TSTP Solution File: ROB003-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB003-1 : TPTP v8.1.0. Released v1.0.0.
% 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 20:56:11 EDT 2022
% Result : Unsatisfiable 0.58s 0.74s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 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(u,c),c),
file('ROB003-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB003-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('ROB003-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB003-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB003-1.p',unknown),
[] ).
cnf(7,plain,
equal(add(c,u),c),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(36,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(38,plain,
equal(negate(add(negate(add(c,u)),negate(c))),c),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(40,plain,
equal(negate(add(negate(c),negate(add(u,negate(c))))),u),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(45,plain,
equal(negate(add(negate(c),negate(c))),c),
inference(rew,[status(thm),theory(equality)],[7,38]),
[iquote('0:Rew:7.0,38.0')] ).
cnf(53,plain,
equal(negate(add(negate(add(u,add(negate(c),negate(c)))),negate(add(u,c)))),u),
inference(spr,[status(thm),theory(equality)],[45,5]),
[iquote('0:SpR:45.0,5.0')] ).
cnf(61,plain,
equal(negate(add(negate(c),negate(add(u,add(negate(c),negate(c)))))),u),
inference(rew,[status(thm),theory(equality)],[3,53,1]),
[iquote('0:Rew:3.0,53.0,1.0,53.0')] ).
cnf(66,plain,
equal(negate(add(negate(c),negate(add(negate(c),u)))),u),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(69,plain,
equal(negate(add(negate(c),negate(add(u,add(v,negate(c)))))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[4,40]),
[iquote('0:SpR:4.0,40.0')] ).
cnf(73,plain,
equal(add(u,negate(c)),u),
inference(rew,[status(thm),theory(equality)],[69,61]),
[iquote('0:Rew:69.0,61.0')] ).
cnf(75,plain,
equal(negate(add(negate(c),negate(u))),u),
inference(rew,[status(thm),theory(equality)],[73,40]),
[iquote('0:Rew:73.0,40.0')] ).
cnf(78,plain,
equal(add(negate(c),u),u),
inference(rew,[status(thm),theory(equality)],[75,66]),
[iquote('0:Rew:75.0,66.0')] ).
cnf(79,plain,
equal(negate(negate(u)),u),
inference(rew,[status(thm),theory(equality)],[78,75]),
[iquote('0:Rew:78.0,75.0')] ).
cnf(966,plain,
equal(add(negate(add(u,v)),negate(add(negate(v),u))),negate(u)),
inference(spr,[status(thm),theory(equality)],[36,79]),
[iquote('0:SpR:36.0,79.0')] ).
cnf(3209,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[3,966]),
[iquote('0:SpR:3.0,966.0')] ).
cnf(3266,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[3209,2]),
[iquote('0:Rew:3209.0,2.0')] ).
cnf(3268,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[79,3266]),
[iquote('0:Rew:79.0,3266.0')] ).
cnf(3269,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3268]),
[iquote('0:Obv:3268.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 13:10:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.74
% 0.58/0.74 SPASS V 3.9
% 0.58/0.74 SPASS beiseite: Proof found.
% 0.58/0.74 % SZS status Theorem
% 0.58/0.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.74 SPASS derived 2112 clauses, backtracked 0 clauses, performed 0 splits and kept 222 clauses.
% 0.58/0.74 SPASS allocated 65660 KBytes.
% 0.58/0.74 SPASS spent 0:00:00.37 on the problem.
% 0.58/0.74 0:00:00.04 for the input.
% 0.58/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.74 0:00:00.02 for inferences.
% 0.58/0.74 0:00:00.00 for the backtracking.
% 0.58/0.74 0:00:00.29 for the reduction.
% 0.58/0.74
% 0.58/0.74
% 0.58/0.74 Here is a proof with depth 3, length 23 :
% 0.58/0.74 % SZS output start Refutation
% See solution above
% 0.58/0.74 Formulae used in the proof : there_exists_a_constant prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 0.58/0.74
%------------------------------------------------------------------------------