TSTP Solution File: RNG080+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG080+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 20:41:25 EDT 2022
% Result : Theorem 13.65s 13.89s
% Output : Refutation 13.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 42 ( 24 unt; 7 nHn; 42 RR)
% Number of literals : 85 ( 0 equ; 38 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aVector0(xs),
file('RNG080+1.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG080+1.p',unknown),
[] ).
cnf(21,axiom,
equal(sziznziztdt0(xs),xp),
file('RNG080+1.p',unknown),
[] ).
cnf(22,axiom,
equal(sziznziztdt0(xt),xq),
file('RNG080+1.p',unknown),
[] ).
cnf(23,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG080+1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(aDimensionOf0(xs),sz00),
file('RNG080+1.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtasasdt0(xp,xp),xC),
file('RNG080+1.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasasdt0(xq,xq),xD),
file('RNG080+1.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasasdt0(xp,xq),xE),
file('RNG080+1.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtasdt0(xA,xA),xF),
file('RNG080+1.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtasdt0(xB,xB),xG),
file('RNG080+1.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtasdt0(xA,xB),xH),
file('RNG080+1.p',unknown),
[] ).
cnf(39,axiom,
equal(sdtlbdtrb0(xs,aDimensionOf0(xs)),xA),
file('RNG080+1.p',unknown),
[] ).
cnf(40,axiom,
equal(sdtlbdtrb0(xt,aDimensionOf0(xt)),xB),
file('RNG080+1.p',unknown),
[] ).
cnf(67,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('RNG080+1.p',unknown),
[] ).
cnf(68,axiom,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
file('RNG080+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| equal(aDimensionOf0(u),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(v),sziznziztdt0(u)),sdtasdt0(sdtlbdtrb0(v,aDimensionOf0(v)),sdtlbdtrb0(u,aDimensionOf0(u)))),sdtasasdt0(v,u)) ),
file('RNG080+1.p',unknown),
[] ).
cnf(89,plain,
equal(sdtlbdtrb0(xt,aDimensionOf0(xs)),xB),
inference(rew,[status(thm),theory(equality)],[23,40]),
[iquote('0:Rew:23.0,40.0')] ).
cnf(1934,plain,
( ~ aVector0(xs)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xA)),sdtasasdt0(u,xs)) ),
inference(spr,[status(thm),theory(equality)],[39,87]),
[iquote('0:SpR:39.0,87.4')] ).
cnf(1951,plain,
( ~ aVector0(xt)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
| equal(aDimensionOf0(xt),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xq),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasasdt0(u,xt)) ),
inference(spr,[status(thm),theory(equality)],[22,87]),
[iquote('0:SpR:22.0,87.4')] ).
cnf(1958,plain,
( ~ aVector0(xs)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xp),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xA)),sdtasasdt0(u,xs)) ),
inference(rew,[status(thm),theory(equality)],[21,1934]),
[iquote('0:Rew:21.0,1934.4')] ).
cnf(1959,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xp),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xA)),sdtasasdt0(u,xs)) ),
inference(ssi,[status(thm)],[1958,3]),
[iquote('0:SSi:1958.0,3.0')] ).
cnf(1960,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xp),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xA)),sdtasasdt0(u,xs)) ),
inference(mrr,[status(thm)],[1959,24]),
[iquote('0:MRR:1959.2,24.0')] ).
cnf(1965,plain,
( ~ aVector0(xt)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xq),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xB)),sdtasasdt0(u,xt)) ),
inference(rew,[status(thm),theory(equality)],[89,1951,23]),
[iquote('0:Rew:89.0,1951.4,23.0,1951.4,23.0,1951.3,23.0,1951.2')] ).
cnf(1966,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xq),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xB)),sdtasasdt0(u,xt)) ),
inference(ssi,[status(thm)],[1965,4]),
[iquote('0:SSi:1965.0,4.0')] ).
cnf(1967,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(u),xq),sdtasdt0(sdtlbdtrb0(u,aDimensionOf0(u)),xB)),sdtasasdt0(u,xt)) ),
inference(mrr,[status(thm)],[1966,24]),
[iquote('0:MRR:1966.2,24.0')] ).
cnf(18009,plain,
( ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs))
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xp),sdtasdt0(xA,xA)),sdtasasdt0(xs,xs)) ),
inference(spr,[status(thm),theory(equality)],[39,1960]),
[iquote('0:SpR:39.0,1960.2')] ).
cnf(18022,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xp),sdtasdt0(xA,xA)),sdtasasdt0(xs,xs)) ),
inference(obv,[status(thm),theory(equality)],[18009]),
[iquote('0:Obv:18009.1')] ).
cnf(18023,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(xC,xF),sdtasasdt0(xs,xs)) ),
inference(rew,[status(thm),theory(equality)],[25,18022,21,28]),
[iquote('0:Rew:25.0,18022.1,21.0,18022.1,28.0,18022.1')] ).
cnf(18024,plain,
equal(sdtpldt0(xC,xF),sdtasasdt0(xs,xs)),
inference(ssi,[status(thm)],[18023,3]),
[iquote('0:SSi:18023.0,3.0')] ).
cnf(18025,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG))),
inference(rew,[status(thm),theory(equality)],[18024,67]),
[iquote('0:Rew:18024.0,67.0')] ).
cnf(18895,plain,
( ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs))
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xq),sdtasdt0(xA,xB)),sdtasasdt0(xs,xt)) ),
inference(spr,[status(thm),theory(equality)],[39,1967]),
[iquote('0:SpR:39.0,1967.2')] ).
cnf(18904,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),aDimensionOf0(xs))
| equal(sdtpldt0(sdtasasdt0(xq,xq),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),xB)),sdtasasdt0(xt,xt)) ),
inference(spr,[status(thm),theory(equality)],[22,1967]),
[iquote('0:SpR:22.0,1967.2')] ).
cnf(18908,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xq),sdtasdt0(xA,xB)),sdtasasdt0(xs,xt)) ),
inference(obv,[status(thm),theory(equality)],[18895]),
[iquote('0:Obv:18895.1')] ).
cnf(18909,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(xE,xH),sdtasasdt0(xs,xt)) ),
inference(rew,[status(thm),theory(equality)],[27,18908,21,30]),
[iquote('0:Rew:27.0,18908.1,21.0,18908.1,30.0,18908.1')] ).
cnf(18910,plain,
equal(sdtpldt0(xE,xH),sdtasasdt0(xs,xt)),
inference(ssi,[status(thm)],[18909,3]),
[iquote('0:SSi:18909.0,3.0')] ).
cnf(18913,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG))),
inference(rew,[status(thm),theory(equality)],[18910,18025]),
[iquote('0:Rew:18910.0,18025.0')] ).
cnf(18960,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs))
| equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)) ),
inference(rew,[status(thm),theory(equality)],[26,18904,29,89,23]),
[iquote('0:Rew:26.0,18904.2,29.0,18904.2,89.0,18904.2,23.0,18904.2,23.0,18904.1')] ).
cnf(18961,plain,
( ~ aVector0(xt)
| equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)) ),
inference(obv,[status(thm),theory(equality)],[18960]),
[iquote('0:Obv:18960.1')] ).
cnf(18962,plain,
equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)),
inference(ssi,[status(thm)],[18961,4]),
[iquote('0:SSi:18961.0,4.0')] ).
cnf(18982,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(rew,[status(thm),theory(equality)],[18962,18913]),
[iquote('0:Rew:18962.0,18913.0')] ).
cnf(18990,plain,
$false,
inference(mrr,[status(thm)],[18982,68]),
[iquote('0:MRR:18982.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG080+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 18:06:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 13.65/13.89
% 13.65/13.89 SPASS V 3.9
% 13.65/13.89 SPASS beiseite: Proof found.
% 13.65/13.89 % SZS status Theorem
% 13.65/13.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.65/13.89 SPASS derived 9741 clauses, backtracked 0 clauses, performed 0 splits and kept 3918 clauses.
% 13.65/13.89 SPASS allocated 119636 KBytes.
% 13.65/13.89 SPASS spent 0:0:11.91 on the problem.
% 13.65/13.89 0:00:00.04 for the input.
% 13.65/13.89 0:00:00.04 for the FLOTTER CNF translation.
% 13.65/13.89 0:00:00.17 for inferences.
% 13.65/13.89 0:00:00.00 for the backtracking.
% 13.65/13.89 0:0:11.58 for the reduction.
% 13.65/13.89
% 13.65/13.89
% 13.65/13.89 Here is a proof with depth 2, length 42 :
% 13.65/13.89 % SZS output start Refutation
% See solution above
% 13.65/13.89 Formulae used in the proof : m__1678 m__1709 m__1726 m__1678_01 m__1692 m__1783 m__1800 m__1820 m__1837 m__1854 m__1873 m__1746 m__1766 m__2733 m__ mDefSPN
% 13.65/13.89
%------------------------------------------------------------------------------