TSTP Solution File: NUN082+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUN082+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 16:38:47 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   44 (  29 unt;   4 nHn;  44 RR)
%            Number of literals    :   62 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-4 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    r1(skf22(u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(2,axiom,
    r1(skf24(u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(3,axiom,
    r1(skf23(u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(6,axiom,
    r2(u,skf20(v,u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(7,axiom,
    r3(u,skf22(u),u),
    file('NUN082+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,skc1)
    | skP0(skc1,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(10,axiom,
    r4(u,v,skf21(v,u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(11,axiom,
    r4(u,skf24(u),skf23(u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ r1(u)
    | ~ skP0(v,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(19,axiom,
    r3(skf21(u,v),v,skf19(v,u)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(20,axiom,
    r4(u,skf20(u,v),skf19(u,v)),
    file('NUN082+2.p',unknown),
    [] ).

cnf(21,axiom,
    ( equal(u,skf13(v))
    | skP1(skf13(v),u,v) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ r2(u,v)
    | ~ skP1(w,v,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ r3(u,v,w)
    | ~ skP2(x,w,v,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ r4(u,v,w)
    | ~ skP3(x,w,v,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(31,axiom,
    ( equal(u,skf14(v,w))
    | skP2(skf14(v,w),u,w,v) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(32,axiom,
    ( equal(u,skf15(v,w))
    | skP3(skf15(v,w),u,w,v) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r2(v,w)
    | ~ r4(x,w,u) ),
    file('NUN082+2.p',unknown),
    [] ).

cnf(47,plain,
    ( ~ r1(u)
    | equal(u,skc1) ),
    inference(res,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Res:8.1,13.1')] ).

cnf(49,plain,
    equal(skf22(u),skc1),
    inference(ems,[status(thm)],[47,1]),
    [iquote('0:EmS:47.0,1.0')] ).

cnf(50,plain,
    equal(skf24(u),skc1),
    inference(ems,[status(thm)],[47,2]),
    [iquote('0:EmS:47.0,2.0')] ).

cnf(51,plain,
    equal(skf23(u),skc1),
    inference(ems,[status(thm)],[47,3]),
    [iquote('0:EmS:47.0,3.0')] ).

cnf(52,plain,
    r1(skc1),
    inference(rew,[status(thm),theory(equality)],[49,1]),
    [iquote('0:Rew:49.0,1.0')] ).

cnf(53,plain,
    r3(u,skc1,u),
    inference(rew,[status(thm),theory(equality)],[49,7]),
    [iquote('0:Rew:49.0,7.0')] ).

cnf(57,plain,
    r4(u,skc1,skf23(u)),
    inference(rew,[status(thm),theory(equality)],[50,11]),
    [iquote('0:Rew:50.0,11.0')] ).

cnf(64,plain,
    r4(u,skc1,skc1),
    inference(rew,[status(thm),theory(equality)],[51,57]),
    [iquote('0:Rew:51.0,57.0')] ).

cnf(85,plain,
    ( ~ r2(u,v)
    | equal(v,skf13(u)) ),
    inference(res,[status(thm),theory(equality)],[21,22]),
    [iquote('0:Res:21.1,22.1')] ).

cnf(88,plain,
    equal(skf20(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[6,85]),
    [iquote('0:Res:6.0,85.0')] ).

cnf(94,plain,
    r4(u,skf13(v),skf19(u,v)),
    inference(rew,[status(thm),theory(equality)],[88,20]),
    [iquote('0:Rew:88.0,20.0')] ).

cnf(95,plain,
    r2(u,skf13(u)),
    inference(rew,[status(thm),theory(equality)],[88,6]),
    [iquote('0:Rew:88.0,6.0')] ).

cnf(302,plain,
    ( ~ r4(u,v,w)
    | equal(w,skf15(u,v)) ),
    inference(res,[status(thm),theory(equality)],[32,29]),
    [iquote('0:Res:32.1,29.1')] ).

cnf(340,plain,
    equal(skf21(u,v),skf15(v,u)),
    inference(res,[status(thm),theory(equality)],[10,302]),
    [iquote('0:Res:10.0,302.0')] ).

cnf(341,plain,
    equal(skf15(u,skc1),skc1),
    inference(res,[status(thm),theory(equality)],[64,302]),
    [iquote('0:Res:64.0,302.0')] ).

cnf(346,plain,
    r3(skf15(u,v),u,skf19(u,v)),
    inference(rew,[status(thm),theory(equality)],[340,19]),
    [iquote('0:Rew:340.0,19.0')] ).

cnf(374,plain,
    r3(skc1,u,skf19(u,skc1)),
    inference(spr,[status(thm),theory(equality)],[341,346]),
    [iquote('0:SpR:341.0,346.0')] ).

cnf(388,plain,
    ( ~ r3(u,v,w)
    | equal(w,skf14(u,v)) ),
    inference(res,[status(thm),theory(equality)],[31,27]),
    [iquote('0:Res:31.1,27.1')] ).

cnf(403,plain,
    equal(skf14(u,skc1),u),
    inference(res,[status(thm),theory(equality)],[53,388]),
    [iquote('0:Res:53.0,388.0')] ).

cnf(409,plain,
    equal(skf19(u,skc1),skf14(skc1,u)),
    inference(res,[status(thm),theory(equality)],[374,388]),
    [iquote('0:Res:374.0,388.0')] ).

cnf(460,plain,
    r4(u,skf13(skc1),skf14(skc1,u)),
    inference(spr,[status(thm),theory(equality)],[409,94]),
    [iquote('0:SpR:409.0,94.0')] ).

cnf(470,plain,
    r4(skc1,skf13(skc1),skc1),
    inference(spr,[status(thm),theory(equality)],[403,460]),
    [iquote('0:SpR:403.0,460.0')] ).

cnf(475,plain,
    ( ~ r1(skc1)
    | ~ r1(u)
    | ~ r2(u,skf13(skc1)) ),
    inference(res,[status(thm),theory(equality)],[470,33]),
    [iquote('0:Res:470.0,33.3')] ).

cnf(477,plain,
    ( ~ r1(u)
    | ~ r2(u,skf13(skc1)) ),
    inference(ssi,[status(thm)],[475,52]),
    [iquote('0:SSi:475.0,52.0')] ).

cnf(479,plain,
    ~ r1(skc1),
    inference(res,[status(thm),theory(equality)],[95,477]),
    [iquote('0:Res:95.0,477.1')] ).

cnf(484,plain,
    $false,
    inference(ssi,[status(thm)],[479,52]),
    [iquote('0:SSi:479.0,52.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUN082+2 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun  2 05:04:04 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 378 clauses, backtracked 0 clauses, performed 0 splits and kept 221 clauses.
% 0.19/0.48  SPASS allocated 97958 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.04 for the input.
% 0.19/0.48  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.01 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.03 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 8, length 44 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : axiom_4a axiom_5a axiom_2a axiom_1 axiom_2 axiom_3 axiom_4 xtimesoneeqzero
% 0.19/0.48  
%------------------------------------------------------------------------------