TSTP Solution File: SWC049+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC049+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 : Tue Jul 19 22:01:22 EDT 2022

% Result   : Theorem 0.65s 0.84s
% Output   : Refutation 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   55 (  35 unt;   5 nHn;  55 RR)
%            Number of literals    :   93 (   0 equ;  44 neg)
%            Maximal clause size   :    7 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc5),
    file('SWC049+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc4),
    file('SWC049+1.p',unknown),
    [] ).

cnf(5,axiom,
    ssList(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(6,axiom,
    cyclefreeP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(7,axiom,
    totalorderP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(8,axiom,
    strictorderP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderedP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderedP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(11,axiom,
    duplicatefreeP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(12,axiom,
    equalelemsP(nil),
    file('SWC049+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ ssList(u)
    | rearsegP(u,u) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ ssList(u)
    | rearsegP(u,nil) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ equal(skc5,nil)
    | equal(nil,skc4) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(67,axiom,
    ( ~ neq(skc5,nil)
    | neq(skc4,nil) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ neq(skc5,nil)
    | rearsegP(skc5,skc4) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ equal(skc5,nil)
    | ~ equal(nil,skc4) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(105,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | neq(v,u)
    | equal(v,u) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(125,axiom,
    ( ~ ssList(u)
    | ~ neq(u,nil)
    | ~ rearsegP(skc4,u)
    | ~ rearsegP(skc5,u) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(185,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(tl(u),tl(v))
    | ~ equal(hd(u),hd(v))
    | equal(u,v)
    | equal(nil,v)
    | equal(nil,u) ),
    file('SWC049+1.p',unknown),
    [] ).

cnf(194,plain,
    ( ~ equal(skc5,nil)
    | ~ equal(skc4,skc4) ),
    inference(rew,[status(thm),theory(equality)],[66,78]),
    [iquote('0:Rew:66.1,78.1')] ).

cnf(195,plain,
    ~ equal(skc5,nil),
    inference(obv,[status(thm),theory(equality)],[194]),
    [iquote('0:Obv:194.1')] ).

cnf(244,plain,
    ( ~ neq(skc4,nil)
    | ~ rearsegP(skc5,skc4)
    | ~ rearsegP(skc4,skc4) ),
    inference(res,[status(thm),theory(equality)],[2,125]),
    [iquote('0:Res:2.0,125.0')] ).

cnf(281,plain,
    rearsegP(skc4,skc4),
    inference(res,[status(thm),theory(equality)],[2,61]),
    [iquote('0:Res:2.0,61.0')] ).

cnf(285,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u)
    | equal(nil,skc4) ),
    inference(res,[status(thm),theory(equality)],[2,185]),
    [iquote('0:Res:2.0,185.1')] ).

cnf(424,plain,
    ( ~ ssList(u)
    | neq(skc5,u)
    | equal(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[1,105]),
    [iquote('0:Res:1.0,105.0')] ).

cnf(454,plain,
    rearsegP(skc5,nil),
    inference(res,[status(thm),theory(equality)],[1,62]),
    [iquote('0:Res:1.0,62.0')] ).

cnf(552,plain,
    ( ~ rearsegP(skc5,skc4)
    | ~ neq(skc4,nil) ),
    inference(mrr,[status(thm)],[244,281]),
    [iquote('0:MRR:244.2,281.0')] ).

cnf(569,plain,
    equal(nil,skc4),
    inference(spt,[spt(split,[position(s1)])],[285]),
    [iquote('1:Spt:285.5')] ).

cnf(583,plain,
    ( ~ neq(skc5,skc4)
    | neq(skc4,nil) ),
    inference(rew,[status(thm),theory(equality)],[569,67]),
    [iquote('1:Rew:569.0,67.0')] ).

cnf(585,plain,
    ( ~ rearsegP(skc5,skc4)
    | ~ neq(skc4,skc4) ),
    inference(rew,[status(thm),theory(equality)],[569,552]),
    [iquote('1:Rew:569.0,552.1')] ).

cnf(623,plain,
    equalelemsP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,12]),
    [iquote('1:Rew:569.0,12.0')] ).

cnf(624,plain,
    duplicatefreeP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,11]),
    [iquote('1:Rew:569.0,11.0')] ).

cnf(625,plain,
    strictorderedP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,10]),
    [iquote('1:Rew:569.0,10.0')] ).

cnf(626,plain,
    totalorderedP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,9]),
    [iquote('1:Rew:569.0,9.0')] ).

cnf(627,plain,
    strictorderP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,8]),
    [iquote('1:Rew:569.0,8.0')] ).

cnf(628,plain,
    totalorderP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,7]),
    [iquote('1:Rew:569.0,7.0')] ).

cnf(629,plain,
    cyclefreeP(skc4),
    inference(rew,[status(thm),theory(equality)],[569,6]),
    [iquote('1:Rew:569.0,6.0')] ).

cnf(632,plain,
    rearsegP(skc5,skc4),
    inference(rew,[status(thm),theory(equality)],[569,454]),
    [iquote('1:Rew:569.0,454.0')] ).

cnf(641,plain,
    ~ equal(skc5,skc4),
    inference(rew,[status(thm),theory(equality)],[569,195]),
    [iquote('1:Rew:569.0,195.0')] ).

cnf(683,plain,
    ( ~ neq(skc5,skc4)
    | neq(skc4,skc4) ),
    inference(rew,[status(thm),theory(equality)],[569,583]),
    [iquote('1:Rew:569.0,583.1')] ).

cnf(694,plain,
    ~ neq(skc4,skc4),
    inference(mrr,[status(thm)],[585,632]),
    [iquote('1:MRR:585.0,632.0')] ).

cnf(695,plain,
    ~ neq(skc5,skc4),
    inference(mrr,[status(thm)],[683,694]),
    [iquote('1:MRR:683.1,694.0')] ).

cnf(963,plain,
    ( ~ ssList(skc4)
    | equal(skc5,skc4) ),
    inference(res,[status(thm),theory(equality)],[424,695]),
    [iquote('1:Res:424.1,695.0')] ).

cnf(964,plain,
    equal(skc5,skc4),
    inference(ssi,[status(thm)],[963,2,623,624,625,626,627,628,629]),
    [iquote('1:SSi:963.0,2.0,623.0,624.0,625.0,626.0,627.0,628.0,629.0')] ).

cnf(965,plain,
    $false,
    inference(mrr,[status(thm)],[964,641]),
    [iquote('1:MRR:964.0,641.0')] ).

cnf(966,plain,
    ~ equal(nil,skc4),
    inference(spt,[spt(split,[position(sa)])],[965,569]),
    [iquote('1:Spt:965.0,285.5,569.0')] ).

cnf(967,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u) ),
    inference(spt,[spt(split,[position(s2)])],[285]),
    [iquote('1:Spt:965.0,285.0,285.1,285.2,285.3,285.4')] ).

cnf(1007,plain,
    ~ neq(skc5,nil),
    inference(spt,[spt(split,[position(s2s1)])],[68]),
    [iquote('2:Spt:68.0')] ).

cnf(1008,plain,
    ( ~ ssList(nil)
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[424,1007]),
    [iquote('2:Res:424.1,1007.0')] ).

cnf(1009,plain,
    equal(skc5,nil),
    inference(ssi,[status(thm)],[1008,5,6,7,8,9]),
    [iquote('2:SSi:1008.0,5.0,6.0,7.0,8.0,9.0')] ).

cnf(1010,plain,
    $false,
    inference(mrr,[status(thm)],[1009,195]),
    [iquote('2:MRR:1009.0,195.0')] ).

cnf(1011,plain,
    neq(skc5,nil),
    inference(spt,[spt(split,[position(s2sa)])],[1010,1007]),
    [iquote('2:Spt:1010.0,68.0,1007.0')] ).

cnf(1012,plain,
    rearsegP(skc5,skc4),
    inference(spt,[spt(split,[position(s2s2)])],[68]),
    [iquote('2:Spt:1010.0,68.1')] ).

cnf(1013,plain,
    ~ neq(skc4,nil),
    inference(mrr,[status(thm)],[552,1012]),
    [iquote('2:MRR:552.0,1012.0')] ).

cnf(1014,plain,
    $false,
    inference(mrr,[status(thm)],[67,1011,1013]),
    [iquote('2:MRR:67.0,67.1,1011.0,1013.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC049+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n019.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 : Sun Jun 12 20:24:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.65/0.84  
% 0.65/0.84  SPASS V 3.9 
% 0.65/0.84  SPASS beiseite: Proof found.
% 0.65/0.84  % SZS status Theorem
% 0.65/0.84  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.65/0.84  SPASS derived 718 clauses, backtracked 237 clauses, performed 15 splits and kept 967 clauses.
% 0.65/0.84  SPASS allocated 98689 KBytes.
% 0.65/0.84  SPASS spent	0:00:00.48 on the problem.
% 0.65/0.84  		0:00:00.04 for the input.
% 0.65/0.84  		0:00:00.07 for the FLOTTER CNF translation.
% 0.65/0.84  		0:00:00.00 for inferences.
% 0.65/0.84  		0:00:00.00 for the backtracking.
% 0.65/0.84  		0:00:00.20 for the reduction.
% 0.65/0.84  
% 0.65/0.84  
% 0.65/0.84  Here is a proof with depth 2, length 55 :
% 0.65/0.84  % SZS output start Refutation
% See solution above
% 0.65/0.84  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax49 ax51 ax15 ax77
% 0.65/0.84  
%------------------------------------------------------------------------------