%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM431+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 167.29s 167.51s
% Output : Refutation 167.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of clauses : 53 ( 13 unt; 0 nHn; 53 RR)
% Number of literals : 153 ( 0 equ; 110 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+3.p',unknown),
[] ).
cnf(3,axiom,
aInteger0(xa),
file('NUM431+3.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xb),
file('NUM431+3.p',unknown),
[] ).
cnf(5,axiom,
aInteger0(xq),
file('NUM431+3.p',unknown),
[] ).
cnf(6,axiom,
aInteger0(xc),
file('NUM431+3.p',unknown),
[] ).
cnf(9,axiom,
aInteger0(xn),
file('NUM431+3.p',unknown),
[] ).
cnf(10,axiom,
aInteger0(xm),
file('NUM431+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM431+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM431+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM431+3.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasdt0(xq,xn),sdtpldt0(xa,smndt0(xb))),
file('NUM431+3.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xq,xm),sdtpldt0(xb,smndt0(xc))),
file('NUM431+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM431+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM431+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM431+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('NUM431+3.p',unknown),
[] ).
cnf(35,axiom,
~ equal(sdtasdt0(xq,sdtpldt0(xn,xm)),sdtpldt0(xa,smndt0(xc))),
file('NUM431+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM431+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM431+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u))) ),
file('NUM431+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('NUM431+3.p',unknown),
[] ).
cnf(200,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)],[28,43]),
[iquote('0:SpR:28.1,43.3')] ).
cnf(202,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)],[29,43]),
[iquote('0:SpR:29.1,43.3')] ).
cnf(205,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)],[37,43]),
[iquote('0:SpR:37.2,43.3')] ).
cnf(210,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[202]),
[iquote('0:Obv:202.0')] ).
cnf(211,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[19,210]),
[iquote('0:Rew:19.1,210.3')] ).
cnf(212,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[211,15]),
[iquote('0:SSi:211.2,15.1')] ).
cnf(213,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[200]),
[iquote('0:Obv:200.0')] ).
cnf(214,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[19,213]),
[iquote('0:Rew:19.1,213.3')] ).
cnf(215,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[214,15]),
[iquote('0:SSi:214.1,15.1')] ).
cnf(219,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[205]),
[iquote('0:Obv:205.1')] ).
cnf(220,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[43,219]),
[iquote('0:Rew:43.3,219.3')] ).
cnf(239,plain,
( ~ aInteger0(u)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(spr,[status(thm),theory(equality)],[29,212]),
[iquote('0:SpR:29.1,212.2')] ).
cnf(250,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(obv,[status(thm),theory(equality)],[239]),
[iquote('0:Obv:239.0')] ).
cnf(251,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(smndt0(u)),sz00),u) ),
inference(ssi,[status(thm)],[250,15]),
[iquote('0:SSi:250.1,15.1')] ).
cnf(262,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(smndt0(u)))
| equal(smndt0(smndt0(u)),u) ),
inference(spr,[status(thm),theory(equality)],[251,18]),
[iquote('0:SpR:251.1,18.1')] ).
cnf(267,plain,
( ~ aInteger0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[262,15]),
[iquote('0:SSi:262.1,15.1,15.1')] ).
cnf(543,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)],[46,34]),
[iquote('0:SpR:46.3,34.1')] ).
cnf(581,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)],[34,543]),
[iquote('0:Rew:34.1,543.4,34.1,543.4')] ).
cnf(582,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(ssi,[status(thm)],[581,31,15,2]),
[iquote('0:SSi:581.3,581.0,31.0,15.1,2.2')] ).
cnf(656,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)],[47,35]),
[iquote('0:SpL:47.3,35.0')] ).
cnf(661,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)],[26,656,27]),
[iquote('0:Rew:26.0,656.3,27.0,656.3')] ).
cnf(662,plain,
~ equal(sdtpldt0(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xb,smndt0(xc))),sdtpldt0(xa,smndt0(xc))),
inference(ssi,[status(thm)],[661,5,9,10]),
[iquote('0:SSi:661.2,661.1,661.0,5.0,9.0,10.0')] ).
cnf(1125,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)],[43,662]),
[iquote('0:SpL:43.3,662.0')] ).
cnf(1126,plain,
~ equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),sdtpldt0(xb,smndt0(xc)))),sdtpldt0(xa,smndt0(xc))),
inference(ssi,[status(thm)],[1125,3,15,4,31,6]),
[iquote('0:SSi:1125.2,1125.1,1125.0,3.0,15.1,4.0,31.2,4.0,15.1,6.0')] ).
cnf(2963,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[267,582]),
[iquote('0:SpR:267.1,582.2')] ).
cnf(2975,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(ssi,[status(thm)],[2963,15]),
[iquote('0:SSi:2963.1,15.1')] ).
cnf(2976,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,smndt0(sdtpldt0(v,smndt0(u)))),u) ),
inference(rew,[status(thm),theory(equality)],[2975,215]),
[iquote('0:Rew:2975.2,215.2')] ).
cnf(64449,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)],[220,1126]),
[iquote('0:SpL:220.3,1126.0')] ).
cnf(64464,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)],[2975,64449]),
[iquote('0:Rew:2975.2,64449.3')] ).
cnf(64465,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb))
| ~ equal(sdtpldt0(xa,smndt0(xc)),sdtpldt0(xa,smndt0(xc))) ),
inference(rew,[status(thm),theory(equality)],[2976,64464]),
[iquote('0:Rew:2976.2,64464.3')] ).
cnf(64466,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xb)) ),
inference(obv,[status(thm),theory(equality)],[64465]),
[iquote('0:Obv:64465.3')] ).
cnf(64467,plain,
$false,
inference(ssi,[status(thm)],[64466,15,4,6]),
[iquote('0:SSi:64466.2,64466.1,64466.0,15.0,4.1,4.0,15.0,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM431+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 11:44:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 167.29/167.51
% 167.29/167.51 SPASS V 3.9
% 167.29/167.51 SPASS beiseite: Proof found.
% 167.29/167.51 % SZS status Theorem
% 167.29/167.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 167.29/167.51 SPASS derived 33716 clauses, backtracked 7285 clauses, performed 7 splits and kept 14326 clauses.
% 167.29/167.51 SPASS allocated 162933 KBytes.
% 167.29/167.51 SPASS spent 0:02:06.35 on the problem.
% 167.29/167.51 0:00:00.04 for the input.
% 167.29/167.51 0:00:00.03 for the FLOTTER CNF translation.
% 167.29/167.51 0:00:00.47 for inferences.
% 167.29/167.51 0:00:00.79 for the backtracking.
% 167.29/167.51 0:02:04.72 for the reduction.
% 167.29/167.51
% 167.29/167.51
% 167.29/167.51 Here is a proof with depth 4, length 53 :
% 167.29/167.51 % SZS output start Refutation
% See solution above
% 167.29/167.51 Formulae used in the proof : mIntOne m__818 m__876 m__899 mIntNeg mAddZero mAddNeg mIntPlus mMulMinOne m__ mAddComm mAddAsso mDistrib
% 167.29/167.51
%------------------------------------------------------------------------------