%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 14:31:06 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   19 (   9 unt;   0 nHn;  19 RR)
%            Number of literals    :   29 (   0 equ;  14 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 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(1,axiom,
    greater(vd481,vd480),
    file('NUM852+2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(vmul(u,v),vmul(v,u)),
    file('NUM852+2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ less(u,v)
    | greater(v,u) ),
    file('NUM852+2.p',unknown),
    [] ).

cnf(9,axiom,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    file('NUM852+2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ equal(u,vplus(v,w))
    | less(v,u) ),
    file('NUM852+2.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ greater(u,v)
    | equal(vplus(v,vskolem9(u,v)),u) ),
    file('NUM852+2.p',unknown),
    [] ).

cnf(19,axiom,
    equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
    file('NUM852+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ greater(u,v)
    | equal(vmul(vplus(v,vskolem9(u,v)),vd469),vplus(vmul(v,vd469),vmul(vskolem9(u,v),vd469))) ),
    file('NUM852+2.p',unknown),
    [] ).

cnf(23,plain,
    ~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
    inference(rew,[status(thm),theory(equality)],[6,9]),
    [iquote('0:Rew:6.0,9.0')] ).

cnf(26,plain,
    ( ~ greater(u,v)
    | equal(vplus(vmul(vd469,v),vmul(vd469,vskolem9(u,v))),vplus(vmul(v,vd469),vmul(vd469,vskolem9(u,v)))) ),
    inference(rew,[status(thm),theory(equality)],[19,22,6]),
    [iquote('0:Rew:19.0,22.1,6.0,22.1,6.0,22.1')] ).

cnf(29,plain,
    ~ less(vmul(vd469,vd480),vmul(vd481,vd469)),
    inference(res,[status(thm),theory(equality)],[7,23]),
    [iquote('0:Res:7.1,23.0')] ).

cnf(41,plain,
    less(u,vplus(u,v)),
    inference(eqr,[status(thm),theory(equality)],[12]),
    [iquote('0:EqR:12.0')] ).

cnf(181,plain,
    ( ~ greater(u,v)
    | equal(vplus(vmul(w,v),vmul(w,vskolem9(u,v))),vmul(w,u)) ),
    inference(spr,[status(thm),theory(equality)],[15,19]),
    [iquote('0:SpR:15.1,19.0')] ).

cnf(186,plain,
    ( ~ greater(u,v)
    | equal(vplus(vmul(v,vd469),vmul(vd469,vskolem9(u,v))),vmul(vd469,u)) ),
    inference(rew,[status(thm),theory(equality)],[181,26]),
    [iquote('0:Rew:181.1,26.1')] ).

cnf(289,plain,
    ( ~ greater(u,v)
    | less(vmul(v,vd469),vmul(vd469,u)) ),
    inference(spr,[status(thm),theory(equality)],[186,41]),
    [iquote('0:SpR:186.1,41.0')] ).

cnf(299,plain,
    ( ~ greater(u,v)
    | less(vmul(v,vd469),vmul(u,vd469)) ),
    inference(spr,[status(thm),theory(equality)],[6,289]),
    [iquote('0:SpR:6.0,289.1')] ).

cnf(324,plain,
    ( ~ greater(u,v)
    | less(vmul(vd469,v),vmul(u,vd469)) ),
    inference(spr,[status(thm),theory(equality)],[6,299]),
    [iquote('0:SpR:6.0,299.1')] ).

cnf(404,plain,
    ~ greater(vd481,vd480),
    inference(res,[status(thm),theory(equality)],[324,29]),
    [iquote('0:Res:324.1,29.0')] ).

cnf(405,plain,
    $false,
    inference(mrr,[status(thm)],[404,1]),
    [iquote('0:MRR:404.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.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 : Tue Jul  5 21:10:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  
% 0.20/0.47  SPASS V 3.9 
% 0.20/0.47  SPASS beiseite: Proof found.
% 0.20/0.47  % SZS status Theorem
% 0.20/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.47  SPASS derived 328 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.20/0.47  SPASS allocated 85436 KBytes.
% 0.20/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.20/0.47  		0:00:00.04 for the input.
% 0.20/0.47  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.47  		0:00:00.00 for inferences.
% 0.20/0.47  		0:00:00.00 for the backtracking.
% 0.20/0.47  		0:00:00.03 for the reduction.
% 0.20/0.47  
% 0.20/0.47  
% 0.20/0.47  Here is a proof with depth 5, length 19 :
% 0.20/0.47  % SZS output start Refutation
% See solution above
% 0.20/0.47  Formulae used in the proof : holds_a40_conseq_conjunct1_a40_conseq_a40_304_a41__a41__a44__a32_483_a44__a32_0_a41_ ass_a40_cond_a40_270_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_147_a44__a32_0_a41__a44__a32_0_a41_ holds_a40_conseq_conjunct1_a40_conseq_conjunct2_a40_conseq_a40_304_a41__a41__a41__a44__a32_484_a44__a32_0_a41_ def_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_12_a41__a44__a32_1_a41_ ass_a40_cond_a40_302_a44__a32_0_a41__a44__a32_3_a41_ ass_a40_cond_a40_281_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_302_a44__a32_0_a41__a44__a32_1_a41_
% 0.20/0.47  
%------------------------------------------------------------------------------