TSTP Solution File: ROB005-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 20:56:12 EDT 2022
% Result : Unsatisfiable 43.11s 43.31s
% Output : Refutation 43.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 52 RR)
% Number of literals : 52 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(c,c),c),
file('ROB005-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB005-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('ROB005-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB005-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB005-1.p',unknown),
[] ).
cnf(13,plain,
equal(add(u,add(v,w)),add(v,add(w,u))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(17,plain,
equal(add(c,add(c,u)),add(c,u)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(18,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(20,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[4,18]),
[iquote('0:Rew:4.0,18.0')] ).
cnf(30,plain,
equal(negate(add(negate(add(u,add(negate(add(v,w)),negate(add(v,negate(w)))))),negate(add(u,v)))),u),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(32,plain,
equal(negate(add(u,negate(add(negate(add(u,v)),negate(negate(add(u,negate(v)))))))),negate(add(u,v))),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(34,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(v),u)))),u),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(37,plain,
equal(negate(add(negate(c),negate(add(c,negate(c))))),c),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(39,plain,
equal(negate(add(negate(add(u,v)),negate(add(v,negate(u))))),v),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(47,plain,
equal(negate(add(negate(add(u,v)),negate(add(u,add(negate(add(v,w)),negate(add(v,negate(w)))))))),u),
inference(rew,[status(thm),theory(equality)],[3,30]),
[iquote('0:Rew:3.0,30.0')] ).
cnf(59,plain,
equal(negate(add(negate(add(negate(c),add(c,negate(c)))),c)),negate(c)),
inference(spr,[status(thm),theory(equality)],[37,5]),
[iquote('0:SpR:37.0,5.0')] ).
cnf(62,plain,
equal(negate(add(c,negate(add(negate(c),add(c,negate(c)))))),negate(c)),
inference(rew,[status(thm),theory(equality)],[3,59]),
[iquote('0:Rew:3.0,59.0')] ).
cnf(63,plain,
equal(negate(add(c,negate(add(c,add(negate(c),negate(c)))))),negate(c)),
inference(rew,[status(thm),theory(equality)],[20,62]),
[iquote('0:Rew:20.0,62.0')] ).
cnf(92,plain,
equal(add(u,add(v,w)),add(w,add(v,u))),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(498,plain,
equal(negate(add(negate(add(negate(add(negate(u),v)),add(v,u))),v)),negate(add(negate(u),v))),
inference(spr,[status(thm),theory(equality)],[34]),
[iquote('0:SpR:34.0,34.0')] ).
cnf(518,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[3,34]),
[iquote('0:SpR:3.0,34.0')] ).
cnf(537,plain,
equal(negate(add(u,negate(add(v,add(u,negate(add(negate(v),u))))))),negate(add(negate(v),u))),
inference(rew,[status(thm),theory(equality)],[3,498,92]),
[iquote('0:Rew:3.0,498.0,92.0,498.0')] ).
cnf(567,plain,
equal(negate(add(negate(add(add(negate(c),negate(add(c,negate(c)))),u)),negate(add(u,c)))),u),
inference(spr,[status(thm),theory(equality)],[37,39]),
[iquote('0:SpR:37.0,39.0')] ).
cnf(576,plain,
equal(negate(add(negate(add(c,u)),negate(add(add(c,u),negate(c))))),add(c,u)),
inference(spr,[status(thm),theory(equality)],[17,39]),
[iquote('0:SpR:17.0,39.0')] ).
cnf(595,plain,
equal(negate(add(negate(add(c,u)),negate(add(c,add(u,negate(c)))))),add(c,u)),
inference(rew,[status(thm),theory(equality)],[4,576]),
[iquote('0:Rew:4.0,576.0')] ).
cnf(602,plain,
equal(negate(add(negate(add(u,c)),negate(add(negate(c),add(negate(add(c,negate(c))),u))))),u),
inference(rew,[status(thm),theory(equality)],[3,567,4]),
[iquote('0:Rew:3.0,567.0,4.0,567.0')] ).
cnf(709,plain,
equal(negate(add(negate(add(c,add(c,add(negate(c),negate(c))))),negate(c))),c),
inference(spr,[status(thm),theory(equality)],[63,5]),
[iquote('0:SpR:63.0,5.0')] ).
cnf(713,plain,
equal(negate(add(negate(c),negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))))),negate(add(c,add(negate(c),negate(c))))),
inference(spr,[status(thm),theory(equality)],[63,518]),
[iquote('0:SpR:63.0,518.0')] ).
cnf(722,plain,
equal(negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))),c),
inference(rew,[status(thm),theory(equality)],[3,709,17]),
[iquote('0:Rew:3.0,709.0,17.0,709.0')] ).
cnf(729,plain,
equal(negate(add(c,add(negate(c),negate(c)))),negate(add(negate(c),c))),
inference(rew,[status(thm),theory(equality)],[722,713]),
[iquote('0:Rew:722.0,713.0')] ).
cnf(730,plain,
equal(negate(add(c,add(negate(c),negate(c)))),negate(add(c,negate(c)))),
inference(rew,[status(thm),theory(equality)],[3,729]),
[iquote('0:Rew:3.0,729.0')] ).
cnf(731,plain,
equal(negate(add(c,negate(add(c,negate(c))))),negate(c)),
inference(rew,[status(thm),theory(equality)],[730,63]),
[iquote('0:Rew:730.0,63.0')] ).
cnf(4183,plain,
equal(negate(add(negate(c),negate(add(c,add(negate(add(c,u)),negate(add(c,negate(u)))))))),c),
inference(spr,[status(thm),theory(equality)],[1,47]),
[iquote('0:SpR:1.0,47.0')] ).
cnf(8635,plain,
equal(negate(add(negate(c),negate(add(c,add(negate(add(c,negate(c))),negate(c)))))),add(c,negate(add(c,negate(c))))),
inference(spr,[status(thm),theory(equality)],[731,595]),
[iquote('0:SpR:731.0,595.0')] ).
cnf(8647,plain,
equal(negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))),add(c,negate(add(c,negate(c))))),
inference(rew,[status(thm),theory(equality)],[3,8635]),
[iquote('0:Rew:3.0,8635.0')] ).
cnf(29596,plain,
equal(negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))),c),
inference(spr,[status(thm),theory(equality)],[1,4183]),
[iquote('0:SpR:1.0,4183.0')] ).
cnf(29722,plain,
equal(add(c,negate(add(c,negate(c)))),c),
inference(rew,[status(thm),theory(equality)],[8647,29596]),
[iquote('0:Rew:8647.0,29596.0')] ).
cnf(29907,plain,
equal(add(negate(add(c,negate(c))),add(c,u)),add(u,c)),
inference(spr,[status(thm),theory(equality)],[29722,92]),
[iquote('0:SpR:29722.0,92.0')] ).
cnf(29993,plain,
equal(add(c,add(negate(add(c,negate(c))),u)),add(u,c)),
inference(rew,[status(thm),theory(equality)],[20,29907]),
[iquote('0:Rew:20.0,29907.0')] ).
cnf(30275,plain,
equal(negate(add(negate(add(u,c)),negate(add(negate(c),add(negate(add(c,negate(c))),u))))),add(negate(add(c,negate(c))),u)),
inference(spr,[status(thm),theory(equality)],[29993,518]),
[iquote('0:SpR:29993.0,518.0')] ).
cnf(30819,plain,
equal(add(negate(add(c,negate(c))),u),u),
inference(rew,[status(thm),theory(equality)],[602,30275]),
[iquote('0:Rew:602.0,30275.0')] ).
cnf(31058,plain,
equal(add(u,negate(add(c,negate(c)))),u),
inference(spr,[status(thm),theory(equality)],[30819,3]),
[iquote('0:SpR:30819.0,3.0')] ).
cnf(31164,plain,
equal(negate(add(negate(add(c,negate(c))),negate(add(negate(u),negate(negate(add(negate(add(c,negate(c))),negate(u)))))))),negate(u)),
inference(spr,[status(thm),theory(equality)],[30819,32]),
[iquote('0:SpR:30819.0,32.0')] ).
cnf(31814,plain,
equal(negate(negate(add(negate(u),negate(negate(negate(u)))))),negate(u)),
inference(rew,[status(thm),theory(equality)],[30819,31164]),
[iquote('0:Rew:30819.0,31164.0,30819.0,31164.0')] ).
cnf(33067,plain,
equal(negate(add(negate(add(c,negate(c))),negate(add(u,add(negate(add(c,negate(c))),negate(negate(u))))))),negate(negate(u))),
inference(spr,[status(thm),theory(equality)],[31058,537]),
[iquote('0:SpR:31058.0,537.0')] ).
cnf(33190,plain,
equal(negate(negate(add(u,negate(negate(u))))),negate(negate(u))),
inference(rew,[status(thm),theory(equality)],[30819,33067]),
[iquote('0:Rew:30819.0,33067.0,30819.0,33067.0')] ).
cnf(33191,plain,
equal(negate(negate(negate(u))),negate(u)),
inference(rew,[status(thm),theory(equality)],[33190,31814]),
[iquote('0:Rew:33190.0,31814.0')] ).
cnf(33506,plain,
equal(negate(negate(u)),u),
inference(spr,[status(thm),theory(equality)],[5,33191]),
[iquote('0:SpR:5.0,33191.0')] ).
cnf(34651,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[518,33506]),
[iquote('0:SpR:518.0,33506.0')] ).
cnf(34808,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[34651,2]),
[iquote('0:Rew:34651.0,2.0')] ).
cnf(34816,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[33506,34808]),
[iquote('0:Rew:33506.0,34808.0')] ).
cnf(34817,plain,
$false,
inference(obv,[status(thm),theory(equality)],[34816]),
[iquote('0:Obv:34816.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ROB005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Thu Jun 9 14:34:37 EDT 2022
% 0.08/0.28 % CPUTime :
% 43.11/43.31
% 43.11/43.31 SPASS V 3.9
% 43.11/43.31 SPASS beiseite: Proof found.
% 43.11/43.31 % SZS status Theorem
% 43.11/43.31 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.11/43.31 SPASS derived 22297 clauses, backtracked 0 clauses, performed 0 splits and kept 3928 clauses.
% 43.11/43.31 SPASS allocated 103769 KBytes.
% 43.11/43.31 SPASS spent 0:0:42.70 on the problem.
% 43.11/43.31 0:00:00.03 for the input.
% 43.11/43.31 0:00:00.00 for the FLOTTER CNF translation.
% 43.11/43.31 0:00:00.23 for inferences.
% 43.11/43.31 0:00:00.00 for the backtracking.
% 43.11/43.31 0:0:42.42 for the reduction.
% 43.11/43.31
% 43.11/43.31
% 43.11/43.31 Here is a proof with depth 8, length 52 :
% 43.11/43.31 % SZS output start Refutation
% See solution above
% 43.11/43.31 Formulae used in the proof : idempotence prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 43.11/43.31
%------------------------------------------------------------------------------