TSTP Solution File: NUM847+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 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 14:31:02 EDT 2022
% Result : Theorem 1.16s 1.38s
% Output : Refutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM847+2.p',unknown),
[] ).
cnf(14,axiom,
equal(vplus(vmul(u,v),u),vmul(u,vsucc(v))),
file('NUM847+2.p',unknown),
[] ).
cnf(15,axiom,
equal(vplus(vplus(u,v),w),vplus(u,vplus(v,w))),
file('NUM847+2.p',unknown),
[] ).
cnf(17,axiom,
equal(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vmul(vd436,vplus(vd437,vd439))),
file('NUM847+2.p',unknown),
[] ).
cnf(21,axiom,
~ equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))),
file('NUM847+2.p',unknown),
[] ).
cnf(24,plain,
equal(vplus(u,vmul(u,v)),vmul(u,vsucc(v))),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(31,plain,
~ equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))),
inference(rew,[status(thm),theory(equality)],[24,21,6,17]),
[iquote('0:Rew:24.0,21.0,6.0,21.0,17.0,21.0,24.0,21.0,6.0,21.0')] ).
cnf(209,plain,
equal(vplus(vplus(u,v),w),vplus(v,vplus(u,w))),
inference(spr,[status(thm),theory(equality)],[6,15]),
[iquote('0:SpR:6.0,15.0')] ).
cnf(222,plain,
equal(vplus(u,vplus(v,w)),vplus(v,vplus(u,w))),
inference(rew,[status(thm),theory(equality)],[15,209]),
[iquote('0:Rew:15.0,209.0')] ).
cnf(566,plain,
equal(vplus(u,vplus(v,vmul(u,w))),vplus(v,vmul(u,vsucc(w)))),
inference(spr,[status(thm),theory(equality)],[24,222]),
[iquote('0:SpR:24.0,222.0')] ).
cnf(6446,plain,
equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))),
inference(spr,[status(thm),theory(equality)],[17,566]),
[iquote('0:SpR:17.0,566.0')] ).
cnf(6482,plain,
equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))),
inference(rew,[status(thm),theory(equality)],[24,6446]),
[iquote('0:Rew:24.0,6446.0')] ).
cnf(6483,plain,
$false,
inference(mrr,[status(thm)],[6482,31]),
[iquote('0:MRR:6482.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % 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 : Fri Jul 8 01:19:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.16/1.38
% 1.16/1.38 SPASS V 3.9
% 1.16/1.38 SPASS beiseite: Proof found.
% 1.16/1.38 % SZS status Theorem
% 1.16/1.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.16/1.38 SPASS derived 3694 clauses, backtracked 0 clauses, performed 0 splits and kept 702 clauses.
% 1.16/1.38 SPASS allocated 90318 KBytes.
% 1.16/1.38 SPASS spent 0:00:01.02 on the problem.
% 1.16/1.38 0:00:00.03 for the input.
% 1.16/1.38 0:00:00.02 for the FLOTTER CNF translation.
% 1.16/1.38 0:00:00.04 for inferences.
% 1.16/1.38 0:00:00.00 for the backtracking.
% 1.16/1.38 0:00:00.90 for the reduction.
% 1.16/1.38
% 1.16/1.38
% 1.16/1.38 Here is a proof with depth 3, length 13 :
% 1.16/1.38 % SZS output start Refutation
% See solution above
% 1.16/1.38 Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_32_a41__a44__a32_and_a40_holds_a40_definiens_a40_249_a41__a44__a32_399_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_249_a41__a44__a32_398_a44__a32_0_a41__a41__a41_ ass_a40_cond_a40_33_a44__a32_0_a41__a44__a32_0_a41_ holds_a40_285_a44__a32_440_a44__a32_0_a41_ holds_a40_286_a44__a32_441_a44__a32_3_a41_
% 1.16/1.38
%------------------------------------------------------------------------------