) aNaturalNumber0(xm) aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xm,xn))** -> .
% 38.45/38.63 175[1:Rew:38.3,163.3] aNaturalNumber0(xl) aNaturalNumber0(xm) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(xm,u)),sdtpldt0(xm,xn))* -> .
% 38.45/38.63 176[1:SSi:175.1,175.0,6.0,3.0] aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(xm,u)),sdtpldt0(xm,xn))* -> .
% 38.45/38.63 215[1:SpL:23.2,176.1] aNaturalNumber0(u) aNaturalNumber0(xm) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(u,xm)),sdtpldt0(xm,xn))* -> .
% 38.45/38.63 219[1:Obv:215.0] aNaturalNumber0(xm) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(u,xm)),sdtpldt0(xm,xn))* -> .
% 38.45/38.63 220[1:SSi:219.0,6.0] aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(u,xm)),sdtpldt0(xm,xn))* -> .
% 38.45/38.63 233[0:SpL:11.0,28.2] aNaturalNumber0(skc1) aNaturalNumber0(xl) || equal(xn,sz00) -> equal(skc1,sz00)**.
% 38.45/38.63 238[0:SSi:233.1,233.0,3.0,5.0] || equal(xn,sz00) -> equal(skc1,sz00)**.
% 38.45/38.63 242[0:SpR:238.1,11.0] || equal(xn,sz00) -> equal(sdtpldt0(xl,sz00),xn)**.
% 38.45/38.63 248[0:SpR:242.1,13.1] aNaturalNumber0(xl) || equal(xn,sz00)** -> equal(xn,xl).
% 38.45/38.63 251[0:SSi:248.0,3.0] || equal(xn,sz00)** -> equal(xn,xl).
% 38.45/38.63 252[0:MRR:251.1,10.0] || equal(xn,sz00)** -> .
% 38.45/38.63 266[1:SpL:23.2,220.1] aNaturalNumber0(xn) aNaturalNumber0(xm) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(u,xm)),sdtpldt0(xn,xm))* -> .
% 38.45/38.63 270[1:SSi:266.1,266.0,6.0,4.0] aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(u,xm)),sdtpldt0(xn,xm))* -> .
% 38.45/38.63 412[0:EqR:32.3] aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 38.45/38.63 418[0:SpL:29.3,32.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(skf1(u,v)) || sdtlseqdt0(v,u)* equal(u,w)* -> sdtlseqdt0(v,w)*.
% 38.45/38.63 419[0:SSi:412.0,20.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 38.45/38.63 426[0:Obv:418.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(skf1(u,w)) || sdtlseqdt0(w,u)* equal(u,v)* -> sdtlseqdt0(w,v)*.
% 38.45/38.63 427[0:SSi:426.3,9.0] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,u)* equal(u,v)* -> sdtlseqdt0(w,v)*.
% 38.45/38.63 441[0:SpR:14.1,419.2] aNaturalNumber0(u) aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 38.45/38.63 442[0:SpR:23.2,419.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(v) aNaturalNumber0(u) || -> sdtlseqdt0(v,sdtpldt0(u,v))*.
% 38.45/38.63 447[0:Obv:441.0] aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 38.45/38.63 448[0:SSi:447.0,1.0] aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 38.45/38.63 451[0:Obv:442.1] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(v,u))*.
% 38.45/38.63 455[0:Res:448.1,30.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 38.45/38.63 456[0:Obv:455.0] aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 38.45/38.63 457[0:SSi:456.1,1.0] aNaturalNumber0(u) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 38.45/38.63 505[0:SpR:38.3,29.3] aNaturalNumber0(skf1(u,sdtpldt0(v,w))) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(v,w)) || sdtlseqdt0(sdtpldt0(v,w),u) -> equal(sdtpldt0(v,sdtpldt0(w,skf1(u,sdtpldt0(v,w)))),u)**.
% 38.45/38.63 507[0:SpR:11.0,38.3] aNaturalNumber0(u) aNaturalNumber0(skc1) aNaturalNumber0(xl) || -> equal(sdtpldt0(xl,sdtpldt0(skc1,u)),sdtpldt0(xn,u))**.
% 38.45/38.63 511[0:SpR:23.2,38.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(u) || -> equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w)))**.
% 38.45/38.63 533[0:SSi:507.2,507.1,3.0,5.0] aNaturalNumber0(u) || -> equal(sdtpldt0(xl,sdtpldt0(skc1,u)),sdtpldt0(xn,u))**.
% 38.45/38.63 553[0:Obv:511.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || -> equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u)))**.
% 38.45/38.63 554[0:Rew:38.3,553.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || -> equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u)))*.
% 38.45/38.63 576[0:SSi:505.4,505.0,20.2,9.0,20.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(sdtpldt0(v,u),w) -> equal(sdtpldt0(v,sdtpldt0(u,skf1(w,sdtpldt0(v,u)))),w)**.
% 38.45/38.63 580[0:SpR:533.1,451.2] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(skc1,u)) aNaturalNumber0(xl) || -> sdtlseqdt0(sdtpldt0(skc1,u),sdtpldt0(xn,u))*.
% 38.45/38.64 581[0:SpR:533.1,419.2] aNaturalNumber0(u) aNaturalNumber0(xl) aNaturalNumber0(sdtpldt0(skc1,u)) || -> sdtlseqdt0(xl,sdtpldt0(xn,u))*.
% 38.45/38.64 583[0:SpR:23.2,533.1] aNaturalNumber0(u) aNaturalNumber0(skc1) aNaturalNumber0(u) || -> equal(sdtpldt0(xl,sdtpldt0(u,skc1)),sdtpldt0(xn,u))*.
% 38.45/38.64 588[1:SpL:533.1,270.1] aNaturalNumber0(xm) aNaturalNumber0(skc1) || equal(sdtpldt0(xn,xm),sdtpldt0(xn,xm))* -> .
% 38.45/38.64 595[1:Obv:588.2] aNaturalNumber0(xm) aNaturalNumber0(skc1) || -> .
% 38.45/38.64 596[1:SSi:595.1,595.0,5.0,6.0] || -> .
% 38.45/38.64 598[0:SSi:581.2,581.1,20.0,5.0,3.2] aNaturalNumber0(u) || -> sdtlseqdt0(xl,sdtpldt0(xn,u))*.
% 38.45/38.64 599[0:SSi:580.2,580.1,3.0,20.2,5.0] aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(skc1,u),sdtpldt0(xn,u))*.
% 38.45/38.64 600[0:Obv:583.0] aNaturalNumber0(skc1) aNaturalNumber0(u) || -> equal(sdtpldt0(xl,sdtpldt0(u,skc1)),sdtpldt0(xn,u))*.
% 38.45/38.64 601[0:SSi:600.0,5.0] aNaturalNumber0(u) || -> equal(sdtpldt0(xl,sdtpldt0(u,skc1)),sdtpldt0(xn,u))*.
% 38.45/38.64 608[1:Spt:596.0,26.2] || -> SkC0*.
% 38.45/38.64 609[1:MRR:45.0,608.0] || sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl))**.
% 38.45/38.64 617[1:MRR:46.1,608.0] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl)).
% 38.45/38.64 686[0:SpR:29.3,598.1] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(skf1(u,xn)) || sdtlseqdt0(xn,u)* -> sdtlseqdt0(xl,u).
% 38.45/38.64 692[0:SSi:686.2,686.1,9.0,4.0,4.0] aNaturalNumber0(u) || sdtlseqdt0(xn,u)* -> sdtlseqdt0(xl,u).
% 38.45/38.64 703[0:SpR:23.2,599.1] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(skc1,u),sdtpldt0(u,xn))*.
% 38.45/38.64 708[0:SpR:23.2,599.1] aNaturalNumber0(u) aNaturalNumber0(skc1) aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(u,skc1),sdtpldt0(xn,u))*.
% 38.45/38.64 715[0:Obv:703.0] aNaturalNumber0(xn) aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(skc1,u),sdtpldt0(u,xn))*.
% 38.45/38.64 716[0:SSi:715.0,4.0] aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(skc1,u),sdtpldt0(u,xn))*.
% 38.45/38.64 718[0:Obv:708.0] aNaturalNumber0(skc1) aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(u,skc1),sdtpldt0(xn,u))*.
% 38.45/38.64 719[0:SSi:718.0,5.0] aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(u,skc1),sdtpldt0(xn,u))*.
% 38.45/38.64 732[0:EqR:47.3] aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtmndt0(sdtpldt0(u,v),u),v)**.
% 38.45/38.64 739[0:SpL:23.2,47.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(u) aNaturalNumber0(v) || equal(sdtpldt0(v,u),w)* -> equal(v,sdtmndt0(w,u))*.
% 38.45/38.64 740[0:SpL:29.3,47.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(skf1(u,v)) || sdtlseqdt0(v,u) equal(u,w) -> equal(skf1(u,v),sdtmndt0(w,v))*.
% 38.45/38.64 742[0:SSi:732.0,20.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtmndt0(sdtpldt0(u,v),u),v)**.
% 38.45/38.64 749[0:Obv:739.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(w,v),u)*+ -> equal(w,sdtmndt0(u,v))*.
% 38.45/38.64 752[0:Obv:740.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(skf1(u,w)) || sdtlseqdt0(w,u) equal(u,v) -> equal(skf1(u,w),sdtmndt0(v,w))*.
% 38.45/38.64 753[0:SSi:752.3,9.0] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,u) equal(u,v) -> equal(skf1(u,w),sdtmndt0(v,w))*.
% 38.45/38.64 758[0:Res:22.2,692.1] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(u) || -> sdtlseqdt0(u,xn)* sdtlseqdt0(xl,u)*.
% 38.45/38.64 763[0:Obv:758.0] aNaturalNumber0(xn) aNaturalNumber0(u) || -> sdtlseqdt0(u,xn)* sdtlseqdt0(xl,u)*.
% 38.45/38.64 764[0:SSi:763.0,4.0] aNaturalNumber0(u) || -> sdtlseqdt0(u,xn)* sdtlseqdt0(xl,u)*.
% 38.45/38.64 770[0:Res:764.2,457.1] aNaturalNumber0(sz00) aNaturalNumber0(xl) || -> sdtlseqdt0(sz00,xn)* equal(xl,sz00).
% 38.45/38.64 772[0:SSi:770.1,770.0,3.0,1.0] || -> sdtlseqdt0(sz00,xn)* equal(xl,sz00).
% 38.45/38.64 776[2:Spt:772.1] || -> equal(xl,sz00)**.
% 38.45/38.64 780[2:Rew:776.0,11.0] || -> equal(sdtpldt0(sz00,skc1),xn)**.
% 38.45/38.64 797[2:Rew:776.0,609.0] || sdtlseqdt0(sdtpldt0(sz00,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl))**.
% 38.45/38.64 798[2:Rew:776.0,617.2] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xn,xm),sdtpldt0(sz00,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl)).
% 38.45/38.64 818[2:Rew:776.0,797.2,776.0,797.1] || sdtlseqdt0(sdtpldt0(sz00,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xn,xm),sdtpldt0(sz00,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,sz00))**.
% 38.45/38.64 827[2:Rew:776.0,798.3,776.0,798.1] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(sz00,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xn,xm),sdtpldt0(sz00,xm)) equal(sdtpldt0(xm,xn),sdtpldt0(xm,sz00)).
% 38.45/38.64 830[2:SpR:780.0,14.1] aNaturalNumber0(skc1) || -> equal(skc1,xn)**.
% 38.45/38.64 840[2:SSi:830.0,5.0] || -> equal(skc1,xn)**.
% 38.45/38.64 849[2:Rew:840.0,716.1] aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(xn,u),sdtpldt0(u,xn))*.
% 38.45/38.64 854[2:Rew:840.0,719.1] aNaturalNumber0(u) || -> sdtlseqdt0(sdtpldt0(u,xn),sdtpldt0(xn,u))*.
% 38.45/38.64 969[2:Res:849.1,30.2] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(u,xn)) aNaturalNumber0(sdtpldt0(xn,u)) || sdtlseqdt0(sdtpldt0(u,xn),sdtpldt0(xn,u))* -> equal(sdtpldt0(xn,u),sdtpldt0(u,xn)).
% 38.45/38.64 979[2:SSi:969.2,969.1,20.0,4.2,20.0,4.2] aNaturalNumber0(u) || sdtlseqdt0(sdtpldt0(u,xn),sdtpldt0(xn,u))* -> equal(sdtpldt0(xn,u),sdtpldt0(u,xn)).
% 38.45/38.64 980[2:MRR:979.1,854.1] aNaturalNumber0(u) || -> equal(sdtpldt0(xn,u),sdtpldt0(u,xn))*.
% 38.45/38.64 1323[3:Spt:818.1] || -> equal(sdtpldt0(xn,xm),sdtpldt0(sz00,xm))**.
% 38.45/38.64 1341[3:SpL:1323.0,35.3] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(xm) || equal(sdtpldt0(sz00,xm),sdtpldt0(u,xm))* -> equal(xn,u).
% 38.45/38.64 1366[3:Rew:14.1,1341.3] aNaturalNumber0(u) aNaturalNumber0(xn) aNaturalNumber0(xm) || equal(sdtpldt0(u,xm),xm)** -> equal(xn,u).
% 38.45/38.64 1367[3:SSi:1366.2,1366.1,6.0,4.0] aNaturalNumber0(u) || equal(sdtpldt0(u,xm),xm)** -> equal(xn,u).
% 38.45/38.64 1546[3:SpL:14.1,1367.1] aNaturalNumber0(xm) aNaturalNumber0(sz00) || equal(xm,xm)* -> equal(xn,sz00).
% 38.45/38.64 1551[3:Obv:1546.2] aNaturalNumber0(xm) aNaturalNumber0(sz00) || -> equal(xn,sz00)**.
% 38.45/38.64 1552[3:SSi:1551.1,1551.0,1.0,6.0] || -> equal(xn,sz00)**.
% 38.45/38.64 1553[3:MRR:1552.0,252.0] || -> .
% 38.45/38.64 1558[3:Spt:1553.0,818.1,1323.0] || equal(sdtpldt0(xn,xm),sdtpldt0(sz00,xm))** -> .
% 38.45/38.64 1559[3:Spt:1553.0,818.0,818.2] || sdtlseqdt0(sdtpldt0(sz00,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,sz00))**.
% 38.45/38.64 1565[3:MRR:827.2,1558.0] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(sz00,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,sz00)).
% 38.45/38.64 1577[3:SpR:1559.1,980.1] aNaturalNumber0(xm) || sdtlseqdt0(sdtpldt0(sz00,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xm,sz00),sdtpldt0(xn,xm))**.
% 38.45/38.64 1598[3:Rew:13.1,1577.2,14.1,1577.1] aNaturalNumber0(xm) || sdtlseqdt0(xm,sdtpldt0(xn,xm))* -> equal(sdtpldt0(xn,xm),xm).
% 38.45/38.64 1599[3:SSi:1598.0,6.0] || sdtlseqdt0(xm,sdtpldt0(xn,xm))* -> equal(sdtpldt0(xn,xm),xm).
% 38.45/38.64 1638[4:Spt:1565.0,1565.1] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(sz00,xm),u),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 1644[4:SpL:980.1,1638.1] aNaturalNumber0(sdtpldt0(sz00,xm)) aNaturalNumber0(xn) || equal(sdtpldt0(xn,sdtpldt0(sz00,xm)),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 1647[4:SSi:1644.1,1644.0,4.0,20.0,1.2,6.0] || equal(sdtpldt0(xn,sdtpldt0(sz00,xm)),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 1715[4:SpL:14.1,1647.0] aNaturalNumber0(xm) || equal(sdtpldt0(xn,xm),sdtpldt0(xn,xm))* -> .
% 38.45/38.64 1716[4:Obv:1715.1] aNaturalNumber0(xm) || -> .
% 38.45/38.64 1717[4:SSi:1716.0,6.0] || -> .
% 38.45/38.64 1718[4:Spt:1717.0,1565.2] || -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,sz00))**.
% 38.45/38.64 1728[4:SpR:1718.0,854.1] aNaturalNumber0(xm) || -> sdtlseqdt0(sdtpldt0(xm,sz00),sdtpldt0(xn,xm))*.
% 38.45/38.64 1749[4:Rew:13.1,1728.1] aNaturalNumber0(xm) || -> sdtlseqdt0(xm,sdtpldt0(xn,xm))*.
% 38.45/38.64 1750[4:SSi:1749.0,6.0] || -> sdtlseqdt0(xm,sdtpldt0(xn,xm))*.
% 38.45/38.64 1752[4:MRR:1599.0,1750.0] || -> equal(sdtpldt0(xn,xm),xm)**.
% 38.45/38.64 1760[4:Rew:1752.0,1558.0] || equal(sdtpldt0(sz00,xm),xm)** -> .
% 38.45/38.64 1793[4:SpL:14.1,1760.0] aNaturalNumber0(xm) || equal(xm,xm)* -> .
% 38.45/38.64 1794[4:Obv:1793.1] aNaturalNumber0(xm) || -> .
% 38.45/38.64 1795[4:SSi:1794.0,6.0] || -> .
% 38.45/38.64 1796[2:Spt:1795.0,772.1,776.0] || equal(xl,sz00)** -> .
% 38.45/38.64 1797[2:Spt:1795.0,772.0] || -> sdtlseqdt0(sz00,xn)*.
% 38.45/38.64 1847[3:Spt:609.1] || -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm))**.
% 38.45/38.64 1853[3:SpR:1847.0,419.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || -> sdtlseqdt0(xn,sdtpldt0(xl,xm))*.
% 38.45/38.64 1867[3:SSi:1853.1,1853.0,6.0,4.0] || -> sdtlseqdt0(xn,sdtpldt0(xl,xm))*.
% 38.45/38.64 2046[3:SpR:1847.0,599.1] aNaturalNumber0(xm) || -> sdtlseqdt0(sdtpldt0(skc1,xm),sdtpldt0(xl,xm))*.
% 38.45/38.64 2053[3:SSi:2046.0,6.0] || -> sdtlseqdt0(sdtpldt0(skc1,xm),sdtpldt0(xl,xm))*.
% 38.45/38.64 2087[3:SpR:23.2,2053.0] aNaturalNumber0(xm) aNaturalNumber0(skc1) || -> sdtlseqdt0(sdtpldt0(xm,skc1),sdtpldt0(xl,xm))*.
% 38.45/38.64 2091[3:SSi:2087.1,2087.0,5.0,6.0] || -> sdtlseqdt0(sdtpldt0(xm,skc1),sdtpldt0(xl,xm))*.
% 38.45/38.64 2273[0:SpR:13.1,742.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(sz00) || -> equal(sdtmndt0(u,u),sz00)**.
% 38.45/38.64 2275[0:SpR:29.3,742.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(v) aNaturalNumber0(skf1(u,v)) || sdtlseqdt0(v,u) -> equal(skf1(u,v),sdtmndt0(u,v))**.
% 38.45/38.64 2277[0:SpR:11.0,742.2] aNaturalNumber0(xl) aNaturalNumber0(skc1) || -> equal(sdtmndt0(xn,xl),skc1)**.
% 38.45/38.64 2278[0:SpR:533.1,742.2] aNaturalNumber0(u) aNaturalNumber0(xl) aNaturalNumber0(sdtpldt0(skc1,u)) || -> equal(sdtmndt0(sdtpldt0(xn,u),xl),sdtpldt0(skc1,u))**.
% 38.45/38.64 2279[3:SpR:1847.0,742.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || -> equal(sdtmndt0(sdtpldt0(xl,xm),xn),xm)**.
% 38.45/38.64 2281[0:SpL:742.2,33.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) || sdtlseqdt0(u,sdtpldt0(u,v))* equal(w,v)* -> aNaturalNumber0(w)*.
% 38.45/38.64 2283[0:SSi:2277.1,2277.0,5.0,3.0] || -> equal(sdtmndt0(xn,xl),skc1)**.
% 38.45/38.64 2284[3:SSi:2279.1,2279.0,6.0,4.0] || -> equal(sdtmndt0(sdtpldt0(xl,xm),xn),xm)**.
% 38.45/38.64 2288[0:Obv:2273.0] aNaturalNumber0(u) aNaturalNumber0(sz00) || -> equal(sdtmndt0(u,u),sz00)**.
% 38.45/38.64 2289[0:SSi:2288.1,1.0] aNaturalNumber0(u) || -> equal(sdtmndt0(u,u),sz00)**.
% 38.45/38.64 2292[0:SSi:2278.2,2278.1,20.0,5.0,3.2] aNaturalNumber0(u) || -> equal(sdtmndt0(sdtpldt0(xn,u),xl),sdtpldt0(skc1,u))**.
% 38.45/38.64 2293[0:Obv:2275.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(skf1(u,v)) || sdtlseqdt0(v,u) -> equal(skf1(u,v),sdtmndt0(u,v))**.
% 38.45/38.64 2294[0:SSi:2293.2,9.0] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) -> equal(skf1(u,v),sdtmndt0(u,v))**.
% 38.45/38.64 2297[0:Rew:2294.3,753.5] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,u) equal(u,v) -> equal(sdtmndt0(u,w),sdtmndt0(v,w))*.
% 38.45/38.64 2303[0:Obv:2281.0] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(v,u)) aNaturalNumber0(v) || sdtlseqdt0(v,sdtpldt0(v,u))* equal(w,u)* -> aNaturalNumber0(w)*.
% 38.45/38.64 2304[0:SSi:2303.1,20.2] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,sdtpldt0(v,u))* equal(w,u)* -> aNaturalNumber0(w)*.
% 38.45/38.64 2305[0:MRR:2304.2,419.2] aNaturalNumber0(u) aNaturalNumber0(v) || equal(w,u)* -> aNaturalNumber0(w)*.
% 38.45/38.64 2307[0:MRR:2297.0,2305.3] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,w) equal(w,u) -> equal(sdtmndt0(w,v),sdtmndt0(u,v))*.
% 38.45/38.64 2308[0:MRR:427.1,2305.3] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ equal(u,w)* -> sdtlseqdt0(v,w)*.
% 38.45/38.64 2325[0:SpL:2283.0,39.3] aNaturalNumber0(xn) aNaturalNumber0(xl) || sdtlseqdt0(xl,xn) equal(u,skc1) -> equal(sdtpldt0(xl,u),xn)**.
% 38.45/38.64 2333[0:SSi:2325.1,2325.0,3.0,4.0] || sdtlseqdt0(xl,xn) equal(u,skc1) -> equal(sdtpldt0(xl,u),xn)**.
% 38.45/38.64 2334[0:MRR:2333.0,7.0] || equal(u,skc1) -> equal(sdtpldt0(xl,u),xn)**.
% 38.45/38.64 2345[3:SpL:2284.0,39.3] aNaturalNumber0(sdtpldt0(xl,xm)) aNaturalNumber0(xn) || sdtlseqdt0(xn,sdtpldt0(xl,xm)) equal(u,xm) -> equal(sdtpldt0(xn,u),sdtpldt0(xl,xm))**.
% 38.45/38.64 2346[3:SpL:2284.0,33.3] aNaturalNumber0(sdtpldt0(xl,xm)) aNaturalNumber0(xn) || sdtlseqdt0(xn,sdtpldt0(xl,xm))* equal(u,xm) -> aNaturalNumber0(u)*.
% 38.45/38.64 2347[3:SSi:2346.1,2346.0,4.0,20.0,3.2,6.0] || sdtlseqdt0(xn,sdtpldt0(xl,xm))* equal(u,xm) -> aNaturalNumber0(u)*.
% 38.45/38.64 2348[3:MRR:2347.0,1867.0] || equal(u,xm) -> aNaturalNumber0(u)*.
% 38.45/38.64 2350[3:SSi:2345.1,2345.0,4.0,20.0,3.2,6.0] || sdtlseqdt0(xn,sdtpldt0(xl,xm)) equal(u,xm) -> equal(sdtpldt0(xn,u),sdtpldt0(xl,xm))**.
% 38.45/38.64 2351[3:MRR:2350.0,1867.0] || equal(u,xm) -> equal(sdtpldt0(xn,u),sdtpldt0(xl,xm))**.
% 38.45/38.64 3719[0:SpR:2334.1,13.1] aNaturalNumber0(xl) || equal(skc1,sz00)** -> equal(xn,xl).
% 38.45/38.64 3768[0:SSi:3719.0,3.0] || equal(skc1,sz00)** -> equal(xn,xl).
% 38.45/38.64 3769[0:MRR:3768.1,10.0] || equal(skc1,sz00)** -> .
% 38.45/38.64 4663[0:Res:12.1,2308.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(u) || equal(u,v) -> sdtlseqdt0(u,v)*.
% 38.45/38.64 4703[0:Obv:4663.1] aNaturalNumber0(u) || equal(u,v) -> sdtlseqdt0(u,v)*.
% 38.45/38.64 5246[0:SpR:11.0,554.3] aNaturalNumber0(skc1) aNaturalNumber0(u) aNaturalNumber0(xl) || -> equal(sdtpldt0(xl,sdtpldt0(u,skc1)),sdtpldt0(u,xn))**.
% 38.45/38.64 5311[0:SSi:5246.2,5246.0,3.0,5.0] aNaturalNumber0(u) || -> equal(sdtpldt0(xl,sdtpldt0(u,skc1)),sdtpldt0(u,xn))**.
% 38.45/38.64 5312[0:Rew:5311.1,601.1] aNaturalNumber0(u) || -> equal(sdtpldt0(u,xn),sdtpldt0(xn,u))*.
% 38.45/38.64 8531[0:SpR:2307.4,2289.1] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(u) || sdtlseqdt0(u,v) equal(v,u) -> equal(sdtmndt0(v,u),sz00)**.
% 38.45/38.64 8552[0:Obv:8531.1] aNaturalNumber0(u) || sdtlseqdt0(u,v) equal(v,u) -> equal(sdtmndt0(v,u),sz00)**.
% 38.45/38.64 8553[0:MRR:8552.1,4703.2] aNaturalNumber0(u) || equal(v,u) -> equal(sdtmndt0(v,u),sz00)**.
% 38.45/38.64 11766[0:SpR:576.4,742.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(sdtpldt0(u,skf1(w,sdtpldt0(v,u)))) || sdtlseqdt0(sdtpldt0(v,u),w) -> equal(sdtpldt0(u,skf1(w,sdtpldt0(v,u))),sdtmndt0(w,v))**.
% 38.45/38.64 11929[0:Obv:11766.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(sdtpldt0(u,skf1(v,sdtpldt0(w,u)))) || sdtlseqdt0(sdtpldt0(w,u),v) -> equal(sdtpldt0(u,skf1(v,sdtpldt0(w,u))),sdtmndt0(v,w))**.
% 38.45/38.64 11930[0:SSi:11929.3,20.2,9.0,20.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(sdtpldt0(w,u),v) -> equal(sdtpldt0(u,skf1(v,sdtpldt0(w,u))),sdtmndt0(v,w))**.
% 38.45/38.64 11931[0:Rew:11930.4,576.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(sdtpldt0(v,u),w)*+ -> equal(sdtpldt0(v,sdtmndt0(w,v)),w)**.
% 38.45/38.64 12069[3:SpR:2351.1,5312.1] aNaturalNumber0(u) || equal(u,xm) -> equal(sdtpldt0(u,xn),sdtpldt0(xl,xm))*.
% 38.45/38.64 12112[3:MRR:12069.0,2348.1] || equal(u,xm) -> equal(sdtpldt0(u,xn),sdtpldt0(xl,xm))*.
% 38.45/38.64 12216[3:Res:2091.0,11931.3] aNaturalNumber0(skc1) aNaturalNumber0(xm) aNaturalNumber0(sdtpldt0(xl,xm)) || -> equal(sdtpldt0(xm,sdtmndt0(sdtpldt0(xl,xm),xm)),sdtpldt0(xl,xm))**.
% 38.45/38.64 12243[3:SSi:12216.2,12216.1,12216.0,20.0,3.0,6.0,6.0,5.2] || -> equal(sdtpldt0(xm,sdtmndt0(sdtpldt0(xl,xm),xm)),sdtpldt0(xl,xm))**.
% 38.45/38.64 13767[3:SpR:12112.1,742.2] aNaturalNumber0(u) aNaturalNumber0(xn) || equal(u,xm) -> equal(sdtmndt0(sdtpldt0(xl,xm),u),xn)**.
% 38.45/38.64 13799[3:SpR:12112.1,742.2] aNaturalNumber0(xl) aNaturalNumber0(xm) || equal(u,xm) -> equal(sdtmndt0(sdtpldt0(u,xn),xl),xm)**.
% 38.45/38.64 13877[3:SSi:13767.1,4.0] aNaturalNumber0(u) || equal(u,xm) -> equal(sdtmndt0(sdtpldt0(xl,xm),u),xn)**.
% 38.45/38.64 13878[3:MRR:13877.0,2348.1] || equal(u,xm) -> equal(sdtmndt0(sdtpldt0(xl,xm),u),xn)**.
% 38.45/38.64 13879[3:SSi:13799.1,13799.0,6.0,3.0] || equal(u,xm) -> equal(sdtmndt0(sdtpldt0(u,xn),xl),xm)**.
% 38.45/38.64 19378[3:SpR:13878.1,12243.0] || equal(xm,xm) -> equal(sdtpldt0(xm,xn),sdtpldt0(xl,xm))**.
% 38.45/38.64 19389[3:Obv:19378.0] || -> equal(sdtpldt0(xm,xn),sdtpldt0(xl,xm))**.
% 38.45/38.64 21423[3:SpR:19389.0,13879.1] || equal(xm,xm) -> equal(sdtmndt0(sdtpldt0(xl,xm),xl),xm)**.
% 38.45/38.64 21428[3:Obv:21423.0] || -> equal(sdtmndt0(sdtpldt0(xl,xm),xl),xm)**.
% 38.45/38.64 25325[3:SpR:1847.0,2292.1] aNaturalNumber0(xm) || -> equal(sdtmndt0(sdtpldt0(xl,xm),xl),sdtpldt0(skc1,xm))**.
% 38.45/38.64 25353[3:Rew:21428.0,25325.1] aNaturalNumber0(xm) || -> equal(sdtpldt0(skc1,xm),xm)**.
% 38.45/38.64 25354[3:SSi:25353.0,6.0] || -> equal(sdtpldt0(skc1,xm),xm)**.
% 38.45/38.64 25530[3:SpL:25354.0,749.3] aNaturalNumber0(u) aNaturalNumber0(xm) aNaturalNumber0(skc1) || equal(xm,u) -> equal(sdtmndt0(u,xm),skc1)**.
% 38.45/38.64 25578[3:Rew:8553.2,25530.4] aNaturalNumber0(u) aNaturalNumber0(xm) aNaturalNumber0(skc1) || equal(xm,u)* -> equal(skc1,sz00)**.
% 38.45/38.64 25579[3:SSi:25578.2,25578.1,5.0,6.0] aNaturalNumber0(u) || equal(xm,u)* -> equal(skc1,sz00)**.
% 38.45/38.64 25580[3:MRR:25579.0,25579.2,2348.1,3769.0] || equal(xm,u)* -> .
% 38.45/38.64 25581[3:UnC:25580.0,21428.0] || -> .
% 38.45/38.64 25606[3:Spt:25581.0,609.1,1847.0] || equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm))** -> .
% 38.45/38.64 25607[3:Spt:25581.0,609.0,609.2] || sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl))**.
% 38.45/38.64 25675[3:MRR:617.2,25606.0] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xn,xm))** -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl)).
% 38.45/38.64 25847[4:Spt:25675.0,25675.1] aNaturalNumber0(u) || equal(sdtpldt0(sdtpldt0(xl,xm),u),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 25850[4:SpL:38.3,25847.1] aNaturalNumber0(u) aNaturalNumber0(xm) aNaturalNumber0(xl) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(xm,u)),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 25870[4:Obv:25850.0] aNaturalNumber0(xm) aNaturalNumber0(xl) aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(xm,u)),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 25871[4:SSi:25870.1,25870.0,3.0,6.0] aNaturalNumber0(u) || equal(sdtpldt0(xl,sdtpldt0(xm,u)),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 30475[4:SpL:5311.1,25871.1] aNaturalNumber0(xm) aNaturalNumber0(skc1) || equal(sdtpldt0(xm,xn),sdtpldt0(xn,xm))** -> .
% 38.45/38.64 30476[4:Rew:5312.1,30475.2] aNaturalNumber0(xm) aNaturalNumber0(skc1) || equal(sdtpldt0(xn,xm),sdtpldt0(xn,xm))* -> .
% 38.45/38.64 30477[4:Obv:30476.2] aNaturalNumber0(xm) aNaturalNumber0(skc1) || -> .
% 38.45/38.64 30478[4:SSi:30477.1,30477.0,5.0,6.0] || -> .
% 38.45/38.64 30489[4:Spt:30478.0,25675.2] || -> equal(sdtpldt0(xm,xn),sdtpldt0(xm,xl))**.
% 38.45/38.64 30518[4:SpR:30489.0,5312.1] aNaturalNumber0(xm) || -> equal(sdtpldt0(xm,xl),sdtpldt0(xn,xm))**.
% 38.45/38.64 30567[4:SSi:30518.0,6.0] || -> equal(sdtpldt0(xm,xl),sdtpldt0(xn,xm))**.
% 46.56/46.78 30755[4:SpR:30567.0,23.2] aNaturalNumber0(xm) aNaturalNumber0(xl) || -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm))**.
% 46.56/46.78 30817[4:SSi:30755.1,30755.0,3.0,6.0] || -> equal(sdtpldt0(xn,xm),sdtpldt0(xl,xm))**.
% 46.56/46.78 30818[4:MRR:30817.0,25606.0] || -> .
% 46.56/46.78 % SZS output end Refutation
% 46.56/46.78 Formulae used in the proof : mSortsC m__840 m__840_03 m__873 mDefLE mLERefl m_AddZero mSortsB mLETotal mAddComm m__ mZeroAdd mLEAsym mDefDiff mAddCanc mAddAsso
% 46.56/46.78
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