TSTP Solution File: NUM431+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM431+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:26:07 EDT 2022
% Result : Theorem 46.85s 47.08s
% Output : Refutation 46.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of clauses : 56 ( 14 unt; 0 nHn; 56 RR)
% Number of literals : 160 ( 0 equ; 114 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aInteger0(sz10),
file('NUM431+1.p',unknown),
[] ).
cnf(3,axiom,
aInteger0(xa),
file('NUM431+1.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xb),
file('NUM431+1.p',unknown),
[] ).
cnf(5,axiom,
aInteger0(xq),
file('NUM431+1.p',unknown),
[] ).
cnf(6,axiom,
aInteger0(xc),
file('NUM431+1.p',unknown),
[] ).
cnf(7,axiom,
aInteger0(xn),
file('NUM431+1.p',unknown),
[] ).
cnf(8,axiom,
aInteger0(xm),
file('NUM431+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM431+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM431+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM431+1.p',unknown),
[] ).
cnf(20,axiom,
equal(sdtasdt0(xq,xn),sdtpldt0(xa,smndt0(xb))),
file('NUM431+1.p',unknown),
[] ).
cnf(21,axiom,
equal(sdtasdt0(xq,xm),sdtpldt0(xb,smndt0(xc))),
file('NUM431+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM431+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM431+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM431+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtasdt0(v,u)) ),
file('NUM431+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('NUM431+1.p',unknown),
[] ).
cnf(29,axiom,
~ equal(sdtasdt0(xq,sdtpldt0(xn,xm)),sdtpldt0(xa,smndt0(xc))),
file('NUM431+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM431+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM431+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u))) ),
file('NUM431+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('NUM431+1.p',unknown),
[] ).
cnf(73,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| aInteger0(sdtpldt0(xb,smndt0(xc))) ),
inference(spr,[status(thm),theory(equality)],[21,26]),
[iquote('0:SpR:21.0,26.2')] ).
cnf(81,plain,
aInteger0(sdtpldt0(xb,smndt0(xc))),
inference(ssi,[status(thm)],[73,5,8]),
[iquote('0:SSi:73.1,73.0,5.0,8.0')] ).
cnf(193,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[22,37]),
[iquote('0:SpR:22.1,37.3')] ).
cnf(195,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[23,37]),
[iquote('0:SpR:23.1,37.3')] ).
cnf(198,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aInteger0(v)
| ~ aInteger0(u)
| equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[31,37]),
[iquote('0:SpR:31.2,37.3')] ).
cnf(203,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[195]),
[iquote('0:Obv:195.0')] ).
cnf(204,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[15,203]),
[iquote('0:Rew:15.1,203.3')] ).
cnf(205,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[204,13]),
[iquote('0:SSi:204.2,13.1')] ).
cnf(206,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[193]),
[iquote('0:Obv:193.0')] ).
cnf(207,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[15,206]),
[iquote('0:Rew:15.1,206.3')] ).
cnf(208,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[207,13]),
[iquote('0:SSi:207.1,13.1')] ).
cnf(212,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[198]),
[iquote('0:Obv:198.1')] ).
cnf(213,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[37,212]),
[iquote('0:Rew:37.3,212.3')] ).
cnf(228,plain,
( ~ aInteger0(u)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(spr,[status(thm),theory(equality)],[23,205]),
[iquote('0:SpR:23.1,205.2')] ).
cnf(240,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(obv,[status(thm),theory(equality)],[228]),
[iquote('0:Obv:228.0')] ).
cnf(241,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(ssi,[status(thm)],[240,13]),
[iquote('0:SSi:240.1,13.1')] ).
cnf(253,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(smndt0(u)))
| equal(smndt0(smndt0(u)),u) ),
inference(spr,[status(thm),theory(equality)],[241,14]),
[iquote('0:SpR:241.1,14.1')] ).
cnf(259,plain,
( ~ aInteger0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[253,13]),
[iquote('0:SSi:253.1,13.1,13.1')] ).
cnf(518,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(sdtpldt0(v,u))
| equal(sdtpldt0(sdtasdt0(v,smndt0(sz10)),sdtasdt0(u,smndt0(sz10))),smndt0(sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[40,28]),
[iquote('0:SpR:40.3,28.1')] ).
cnf(554,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(sdtpldt0(v,u))
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[28,518]),
[iquote('0:Rew:28.1,518.4,28.1,518.4')] ).
cnf(555,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(ssi,[status(thm)],[554,25,13,2]),
[iquote('0:SSi:554.3,554.0,25.0,13.1,2.2')] ).
cnf(610,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ equal(sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)),sdtpldt0(xa,smndt0(xc))) ),
inference(spl,[status(thm),theory(equality)],[41,29]),
[iquote('0:SpL:41.3,29.0')] ).
cnf(613,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xn)
| ~ aInteger0(xq)
| ~ equal(sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))),sdtpldt0(xa,smndt0(xc))) ),
inference(rew,[status(thm),theory(equality)],[20,610,21]),
[iquote('0:Rew:20.0,610.3,21.0,610.3')] ).
cnf(614,plain,
~ equal(sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))),sdtpldt0(xa,smndt0(xc))),
inference(ssi,[status(thm)],[613,5,7,8]),
[iquote('0:SSi:613.2,613.1,613.0,5.0,7.0,8.0')] ).
cnf(1092,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa)
| ~ equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xc)))),sdtpldt0(xa,smndt0(xc))) ),
inference(spl,[status(thm),theory(equality)],[37,614]),
[iquote('0:SpL:37.3,614.0')] ).
cnf(1095,plain,
~ equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xc)))),sdtpldt0(xa,smndt0(xc))),
inference(ssi,[status(thm)],[1092,3,13,4,81]),
[iquote('0:SSi:1092.2,1092.1,1092.0,3.0,13.0,4.1,81.0')] ).
cnf(2970,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[259,555]),
[iquote('0:SpR:259.1,555.2')] ).
cnf(2983,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(ssi,[status(thm)],[2970,13]),
[iquote('0:SSi:2970.1,13.1')] ).
cnf(2984,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,smndt0(sdtpldt0(v,smndt0(u)))),u) ),
inference(rew,[status(thm),theory(equality)],[2983,208]),
[iquote('0:Rew:2983.2,208.2')] ).
cnf(31727,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ equal(sdtpldt0(xa,sdtpldt0(xb,sdtpldt0(smndt0(xb),smndt0(xc)))),sdtpldt0(xa,smndt0(xc))) ),
inference(spl,[status(thm),theory(equality)],[213,1095]),
[iquote('0:SpL:213.3,1095.0')] ).
cnf(31742,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ equal(sdtpldt0(xa,sdtpldt0(xb,smndt0(sdtpldt0(xb,smndt0(smndt0(xc)))))),sdtpldt0(xa,smndt0(xc))) ),
inference(rew,[status(thm),theory(equality)],[2983,31727]),
[iquote('0:Rew:2983.2,31727.3')] ).
cnf(31743,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ equal(sdtpldt0(xa,smndt0(xc)),sdtpldt0(xa,smndt0(xc))) ),
inference(rew,[status(thm),theory(equality)],[2984,31742]),
[iquote('0:Rew:2984.2,31742.3')] ).
cnf(31744,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb)) ),
inference(obv,[status(thm),theory(equality)],[31743]),
[iquote('0:Obv:31743.3')] ).
cnf(31745,plain,
$false,
inference(ssi,[status(thm)],[31744,13,4,6]),
[iquote('0:SSi:31744.2,31744.1,31744.0,13.0,4.1,4.0,13.0,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM431+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 21:51:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 46.85/47.08
% 46.85/47.08 SPASS V 3.9
% 46.85/47.08 SPASS beiseite: Proof found.
% 46.85/47.08 % SZS status Theorem
% 46.85/47.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.85/47.08 SPASS derived 16865 clauses, backtracked 1554 clauses, performed 4 splits and kept 5235 clauses.
% 46.85/47.08 SPASS allocated 135424 KBytes.
% 46.85/47.08 SPASS spent 0:0:37.81 on the problem.
% 46.85/47.08 0:00:00.04 for the input.
% 46.85/47.08 0:00:00.03 for the FLOTTER CNF translation.
% 46.85/47.08 0:00:00.25 for inferences.
% 46.85/47.08 0:00:00.23 for the backtracking.
% 46.85/47.08 0:0:37.17 for the reduction.
% 46.85/47.08
% 46.85/47.08
% 46.85/47.08 Here is a proof with depth 4, length 56 :
% 46.85/47.08 % SZS output start Refutation
% See solution above
% 46.91/47.08 Formulae used in the proof : mIntOne m__818 m__876 m__899 mIntNeg mAddZero mAddNeg mIntPlus mIntMult mMulMinOne m__ mAddComm mAddAsso mDistrib
% 46.91/47.08
%------------------------------------------------------------------------------