TSTP Solution File: KLE120+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE120+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:37 EDT 2022
% Result : Theorem 1.86s 2.03s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of clauses : 94 ( 88 unt; 0 nHn; 94 RR)
% Number of literals : 100 ( 0 equ; 14 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE120+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE120+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE120+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE120+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE120+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE120+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE120+1.p',unknown),
[] ).
cnf(10,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE120+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE120+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE120+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE120+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE120+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE120+1.p',unknown),
[] ).
cnf(19,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE120+1.p',unknown),
[] ).
cnf(22,axiom,
~ equal(addition(backward_diamond(one,domain__dfg(skc1)),domain__dfg(skc1)),domain__dfg(skc1)),
file('KLE120+1.p',unknown),
[] ).
cnf(23,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE120+1.p',unknown),
[] ).
cnf(24,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE120+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE120+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE120+1.p',unknown),
[] ).
cnf(27,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE120+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE120+1.p',unknown),
[] ).
cnf(30,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,14]),
[iquote('0:Rew:12.0,14.0')] ).
cnf(31,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,13]),
[iquote('0:Rew:12.0,13.0')] ).
cnf(34,plain,
equal(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(u)),v))),backward_diamond(v,u)),
inference(rew,[status(thm),theory(equality)],[10,19]),
[iquote('0:Rew:10.0,19.0,10.0,19.0')] ).
cnf(38,plain,
~ equal(addition(antidomain(antidomain(skc1)),backward_diamond(one,antidomain(antidomain(skc1)))),antidomain(antidomain(skc1))),
inference(rew,[status(thm),theory(equality)],[12,22,8]),
[iquote('0:Rew:12.0,22.0,8.0,22.0')] ).
cnf(52,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(56,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(63,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(72,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[56,30]),
[iquote('0:SpR:56.0,30.0')] ).
cnf(74,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[63,72]),
[iquote('0:Rew:63.0,72.0')] ).
cnf(86,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[52,31]),
[iquote('0:SpR:52.0,31.0')] ).
cnf(88,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[63,86]),
[iquote('0:Rew:63.0,86.0')] ).
cnf(162,plain,
equal(backward_diamond(one,u),coantidomain(coantidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[3,34]),
[iquote('0:SpR:3.0,34.0')] ).
cnf(165,plain,
~ equal(addition(antidomain(antidomain(skc1)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(skc1))))))),antidomain(antidomain(skc1))),
inference(rew,[status(thm),theory(equality)],[162,38]),
[iquote('0:Rew:162.0,38.0')] ).
cnf(264,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(293,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[30,264]),
[iquote('0:SpR:30.0,264.0')] ).
cnf(294,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,264]),
[iquote('0:SpR:31.0,264.0')] ).
cnf(296,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[264,16]),
[iquote('0:SpL:264.0,16.0')] ).
cnf(298,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,293]),
[iquote('0:Rew:12.0,293.0')] ).
cnf(299,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,294]),
[iquote('0:Rew:12.0,294.0')] ).
cnf(302,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[296]),
[iquote('0:Obv:296.0')] ).
cnf(308,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,302]),
[iquote('0:SpR:12.0,302.0')] ).
cnf(365,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[26,9]),
[iquote('0:SpR:26.0,9.0')] ).
cnf(378,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[30,26]),
[iquote('0:SpR:30.0,26.0')] ).
cnf(380,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(381,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[299,26]),
[iquote('0:SpR:299.0,26.0')] ).
cnf(388,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,381]),
[iquote('0:Rew:4.0,381.0')] ).
cnf(392,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,378]),
[iquote('0:Rew:4.0,378.0')] ).
cnf(393,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,380]),
[iquote('0:Rew:4.0,380.0')] ).
cnf(475,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[30,25]),
[iquote('0:SpR:30.0,25.0')] ).
cnf(477,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[31,25]),
[iquote('0:SpR:31.0,25.0')] ).
cnf(478,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[299,25]),
[iquote('0:SpR:299.0,25.0')] ).
cnf(487,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,478]),
[iquote('0:Rew:3.0,478.0')] ).
cnf(492,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,475]),
[iquote('0:Rew:3.0,475.0')] ).
cnf(493,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,477]),
[iquote('0:Rew:3.0,477.0')] ).
cnf(551,plain,
( ~ leq(antidomain(antidomain(skc1)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(skc1)))))))
| ~ equal(coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(skc1)))))),antidomain(antidomain(skc1))) ),
inference(spl,[status(thm),theory(equality)],[15,165]),
[iquote('0:SpL:15.1,165.0')] ).
cnf(680,plain,
equal(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(702,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[298,680,74]),
[iquote('0:Rew:298.0,680.0,74.0,680.0')] ).
cnf(822,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[7,27]),
[iquote('0:SpR:7.0,27.0')] ).
cnf(844,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[299,822,88]),
[iquote('0:Rew:299.0,822.0,88.0,822.0')] ).
cnf(875,plain,
leq(multiplication(antidomain(u),v),v),
inference(spr,[status(thm),theory(equality)],[388,308]),
[iquote('0:SpR:388.0,308.0')] ).
cnf(927,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[702,9]),
[iquote('0:SpR:702.0,9.0')] ).
cnf(958,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,927,24]),
[iquote('0:Rew:3.0,927.0,24.0,927.0')] ).
cnf(1203,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[844,7]),
[iquote('0:SpR:844.0,7.0')] ).
cnf(1240,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1203]),
[iquote('0:Rew:4.0,1203.0')] ).
cnf(3676,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[958,392]),
[iquote('0:SpR:958.0,392.0')] ).
cnf(3679,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[9,392]),
[iquote('0:SpR:9.0,392.0')] ).
cnf(3704,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[63,3676,12]),
[iquote('0:Rew:63.0,3676.0,12.0,3676.0')] ).
cnf(3717,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[63,3679,12]),
[iquote('0:Rew:63.0,3679.0,12.0,3679.0')] ).
cnf(3851,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1240,393]),
[iquote('0:SpR:1240.0,393.0')] ).
cnf(3887,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[63,3851,12]),
[iquote('0:Rew:63.0,3851.0,12.0,3851.0')] ).
cnf(4093,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,492]),
[iquote('0:SpR:9.0,492.0')] ).
cnf(4106,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[63,4093]),
[iquote('0:Rew:63.0,4093.0')] ).
cnf(4107,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4106,3717]),
[iquote('0:Rew:4106.0,3717.0')] ).
cnf(4125,plain,
( ~ leq(antidomain(antidomain(skc1)),coantidomain(coantidomain(antidomain(antidomain(skc1)))))
| ~ equal(coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(skc1)))))),antidomain(antidomain(skc1))) ),
inference(rew,[status(thm),theory(equality)],[4107,551]),
[iquote('0:Rew:4107.0,551.0')] ).
cnf(4175,plain,
( ~ leq(antidomain(antidomain(skc1)),coantidomain(coantidomain(antidomain(antidomain(skc1)))))
| ~ equal(coantidomain(coantidomain(antidomain(antidomain(skc1)))),antidomain(antidomain(skc1))) ),
inference(rew,[status(thm),theory(equality)],[4107,4125]),
[iquote('0:Rew:4107.0,4125.1')] ).
cnf(4446,plain,
leq(antidomain(u),coantidomain(coantidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[4106,875]),
[iquote('0:SpR:4106.0,875.0')] ).
cnf(4477,plain,
~ equal(coantidomain(coantidomain(antidomain(antidomain(skc1)))),antidomain(antidomain(skc1))),
inference(mrr,[status(thm)],[4175,4446]),
[iquote('0:MRR:4175.0,4446.0')] ).
cnf(4890,plain,
equal(addition(multiplication(coantidomain(antidomain(antidomain(antidomain(u)))),antidomain(u)),antidomain(antidomain(u))),coantidomain(antidomain(antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[3704,493]),
[iquote('0:SpR:3704.0,493.0')] ).
cnf(4902,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1240,493]),
[iquote('0:SpR:1240.0,493.0')] ).
cnf(4905,plain,
equal(addition(antidomain(u),multiplication(coantidomain(antidomain(antidomain(u))),antidomain(antidomain(u)))),coantidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[3704,493]),
[iquote('0:SpR:3704.0,493.0')] ).
cnf(4925,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[63,4902]),
[iquote('0:Rew:63.0,4902.0')] ).
cnf(4926,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[3887,4925]),
[iquote('0:Rew:3887.0,4925.0')] ).
cnf(4988,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(antidomain(antidomain(u)))),antidomain(u))),coantidomain(antidomain(antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[12,4890]),
[iquote('0:Rew:12.0,4890.0')] ).
cnf(4989,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4926,4988]),
[iquote('0:Rew:4926.0,4988.0')] ).
cnf(6950,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[487,365]),
[iquote('0:SpR:487.0,365.0')] ).
cnf(7065,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[63,6950,9,24]),
[iquote('0:Rew:63.0,6950.0,9.0,6950.0,24.0,6950.0')] ).
cnf(13745,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4106,7065]),
[iquote('0:SpR:4106.0,7065.0')] ).
cnf(13761,plain,
equal(addition(antidomain(u),zero),coantidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[13745,4905]),
[iquote('0:Rew:13745.0,4905.0')] ).
cnf(13762,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[13745,4989]),
[iquote('0:Rew:13745.0,4989.0')] ).
cnf(13763,plain,
equal(coantidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[63,13761,12]),
[iquote('0:Rew:63.0,13761.0,12.0,13761.0')] ).
cnf(13765,plain,
~ equal(coantidomain(antidomain(skc1)),antidomain(antidomain(skc1))),
inference(rew,[status(thm),theory(equality)],[13763,4477]),
[iquote('0:Rew:13763.0,4477.0')] ).
cnf(13797,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[63,13762,12]),
[iquote('0:Rew:63.0,13762.0,12.0,13762.0')] ).
cnf(13798,plain,
$false,
inference(unc,[status(thm)],[13797,13765]),
[iquote('0:UnC:13797.0,13765.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE120+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 16 15:07:48 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.86/2.03
% 1.86/2.03 SPASS V 3.9
% 1.86/2.03 SPASS beiseite: Proof found.
% 1.86/2.03 % SZS status Theorem
% 1.86/2.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.86/2.03 SPASS derived 9476 clauses, backtracked 0 clauses, performed 0 splits and kept 1818 clauses.
% 1.86/2.03 SPASS allocated 96224 KBytes.
% 1.86/2.03 SPASS spent 0:00:01.70 on the problem.
% 1.86/2.03 0:00:00.04 for the input.
% 1.86/2.03 0:00:00.03 for the FLOTTER CNF translation.
% 1.86/2.03 0:00:00.07 for inferences.
% 1.86/2.03 0:00:00.00 for the backtracking.
% 1.86/2.03 0:00:01.53 for the reduction.
% 1.86/2.03
% 1.86/2.03
% 1.86/2.03 Here is a proof with depth 5, length 94 :
% 1.86/2.03 % SZS output start Refutation
% See solution above
% 1.87/2.10 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 codomain1 codomain4 additive_commutativity domain3 codomain3 order backward_diamond goals additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 1.87/2.10
%------------------------------------------------------------------------------