TSTP Solution File: RNG047+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG047+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 20:41:19 EDT 2022
% Result : Theorem 44.84s 45.02s
% Output : Refutation 44.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 9 unt; 17 nHn; 31 RR)
% Number of literals : 80 ( 0 equ; 36 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aVector0(xs),
file('RNG047+1.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG047+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(skf2(u)),
file('RNG047+1.p',unknown),
[] ).
cnf(7,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG047+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(aDimensionOf0(xt),sz00),
file('RNG047+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ aNaturalNumber0(u)
| aNaturalNumber0(szszuzczcdt0(u)) ),
file('RNG047+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aVector0(u)
| aNaturalNumber0(aDimensionOf0(u)) ),
file('RNG047+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(aDimensionOf0(sziznziztdt0(xt)),aDimensionOf0(sziznziztdt0(xs))),
file('RNG047+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(szszuzczcdt0(u),sz00) ),
file('RNG047+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| equal(szszuzczcdt0(skf2(u)),u) ),
file('RNG047+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aVector0(u)
| ~ equal(v,sziznziztdt0(u))
| aVector0(v)
| equal(aDimensionOf0(u),sz00) ),
file('RNG047+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(szszuzczcdt0(v),szszuzczcdt0(u))
| equal(v,u) ),
file('RNG047+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aVector0(u)
| ~ equal(v,sziznziztdt0(u))
| equal(aDimensionOf0(u),sz00)
| equal(szszuzczcdt0(aDimensionOf0(v)),aDimensionOf0(u)) ),
file('RNG047+1.p',unknown),
[] ).
cnf(52,plain,
~ equal(aDimensionOf0(xs),sz00),
inference(rew,[status(thm),theory(equality)],[7,8]),
[iquote('0:Rew:7.0,8.0')] ).
cnf(143,plain,
( ~ aVector0(u)
| aVector0(sziznziztdt0(u))
| equal(aDimensionOf0(u),sz00) ),
inference(eqr,[status(thm),theory(equality)],[32]),
[iquote('0:EqR:32.1')] ).
cnf(263,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skf2(u))
| ~ aNaturalNumber0(v)
| ~ equal(szszuzczcdt0(v),u)
| equal(u,sz00)
| equal(v,skf2(u)) ),
inference(spl,[status(thm),theory(equality)],[28,33]),
[iquote('0:SpL:28.2,33.2')] ).
cnf(264,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(szszuzczcdt0(v),u)
| equal(u,sz00)
| equal(v,skf2(u)) ),
inference(ssi,[status(thm)],[263,5]),
[iquote('0:SSi:263.1,5.0')] ).
cnf(500,plain,
( ~ aVector0(u)
| equal(aDimensionOf0(u),sz00)
| equal(szszuzczcdt0(aDimensionOf0(sziznziztdt0(u))),aDimensionOf0(u)) ),
inference(eqr,[status(thm),theory(equality)],[38]),
[iquote('0:EqR:38.1')] ).
cnf(6667,plain,
( ~ aNaturalNumber0(szszuzczcdt0(u))
| ~ aNaturalNumber0(u)
| equal(szszuzczcdt0(u),sz00)
| equal(skf2(szszuzczcdt0(u)),u) ),
inference(eqr,[status(thm),theory(equality)],[264]),
[iquote('0:EqR:264.2')] ).
cnf(6670,plain,
( ~ aNaturalNumber0(u)
| equal(szszuzczcdt0(u),sz00)
| equal(skf2(szszuzczcdt0(u)),u) ),
inference(ssi,[status(thm)],[6667,9]),
[iquote('0:SSi:6667.0,9.1')] ).
cnf(6671,plain,
( ~ aNaturalNumber0(u)
| equal(skf2(szszuzczcdt0(u)),u) ),
inference(mrr,[status(thm)],[6670,16]),
[iquote('0:MRR:6670.1,16.1')] ).
cnf(6678,plain,
( ~ aVector0(u)
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(u)))
| equal(aDimensionOf0(u),sz00)
| equal(skf2(aDimensionOf0(u)),aDimensionOf0(sziznziztdt0(u))) ),
inference(spr,[status(thm),theory(equality)],[500,6671]),
[iquote('0:SpR:500.2,6671.1')] ).
cnf(33046,plain,
( ~ aVector0(u)
| ~ aVector0(sziznziztdt0(u))
| equal(aDimensionOf0(u),sz00)
| equal(skf2(aDimensionOf0(u)),aDimensionOf0(sziznziztdt0(u))) ),
inference(sor,[status(thm)],[6678,12]),
[iquote('0:SoR:6678.1,12.1')] ).
cnf(33047,plain,
( ~ aVector0(u)
| equal(aDimensionOf0(u),sz00)
| equal(skf2(aDimensionOf0(u)),aDimensionOf0(sziznziztdt0(u))) ),
inference(mrr,[status(thm)],[33046,143]),
[iquote('0:MRR:33046.1,143.1')] ).
cnf(33052,plain,
( ~ aVector0(xt)
| equal(aDimensionOf0(xt),sz00)
| equal(skf2(aDimensionOf0(xs)),aDimensionOf0(sziznziztdt0(xt))) ),
inference(spr,[status(thm),theory(equality)],[7,33047]),
[iquote('0:SpR:7.0,33047.2')] ).
cnf(33055,plain,
( ~ aVector0(xt)
| equal(aDimensionOf0(xs),sz00)
| equal(skf2(aDimensionOf0(xs)),aDimensionOf0(sziznziztdt0(xt))) ),
inference(rew,[status(thm),theory(equality)],[7,33052]),
[iquote('0:Rew:7.0,33052.1')] ).
cnf(33056,plain,
( equal(aDimensionOf0(xs),sz00)
| equal(skf2(aDimensionOf0(xs)),aDimensionOf0(sziznziztdt0(xt))) ),
inference(ssi,[status(thm)],[33055,4]),
[iquote('0:SSi:33055.0,4.0')] ).
cnf(33057,plain,
equal(skf2(aDimensionOf0(xs)),aDimensionOf0(sziznziztdt0(xt))),
inference(mrr,[status(thm)],[33056,52]),
[iquote('0:MRR:33056.0,52.0')] ).
cnf(33063,plain,
( ~ aVector0(xs)
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(sziznziztdt0(xt)),aDimensionOf0(sziznziztdt0(xs))) ),
inference(spr,[status(thm),theory(equality)],[33057,33047]),
[iquote('0:SpR:33057.0,33047.2')] ).
cnf(33065,plain,
( equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(sziznziztdt0(xt)),aDimensionOf0(sziznziztdt0(xs))) ),
inference(ssi,[status(thm)],[33063,3]),
[iquote('0:SSi:33063.0,3.0')] ).
cnf(33066,plain,
$false,
inference(mrr,[status(thm)],[33065,52,15]),
[iquote('0:MRR:33065.0,33065.1,52.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG047+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 21:00:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 44.84/45.02
% 44.84/45.02 SPASS V 3.9
% 44.84/45.02 SPASS beiseite: Proof found.
% 44.84/45.02 % SZS status Theorem
% 44.84/45.02 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.84/45.02 SPASS derived 14523 clauses, backtracked 0 clauses, performed 0 splits and kept 2550 clauses.
% 44.84/45.02 SPASS allocated 130839 KBytes.
% 44.84/45.02 SPASS spent 0:0:24.75 on the problem.
% 44.84/45.02 0:00:00.03 for the input.
% 44.84/45.02 0:00:00.04 for the FLOTTER CNF translation.
% 44.84/45.02 0:00:00.12 for inferences.
% 44.84/45.02 0:00:00.00 for the backtracking.
% 44.84/45.02 0:0:24.51 for the reduction.
% 44.84/45.02
% 44.84/45.02
% 44.84/45.02 Here is a proof with depth 6, length 31 :
% 44.84/45.02 % SZS output start Refutation
% See solution above
% 44.84/45.02 Formulae used in the proof : m__1329 mNatExtr mZeroNat m__1329_01 mSuccNat mDimNat m__ mDefInit mSuccEqu
% 44.84/45.02
%------------------------------------------------------------------------------