TSTP Solution File: RNG123+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG123+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 20:41:33 EDT 2022
% Result : Theorem 2.84s 3.07s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of clauses : 60 ( 26 unt; 0 nHn; 60 RR)
% Number of literals : 131 ( 0 equ; 72 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aElement0(xa),
file('RNG123+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xb),
file('RNG123+1.p',unknown),
[] ).
cnf(5,axiom,
aIdeal0(xI),
file('RNG123+1.p',unknown),
[] ).
cnf(8,axiom,
aElement0(xq),
file('RNG123+1.p',unknown),
[] ).
cnf(9,axiom,
aElement0(xr),
file('RNG123+1.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(xu,xI),
file('RNG123+1.p',unknown),
[] ).
cnf(13,axiom,
aElementOf0(xb,xI),
file('RNG123+1.p',unknown),
[] ).
cnf(14,axiom,
~ aElementOf0(xr,xI),
file('RNG123+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG123+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG123+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aElement0(u)
| aIdeal0(slsdtgt0(u)) ),
file('RNG123+1.p',unknown),
[] ).
cnf(34,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('RNG123+1.p',unknown),
[] ).
cnf(35,axiom,
equal(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),xI),
file('RNG123+1.p',unknown),
[] ).
cnf(37,axiom,
equal(sdtpldt0(sdtasdt0(xq,xu),xr),xb),
file('RNG123+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG123+1.p',unknown),
[] ).
cnf(48,axiom,
equal(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xr),
file('RNG123+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG123+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG123+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG123+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG123+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ aElement0(u)
| ~ equal(v,slsdtgt0(u))
| aSet0(v) ),
file('RNG123+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG123+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ equal(w,sdtpldt1(v,u))
| aSet0(w) ),
file('RNG123+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ aIdeal0(u)
| ~ aElementOf0(v,u)
| ~ aElementOf0(w,u)
| aElementOf0(sdtpldt0(w,v),u) ),
file('RNG123+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG123+1.p',unknown),
[] ).
cnf(149,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(res,[status(thm),theory(equality)],[11,51]),
[iquote('0:Res:11.0,51.1')] ).
cnf(158,plain,
aElement0(xu),
inference(ssi,[status(thm)],[149,30,5]),
[iquote('0:SSi:149.0,30.0,5.1')] ).
cnf(189,plain,
( ~ aElement0(u)
| aSet0(slsdtgt0(u)) ),
inference(eqr,[status(thm),theory(equality)],[64]),
[iquote('0:EqR:64.1')] ).
cnf(241,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| equal(sdtpldt0(xr,sdtasdt0(xq,xu)),xb) ),
inference(spr,[status(thm),theory(equality)],[69,37]),
[iquote('0:SpR:69.2,37.0')] ).
cnf(243,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| equal(sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))),xr) ),
inference(spr,[status(thm),theory(equality)],[69,48]),
[iquote('0:SpR:69.2,48.0')] ).
cnf(263,plain,
equal(sdtpldt0(xr,sdtasdt0(xq,xu)),xb),
inference(ssi,[status(thm)],[241,58,8,158,9]),
[iquote('0:SSi:241.1,241.0,58.0,8.0,158.0,9.2')] ).
cnf(269,plain,
equal(sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))),xr),
inference(ssi,[status(thm)],[243,31,58,8,158,4]),
[iquote('0:SSi:243.1,243.0,31.0,58.0,8.0,158.2,4.1')] ).
cnf(292,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| aSet0(sdtpldt1(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[74]),
[iquote('0:EqR:74.2')] ).
cnf(295,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| aSet0(xI) ),
inference(spr,[status(thm),theory(equality)],[35,292]),
[iquote('0:SpR:35.0,292.2')] ).
cnf(296,plain,
aSet0(xI),
inference(ssi,[status(thm)],[295,33,3,189,4]),
[iquote('0:SSi:295.1,295.0,33.0,3.1,189.0,3.1,33.0,4.1,189.0,4.1')] ).
cnf(347,plain,
( ~ aIdeal0(u)
| ~ aElementOf0(xb,u)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),u)
| aElementOf0(xr,u) ),
inference(spr,[status(thm),theory(equality)],[48,82]),
[iquote('0:SpR:48.0,82.3')] ).
cnf(887,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[50,99]),
[iquote('0:SpR:50.1,99.3')] ).
cnf(918,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[887]),
[iquote('0:Obv:887.0')] ).
cnf(919,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[39,918]),
[iquote('0:Rew:39.1,918.3')] ).
cnf(920,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[919,31]),
[iquote('0:SSi:919.2,31.1')] ).
cnf(3074,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(xr)
| equal(sdtasdt0(xq,xu),sdtpldt0(smndt0(xr),xb)) ),
inference(spr,[status(thm),theory(equality)],[263,920]),
[iquote('0:SpR:263.0,920.2')] ).
cnf(3079,plain,
( ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| ~ aElement0(xb)
| equal(smndt0(sdtasdt0(xq,xu)),sdtpldt0(smndt0(xb),xr)) ),
inference(spr,[status(thm),theory(equality)],[269,920]),
[iquote('0:SpR:269.0,920.2')] ).
cnf(3093,plain,
equal(sdtasdt0(xq,xu),sdtpldt0(smndt0(xr),xb)),
inference(ssi,[status(thm)],[3074,9,58,8,158]),
[iquote('0:SSi:3074.1,3074.0,9.0,58.0,8.2,158.0')] ).
cnf(3094,plain,
aElementOf0(smndt0(sdtpldt0(smndt0(xr),xb)),xI),
inference(rew,[status(thm),theory(equality)],[3093,34]),
[iquote('0:Rew:3093.0,34.0')] ).
cnf(3101,plain,
equal(sdtpldt0(xr,sdtpldt0(smndt0(xr),xb)),xb),
inference(rew,[status(thm),theory(equality)],[3093,263]),
[iquote('0:Rew:3093.0,263.0')] ).
cnf(3109,plain,
( ~ aIdeal0(u)
| ~ aElementOf0(xb,u)
| ~ aElementOf0(smndt0(sdtpldt0(smndt0(xr),xb)),u)
| aElementOf0(xr,u) ),
inference(rew,[status(thm),theory(equality)],[3093,347]),
[iquote('0:Rew:3093.0,347.2')] ).
cnf(3187,plain,
( ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| ~ aElement0(xb)
| equal(smndt0(sdtpldt0(smndt0(xr),xb)),sdtpldt0(smndt0(xb),xr)) ),
inference(rew,[status(thm),theory(equality)],[3093,3079]),
[iquote('0:Rew:3093.0,3079.2')] ).
cnf(3188,plain,
equal(smndt0(sdtpldt0(smndt0(xr),xb)),sdtpldt0(smndt0(xb),xr)),
inference(ssi,[status(thm)],[3187,4,31,58,8,158]),
[iquote('0:SSi:3187.1,3187.0,4.0,31.0,58.2,8.1,158.0')] ).
cnf(3190,plain,
aElementOf0(sdtpldt0(smndt0(xb),xr),xI),
inference(rew,[status(thm),theory(equality)],[3188,3094]),
[iquote('0:Rew:3188.0,3094.0')] ).
cnf(3202,plain,
( ~ aIdeal0(u)
| ~ aElementOf0(xb,u)
| ~ aElementOf0(sdtpldt0(smndt0(xb),xr),u)
| aElementOf0(xr,u) ),
inference(rew,[status(thm),theory(equality)],[3188,3109]),
[iquote('0:Rew:3188.0,3109.2')] ).
cnf(3411,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(xr))
| equal(sdtpldt0(xr,sdtpldt0(xb,smndt0(xr))),xb) ),
inference(spr,[status(thm),theory(equality)],[69,3101]),
[iquote('0:SpR:69.2,3101.0')] ).
cnf(3414,plain,
equal(sdtpldt0(xr,sdtpldt0(xb,smndt0(xr))),xb),
inference(ssi,[status(thm)],[3411,31,9,4]),
[iquote('0:SSi:3411.1,3411.0,31.0,9.0,4.1')] ).
cnf(3545,plain,
( ~ aElement0(sdtpldt0(xb,smndt0(xr)))
| ~ aElement0(xr)
| equal(sdtpldt0(smndt0(xr),xb),sdtpldt0(xb,smndt0(xr))) ),
inference(spr,[status(thm),theory(equality)],[3414,920]),
[iquote('0:SpR:3414.0,920.2')] ).
cnf(3551,plain,
equal(sdtpldt0(smndt0(xr),xb),sdtpldt0(xb,smndt0(xr))),
inference(ssi,[status(thm)],[3545,9,57,4,31]),
[iquote('0:SSi:3545.1,3545.0,9.0,57.1,4.0,31.2,9.0')] ).
cnf(3584,plain,
equal(sdtpldt0(smndt0(xb),xr),smndt0(sdtpldt0(xb,smndt0(xr)))),
inference(rew,[status(thm),theory(equality)],[3551,3188]),
[iquote('0:Rew:3551.0,3188.0')] ).
cnf(3599,plain,
aElementOf0(smndt0(sdtpldt0(xb,smndt0(xr))),xI),
inference(rew,[status(thm),theory(equality)],[3584,3190]),
[iquote('0:Rew:3584.0,3190.0')] ).
cnf(3610,plain,
( ~ aIdeal0(u)
| ~ aElementOf0(xb,u)
| ~ aElementOf0(smndt0(sdtpldt0(xb,smndt0(xr))),u)
| aElementOf0(xr,u) ),
inference(rew,[status(thm),theory(equality)],[3584,3202]),
[iquote('0:Rew:3584.0,3202.2')] ).
cnf(8657,plain,
( ~ aIdeal0(xI)
| ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI) ),
inference(res,[status(thm),theory(equality)],[3599,3610]),
[iquote('0:Res:3599.0,3610.2')] ).
cnf(8660,plain,
( ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI) ),
inference(ssi,[status(thm)],[8657,5,296]),
[iquote('0:SSi:8657.0,5.0,296.0')] ).
cnf(8661,plain,
$false,
inference(mrr,[status(thm)],[8660,13,14]),
[iquote('0:MRR:8660.0,8660.1,13.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG123+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 13:51:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.84/3.07
% 2.84/3.07 SPASS V 3.9
% 2.84/3.07 SPASS beiseite: Proof found.
% 2.84/3.07 % SZS status Theorem
% 2.84/3.07 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.84/3.07 SPASS derived 5496 clauses, backtracked 0 clauses, performed 4 splits and kept 2063 clauses.
% 2.84/3.07 SPASS allocated 106482 KBytes.
% 2.84/3.07 SPASS spent 0:00:02.42 on the problem.
% 2.84/3.07 0:00:00.04 for the input.
% 2.84/3.07 0:00:00.14 for the FLOTTER CNF translation.
% 2.84/3.07 0:00:00.11 for inferences.
% 2.84/3.07 0:00:00.00 for the backtracking.
% 2.84/3.07 0:00:02.08 for the reduction.
% 2.84/3.07
% 2.84/3.07
% 2.84/3.07 Here is a proof with depth 3, length 60 :
% 2.84/3.07 % SZS output start Refutation
% See solution above
% 2.84/3.07 Formulae used in the proof : m__2091 m__2174 m__2666 m__2273 m__2699 m__ mDefIdeal mSortsU mPrIdeal m__2690 mAddZero m__2718 mAddInvr mEOfElem mSortsB mSortsB_02 mDefPrIdeal mAddComm mDefSSum mAddAsso
% 2.84/3.07
%------------------------------------------------------------------------------