TSTP Solution File: NUM849+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 14:31:03 EDT 2022

% Result   : Theorem 0.17s 0.43s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   12 (   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(14,axiom,
    equal(vmul(u,v),vmul(v,u)),
    file('NUM849+1.p',unknown),
    [] ).

cnf(24,axiom,
    equal(vplus(u,v),vplus(v,u)),
    file('NUM849+1.p',unknown),
    [] ).

cnf(38,axiom,
    equal(vmul(vsucc(u),v),vplus(vmul(u,v),v)),
    file('NUM849+1.p',unknown),
    [] ).

cnf(39,axiom,
    equal(vmul(u,vsucc(v)),vplus(vmul(u,v),u)),
    file('NUM849+1.p',unknown),
    [] ).

cnf(42,axiom,
    equal(vmul(vmul(vd448,vd449),skc1),vmul(vd448,vmul(vd449,skc1))),
    file('NUM849+1.p',unknown),
    [] ).

cnf(57,axiom,
    equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
    file('NUM849+1.p',unknown),
    [] ).

cnf(58,axiom,
    ~ equal(vmul(vmul(vd448,vd449),vsucc(skc1)),vmul(vd448,vmul(vd449,vsucc(skc1)))),
    file('NUM849+1.p',unknown),
    [] ).

cnf(70,plain,
    equal(vmul(u,vsucc(v)),vplus(u,vmul(u,v))),
    inference(rew,[status(thm),theory(equality)],[24,39]),
    [iquote('0:Rew:24.0,39.0')] ).

cnf(71,plain,
    equal(vmul(vsucc(u),v),vplus(v,vmul(u,v))),
    inference(rew,[status(thm),theory(equality)],[24,38]),
    [iquote('0:Rew:24.0,38.0')] ).

cnf(72,plain,
    equal(vmul(skc1,vmul(vd448,vd449)),vmul(vd448,vmul(vd449,skc1))),
    inference(rew,[status(thm),theory(equality)],[14,42]),
    [iquote('0:Rew:14.0,42.0')] ).

cnf(73,plain,
    ~ equal(vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,skc1))),vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,skc1)))),
    inference(rew,[status(thm),theory(equality)],[72,58,71,14,57,70]),
    [iquote('0:Rew:72.0,58.0,71.0,58.0,14.0,58.0,57.0,58.0,70.0,58.0')] ).

cnf(74,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[73]),
    [iquote('0:Obv:73.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n004.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 : Wed Jul  6 23:39:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.17/0.43  
% 0.17/0.43  SPASS V 3.9 
% 0.17/0.43  SPASS beiseite: Proof found.
% 0.17/0.43  % SZS status Theorem
% 0.17/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.17/0.43  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.17/0.43  SPASS allocated 85306 KBytes.
% 0.17/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.17/0.43  		0:00:00.04 for the input.
% 0.17/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.17/0.43  		0:00:00.00 for inferences.
% 0.17/0.43  		0:00:00.00 for the backtracking.
% 0.17/0.43  		0:00:00.00 for the reduction.
% 0.17/0.43  
% 0.17/0.43  
% 0.17/0.43  Here is a proof with depth 0, length 12 :
% 0.17/0.43  % SZS output start Refutation
% See solution above
% 0.17/0.43  Formulae used in the proof : ass_a40_cond_a40_270_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_261_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_ qu_a40_ind_a40_296_a41__a44__a32_imp_a40_296_a41__a41_ ass_a40_cond_a40_281_a44__a32_0_a41__a44__a32_0_a41_
% 0.17/0.43  
%------------------------------------------------------------------------------