TSTP Solution File: ROB023-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB023-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 20:56:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(u,u),u),
file('ROB023-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB023-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('ROB023-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB023-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB023-1.p',unknown),
[] ).
cnf(14,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(18,plain,
equal(add(u,add(u,v)),add(u,v)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(19,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(21,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[4,19]),
[iquote('0:Rew:4.0,19.0')] ).
cnf(29,plain,
equal(add(u,add(v,u)),add(v,u)),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(40,plain,
equal(negate(add(negate(add(negate(u),u)),negate(negate(u)))),negate(u)),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(41,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(44,plain,
equal(negate(add(negate(u),negate(add(u,negate(u))))),u),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(49,plain,
equal(negate(add(negate(negate(u)),negate(add(u,negate(u))))),negate(u)),
inference(rew,[status(thm),theory(equality)],[3,40]),
[iquote('0:Rew:3.0,40.0,3.0,40.0')] ).
cnf(72,plain,
equal(negate(add(negate(add(negate(u),add(u,negate(u)))),u)),negate(u)),
inference(spr,[status(thm),theory(equality)],[44,5]),
[iquote('0:SpR:44.0,5.0')] ).
cnf(75,plain,
equal(negate(add(u,negate(add(add(negate(u),negate(add(u,negate(u)))),u)))),add(negate(u),negate(add(u,negate(u))))),
inference(spr,[status(thm),theory(equality)],[44]),
[iquote('0:SpR:44.0,44.0')] ).
cnf(79,plain,
equal(negate(add(u,negate(add(u,negate(u))))),negate(u)),
inference(rew,[status(thm),theory(equality)],[3,72,29]),
[iquote('0:Rew:3.0,72.0,29.0,72.0')] ).
cnf(81,plain,
equal(negate(add(u,negate(add(negate(u),add(u,negate(add(u,negate(u)))))))),add(negate(u),negate(add(u,negate(u))))),
inference(rew,[status(thm),theory(equality)],[3,75,4]),
[iquote('0:Rew:3.0,75.0,4.0,75.0')] ).
cnf(82,plain,
equal(negate(add(u,negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),add(negate(u),negate(add(u,negate(u))))),
inference(rew,[status(thm),theory(equality)],[21,81]),
[iquote('0:Rew:21.0,81.0')] ).
cnf(91,plain,
equal(negate(add(negate(u),negate(add(add(u,negate(add(u,negate(u)))),negate(u))))),add(u,negate(add(u,negate(u))))),
inference(spr,[status(thm),theory(equality)],[79,44]),
[iquote('0:SpR:79.0,44.0')] ).
cnf(104,plain,
equal(negate(add(negate(u),negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),add(u,negate(add(u,negate(u))))),
inference(rew,[status(thm),theory(equality)],[3,91,4]),
[iquote('0:Rew:3.0,91.0,4.0,91.0')] ).
cnf(136,plain,
equal(add(u,add(v,w)),add(w,add(v,u))),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(478,plain,
equal(negate(add(negate(u),negate(add(add(negate(u),negate(add(u,negate(u)))),u)))),u),
inference(spr,[status(thm),theory(equality)],[44,49]),
[iquote('0:SpR:44.0,49.0')] ).
cnf(484,plain,
equal(negate(add(negate(u),negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),u),
inference(rew,[status(thm),theory(equality)],[21,478,3,4]),
[iquote('0:Rew:21.0,478.0,3.0,478.0,4.0,478.0')] ).
cnf(485,plain,
equal(add(u,negate(add(u,negate(u)))),u),
inference(rew,[status(thm),theory(equality)],[104,484]),
[iquote('0:Rew:104.0,484.0')] ).
cnf(529,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[3,41]),
[iquote('0:SpR:3.0,41.0')] ).
cnf(578,plain,
equal(add(negate(add(u,negate(u))),add(v,u)),add(v,u)),
inference(spr,[status(thm),theory(equality)],[485,14]),
[iquote('0:SpR:485.0,14.0')] ).
cnf(599,plain,
equal(add(u,add(v,negate(add(u,negate(u))))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[136,578]),
[iquote('0:Rew:136.0,578.0')] ).
cnf(600,plain,
equal(add(negate(u),negate(add(u,negate(u)))),negate(add(u,negate(add(negate(u),u))))),
inference(rew,[status(thm),theory(equality)],[599,82]),
[iquote('0:Rew:599.0,82.0')] ).
cnf(616,plain,
equal(add(negate(u),negate(add(u,negate(u)))),negate(u)),
inference(rew,[status(thm),theory(equality)],[485,600,3]),
[iquote('0:Rew:485.0,600.0,3.0,600.0')] ).
cnf(617,plain,
equal(negate(negate(u)),u),
inference(rew,[status(thm),theory(equality)],[616,44]),
[iquote('0:Rew:616.0,44.0')] ).
cnf(826,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[529,617]),
[iquote('0:SpR:529.0,617.0')] ).
cnf(863,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[826,2]),
[iquote('0:Rew:826.0,2.0')] ).
cnf(864,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[617,863]),
[iquote('0:Rew:617.0,863.0')] ).
cnf(865,plain,
$false,
inference(obv,[status(thm),theory(equality)],[864]),
[iquote('0:Obv:864.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ROB023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.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 Jun 9 15:10:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.51
% 0.20/0.51 SPASS V 3.9
% 0.20/0.51 SPASS beiseite: Proof found.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51 SPASS derived 538 clauses, backtracked 0 clauses, performed 0 splits and kept 143 clauses.
% 0.20/0.51 SPASS allocated 64178 KBytes.
% 0.20/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.51 0:00:00.03 for the input.
% 0.20/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.51 0:00:00.01 for inferences.
% 0.20/0.51 0:00:00.00 for the backtracking.
% 0.20/0.51 0:00:00.10 for the reduction.
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 Here is a proof with depth 3, length 35 :
% 0.20/0.51 % SZS output start Refutation
% See solution above
% 0.20/0.51 Formulae used in the proof : x_plus_x_is_x prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 0.20/0.51
%------------------------------------------------------------------------------