TSTP Solution File: ROB002-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(negate(negate(u)),u),
file('ROB002-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB002-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('ROB002-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB002-1.p',unknown),
[] ).
cnf(53,plain,
equal(add(negate(add(u,v)),negate(add(u,negate(v)))),negate(u)),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(295,plain,
equal(add(negate(add(u,v)),negate(add(negate(v),u))),negate(u)),
inference(spr,[status(thm),theory(equality)],[3,53]),
[iquote('0:SpR:3.0,53.0')] ).
cnf(348,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[3,295]),
[iquote('0:SpR:3.0,295.0')] ).
cnf(361,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[348,2]),
[iquote('0:Rew:348.0,2.0')] ).
cnf(362,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[1,361]),
[iquote('0:Rew:1.0,361.0')] ).
cnf(363,plain,
$false,
inference(obv,[status(thm),theory(equality)],[362]),
[iquote('0:Obv:362.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 16:17:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 256 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.20/0.46 SPASS allocated 63443 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.46 0:00:00.03 for the input.
% 0.20/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.00 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.04 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 3, length 10 :
% 0.20/0.46 % SZS output start Refutation
% See solution above
% 0.20/0.46 Formulae used in the proof : double_negation prove_huntingtons_axiom commutativity_of_add robbins_axiom
% 0.20/0.46
%------------------------------------------------------------------------------