TSTP Solution File: RNG080+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG080+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 26.93s 27.18s
% Output : Refutation 26.93s
% 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+2.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG080+2.p',unknown),
[] ).
cnf(21,axiom,
equal(sziznziztdt0(xs),xp),
file('RNG080+2.p',unknown),
[] ).
cnf(22,axiom,
equal(sziznziztdt0(xt),xq),
file('RNG080+2.p',unknown),
[] ).
cnf(23,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG080+2.p',unknown),
[] ).
cnf(24,axiom,
~ equal(aDimensionOf0(xs),sz00),
file('RNG080+2.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtasasdt0(xp,xp),xC),
file('RNG080+2.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasasdt0(xq,xq),xD),
file('RNG080+2.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasasdt0(xp,xq),xE),
file('RNG080+2.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtasdt0(xA,xA),xF),
file('RNG080+2.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtasdt0(xB,xB),xG),
file('RNG080+2.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtasdt0(xA,xB),xH),
file('RNG080+2.p',unknown),
[] ).
cnf(41,axiom,
equal(sdtlbdtrb0(xs,aDimensionOf0(xs)),xA),
file('RNG080+2.p',unknown),
[] ).
cnf(42,axiom,
equal(sdtlbdtrb0(xt,aDimensionOf0(xt)),xB),
file('RNG080+2.p',unknown),
[] ).
cnf(71,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('RNG080+2.p',unknown),
[] ).
cnf(72,axiom,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
file('RNG080+2.p',unknown),
[] ).
cnf(91,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+2.p',unknown),
[] ).
cnf(93,plain,
equal(sdtlbdtrb0(xt,aDimensionOf0(xs)),xB),
inference(rew,[status(thm),theory(equality)],[23,42]),
[iquote('0:Rew:23.0,42.0')] ).
cnf(2092,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)],[41,91]),
[iquote('0:SpR:41.0,91.4')] ).
cnf(2114,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)],[22,91]),
[iquote('0:SpR:22.0,91.4')] ).
cnf(2121,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)],[21,2092]),
[iquote('0:Rew:21.0,2092.4')] ).
cnf(2122,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)],[2121,3]),
[iquote('0:SSi:2121.0,3.0')] ).
cnf(2123,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)],[2122,24]),
[iquote('0:MRR:2122.2,24.0')] ).
cnf(2128,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)],[93,2114,23]),
[iquote('0:Rew:93.0,2114.4,23.0,2114.4,23.0,2114.3,23.0,2114.2')] ).
cnf(2129,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)],[2128,4]),
[iquote('0:SSi:2128.0,4.0')] ).
cnf(2130,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)],[2129,24]),
[iquote('0:MRR:2129.2,24.0')] ).
cnf(30632,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)],[41,2130]),
[iquote('0:SpR:41.0,2130.2')] ).
cnf(30651,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)],[22,2130]),
[iquote('0:SpR:22.0,2130.2')] ).
cnf(30655,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xq),sdtasdt0(xA,xB)),sdtasasdt0(xs,xt)) ),
inference(obv,[status(thm),theory(equality)],[30632]),
[iquote('0:Obv:30632.1')] ).
cnf(30656,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(xE,xH),sdtasasdt0(xs,xt)) ),
inference(rew,[status(thm),theory(equality)],[27,30655,21,30]),
[iquote('0:Rew:27.0,30655.1,21.0,30655.1,30.0,30655.1')] ).
cnf(30657,plain,
equal(sdtpldt0(xE,xH),sdtasasdt0(xs,xt)),
inference(ssi,[status(thm)],[30656,3]),
[iquote('0:SSi:30656.0,3.0')] ).
cnf(30658,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(rew,[status(thm),theory(equality)],[30657,71]),
[iquote('0:Rew:30657.0,71.0')] ).
cnf(30711,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs))
| equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)) ),
inference(rew,[status(thm),theory(equality)],[26,30651,29,93,23]),
[iquote('0:Rew:26.0,30651.2,29.0,30651.2,93.0,30651.2,23.0,30651.2,23.0,30651.1')] ).
cnf(30712,plain,
( ~ aVector0(xt)
| equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)) ),
inference(obv,[status(thm),theory(equality)],[30711]),
[iquote('0:Obv:30711.1')] ).
cnf(30713,plain,
equal(sdtpldt0(xD,xG),sdtasasdt0(xt,xt)),
inference(ssi,[status(thm)],[30712,4]),
[iquote('0:SSi:30712.0,4.0')] ).
cnf(30729,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtasasdt0(xt,xt))),
inference(rew,[status(thm),theory(equality)],[30713,30658]),
[iquote('0:Rew:30713.0,30658.0')] ).
cnf(31907,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)],[41,2123]),
[iquote('0:SpR:41.0,2123.2')] ).
cnf(31930,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xp),sdtasdt0(xA,xA)),sdtasasdt0(xs,xs)) ),
inference(obv,[status(thm),theory(equality)],[31907]),
[iquote('0:Obv:31907.1')] ).
cnf(31931,plain,
( ~ aVector0(xs)
| equal(sdtpldt0(xC,xF),sdtasasdt0(xs,xs)) ),
inference(rew,[status(thm),theory(equality)],[25,31930,21,28]),
[iquote('0:Rew:25.0,31930.1,21.0,31930.1,28.0,31930.1')] ).
cnf(31932,plain,
equal(sdtpldt0(xC,xF),sdtasasdt0(xs,xs)),
inference(ssi,[status(thm)],[31931,3]),
[iquote('0:SSi:31931.0,3.0')] ).
cnf(31933,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(rew,[status(thm),theory(equality)],[31932,30729]),
[iquote('0:Rew:31932.0,30729.0')] ).
cnf(31985,plain,
$false,
inference(mrr,[status(thm)],[31933,72]),
[iquote('0:MRR:31933.0,72.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG080+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 19:49:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 26.93/27.18
% 26.93/27.18 SPASS V 3.9
% 26.93/27.18 SPASS beiseite: Proof found.
% 26.93/27.18 % SZS status Theorem
% 26.93/27.18 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.93/27.18 SPASS derived 17050 clauses, backtracked 1919 clauses, performed 4 splits and kept 6457 clauses.
% 26.93/27.18 SPASS allocated 128422 KBytes.
% 26.93/27.18 SPASS spent 0:0:22.20 on the problem.
% 26.93/27.18 0:00:00.04 for the input.
% 26.93/27.18 0:00:00.04 for the FLOTTER CNF translation.
% 26.93/27.18 0:00:00.30 for inferences.
% 26.93/27.18 0:00:00.16 for the backtracking.
% 26.93/27.18 0:0:21.51 for the reduction.
% 26.93/27.18
% 26.93/27.18
% 26.93/27.18 Here is a proof with depth 2, length 42 :
% 26.93/27.18 % SZS output start Refutation
% See solution above
% 26.93/27.18 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
% 26.93/27.18
%------------------------------------------------------------------------------