TSTP Solution File: NUM421+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM421+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14:26:01 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 6 unt; 0 nHn; 40 RR)
% Number of literals : 115 ( 0 equ; 81 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aInteger0(sz00),
file('NUM421+1.p',unknown),
[] ).
cnf(3,axiom,
aInteger0(xa),
file('NUM421+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM421+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM421+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM421+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtasdt0(v,u)) ),
file('NUM421+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(sdtasdt0(sz00,xa),sz00)
| ~ equal(sdtasdt0(xa,sz00),sz00) ),
file('NUM421+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM421+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM421+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM421+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('NUM421+1.p',unknown),
[] ).
cnf(59,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(xa)
| ~ equal(sdtasdt0(sz00,xa),sz00)
| ~ equal(sdtasdt0(sz00,xa),sz00) ),
inference(spl,[status(thm),theory(equality)],[15,13]),
[iquote('0:SpL:15.2,13.1')] ).
cnf(67,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(xa)
| ~ equal(sdtasdt0(sz00,xa),sz00) ),
inference(obv,[status(thm),theory(equality)],[59]),
[iquote('0:Obv:59.2')] ).
cnf(68,plain,
~ equal(sdtasdt0(sz00,xa),sz00),
inference(ssi,[status(thm)],[67,3,1]),
[iquote('0:SSi:67.1,67.0,3.0,1.0')] ).
cnf(97,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(u)
| ~ aInteger0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(u,v)),sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.1,17.3')] ).
cnf(98,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)],[10,17]),
[iquote('0:SpR:10.1,17.3')] ).
cnf(105,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[97]),
[iquote('0:Obv:97.0')] ).
cnf(106,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(ssi,[status(thm)],[105,1]),
[iquote('0:SSi:105.2,1.0')] ).
cnf(110,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[98]),
[iquote('0:Obv:98.0')] ).
cnf(111,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[6,110]),
[iquote('0:Rew:6.1,110.3')] ).
cnf(112,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[111,4]),
[iquote('0:SSi:111.2,4.1')] ).
cnf(194,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(v)
| ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),sdtpldt0(v,u)),v) ),
inference(spr,[status(thm),theory(equality)],[14,112]),
[iquote('0:SpR:14.2,112.2')] ).
cnf(205,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(u,v)),u) ),
inference(obv,[status(thm),theory(equality)],[194]),
[iquote('0:Obv:194.1')] ).
cnf(352,plain,
( ~ aInteger0(u)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(spr,[status(thm),theory(equality)],[10,106]),
[iquote('0:SpR:10.1,106.2')] ).
cnf(364,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(obv,[status(thm),theory(equality)],[352]),
[iquote('0:Obv:352.0')] ).
cnf(365,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(ssi,[status(thm)],[364,4]),
[iquote('0:SSi:364.1,4.1')] ).
cnf(381,plain,
equal(sdtpldt0(sz00,sz00),sz00),
inference(ems,[status(thm)],[365,1]),
[iquote('0:EmS:365.0,1.0')] ).
cnf(463,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(sz00)
| ~ aInteger0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(spr,[status(thm),theory(equality)],[381,19]),
[iquote('0:SpR:381.0,19.3')] ).
cnf(464,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(obv,[status(thm),theory(equality)],[463]),
[iquote('0:Obv:463.0')] ).
cnf(465,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(ssi,[status(thm)],[464,1]),
[iquote('0:SSi:464.0,1.0')] ).
cnf(509,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtasdt0(u,sz00))
| ~ aInteger0(sdtasdt0(u,sz00))
| equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(spr,[status(thm),theory(equality)],[465,205]),
[iquote('0:SpR:465.1,205.2')] ).
cnf(532,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtasdt0(u,sz00))
| equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(obv,[status(thm),theory(equality)],[509]),
[iquote('0:Obv:509.1')] ).
cnf(533,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtasdt0(u,sz00))
| equal(sdtasdt0(u,sz00),sz00) ),
inference(rew,[status(thm),theory(equality)],[10,532]),
[iquote('0:Rew:10.1,532.2')] ).
cnf(534,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
inference(ssi,[status(thm)],[533,12,1]),
[iquote('0:SSi:533.1,12.0,1.2')] ).
cnf(557,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz00)
| ~ aInteger0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
inference(spr,[status(thm),theory(equality)],[534,15]),
[iquote('0:SpR:534.1,15.2')] ).
cnf(563,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
inference(obv,[status(thm),theory(equality)],[557]),
[iquote('0:Obv:557.0')] ).
cnf(564,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
inference(ssi,[status(thm)],[563,1]),
[iquote('0:SSi:563.0,1.0')] ).
cnf(585,plain,
( ~ aInteger0(xa)
| ~ equal(sz00,sz00) ),
inference(spl,[status(thm),theory(equality)],[564,68]),
[iquote('0:SpL:564.1,68.0')] ).
cnf(586,plain,
~ aInteger0(xa),
inference(obv,[status(thm),theory(equality)],[585]),
[iquote('0:Obv:585.1')] ).
cnf(587,plain,
$false,
inference(ssi,[status(thm)],[586,3]),
[iquote('0:SSi:586.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM421+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 22:56:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 286 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.19/0.50 SPASS allocated 104525 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.00 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.05 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 7, length 40 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : mIntZero m__419 mIntNeg mAddZero mAddNeg mIntMult m__ mAddComm mMulComm mAddAsso mDistrib
% 0.19/0.50
%------------------------------------------------------------------------------