TSTP Solution File: NUN072+2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUN072+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 16:38:45 EDT 2022

% Result   : Theorem 11.61s 11.85s
% Output   : Refutation 11.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   22
% Syntax   : Number of clauses     :   66 (  47 unt;   4 nHn;  66 RR)
%            Number of literals    :  112 (   0 equ;  54 neg)
%            Maximal clause size   :    9 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-4 aty)
%            Number of functors    :   21 (  21 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    r1(skf22(u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(2,axiom,
    r1(skf24(u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(3,axiom,
    r1(skf23(u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(5,axiom,
    r2(u,skf17(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(6,axiom,
    r2(u,skf20(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(7,axiom,
    r3(u,skf22(u),u),
    file('NUN072+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,skc1)
    | skP0(skc1,u) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(9,axiom,
    r3(u,v,skf18(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(10,axiom,
    r4(u,v,skf21(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(11,axiom,
    r4(u,skf24(u),skf23(u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ r1(u)
    | ~ skP0(v,u) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(14,axiom,
    r2(skf18(u,v),skf16(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(18,axiom,
    r3(u,skf17(u,v),skf16(u,v)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(19,axiom,
    r3(skf21(u,v),v,skf19(v,u)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(20,axiom,
    r4(u,skf20(u,v),skf19(u,v)),
    file('NUN072+2.p',unknown),
    [] ).

cnf(21,axiom,
    ( equal(u,skf13(v))
    | skP1(skf13(v),u,v) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ r2(u,v)
    | ~ skP1(w,v,u) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ r3(u,v,w)
    | ~ skP2(x,w,v,u) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ r4(u,v,w)
    | ~ skP3(x,w,v,u) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(31,axiom,
    ( equal(u,skf14(v,w))
    | skP2(skf14(v,w),u,w,v) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(32,axiom,
    ( equal(u,skf15(v,w))
    | skP3(skf15(v,w),u,w,v) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(w,y)
    | ~ r2(x,z)
    | ~ r2(v,x1)
    | ~ r2(y,x2)
    | ~ r4(x1,x2,z) ),
    file('NUN072+2.p',unknown),
    [] ).

cnf(49,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(w,y)
    | ~ r2(x,z)
    | ~ r2(y,x1)
    | ~ r4(skf20(x2,v),x1,z) ),
    inference(res,[status(thm),theory(equality)],[6,33]),
    [iquote('0:Res:6.0,33.5')] ).

cnf(61,plain,
    ( ~ r1(u)
    | equal(u,skc1) ),
    inference(res,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Res:8.1,13.1')] ).

cnf(63,plain,
    equal(skf22(u),skc1),
    inference(ems,[status(thm)],[61,1]),
    [iquote('0:EmS:61.0,1.0')] ).

cnf(64,plain,
    equal(skf24(u),skc1),
    inference(ems,[status(thm)],[61,2]),
    [iquote('0:EmS:61.0,2.0')] ).

cnf(65,plain,
    equal(skf23(u),skc1),
    inference(ems,[status(thm)],[61,3]),
    [iquote('0:EmS:61.0,3.0')] ).

cnf(66,plain,
    r1(skc1),
    inference(rew,[status(thm),theory(equality)],[63,1]),
    [iquote('0:Rew:63.0,1.0')] ).

cnf(67,plain,
    r3(u,skc1,u),
    inference(rew,[status(thm),theory(equality)],[63,7]),
    [iquote('0:Rew:63.0,7.0')] ).

cnf(72,plain,
    r4(u,skc1,skf23(u)),
    inference(rew,[status(thm),theory(equality)],[64,11]),
    [iquote('0:Rew:64.0,11.0')] ).

cnf(81,plain,
    r4(u,skc1,skc1),
    inference(rew,[status(thm),theory(equality)],[65,72]),
    [iquote('0:Rew:65.0,72.0')] ).

cnf(104,plain,
    ( ~ r2(u,v)
    | equal(v,skf13(u)) ),
    inference(res,[status(thm),theory(equality)],[21,22]),
    [iquote('0:Res:21.1,22.1')] ).

cnf(105,plain,
    equal(skf20(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[6,104]),
    [iquote('0:Res:6.0,104.0')] ).

cnf(106,plain,
    equal(skf17(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[5,104]),
    [iquote('0:Res:5.0,104.0')] ).

cnf(111,plain,
    r4(u,skf13(v),skf19(u,v)),
    inference(rew,[status(thm),theory(equality)],[105,20]),
    [iquote('0:Rew:105.0,20.0')] ).

cnf(112,plain,
    r2(u,skf13(u)),
    inference(rew,[status(thm),theory(equality)],[105,6]),
    [iquote('0:Rew:105.0,6.0')] ).

cnf(117,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(w,y)
    | ~ r2(x,z)
    | ~ r2(y,x1)
    | ~ r4(skf13(v),x1,z) ),
    inference(rew,[status(thm),theory(equality)],[105,49]),
    [iquote('0:Rew:105.0,49.7')] ).

cnf(120,plain,
    r3(u,skf13(v),skf16(u,v)),
    inference(rew,[status(thm),theory(equality)],[106,18]),
    [iquote('0:Rew:106.0,18.0')] ).

cnf(288,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(289,plain,
    equal(skf21(u,v),skf15(v,u)),
    inference(res,[status(thm),theory(equality)],[10,288]),
    [iquote('0:Res:10.0,288.0')] ).

cnf(290,plain,
    equal(skf15(u,skc1),skc1),
    inference(res,[status(thm),theory(equality)],[81,288]),
    [iquote('0:Res:81.0,288.0')] ).

cnf(291,plain,
    equal(skf15(u,skf13(v)),skf19(u,v)),
    inference(res,[status(thm),theory(equality)],[111,288]),
    [iquote('0:Res:111.0,288.0')] ).

cnf(295,plain,
    r3(skf15(u,v),u,skf19(u,v)),
    inference(rew,[status(thm),theory(equality)],[289,19]),
    [iquote('0:Rew:289.0,19.0')] ).

cnf(306,plain,
    r3(skc1,u,skf19(u,skc1)),
    inference(spr,[status(thm),theory(equality)],[290,295]),
    [iquote('0:SpR:290.0,295.0')] ).

cnf(315,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(318,plain,
    r3(skf19(u,v),u,skf19(u,skf13(v))),
    inference(spr,[status(thm),theory(equality)],[291,295]),
    [iquote('0:SpR:291.0,295.0')] ).

cnf(353,plain,
    equal(skf18(u,v),skf14(v,u)),
    inference(res,[status(thm),theory(equality)],[9,315]),
    [iquote('0:Res:9.0,315.0')] ).

cnf(354,plain,
    equal(skf14(u,skc1),u),
    inference(res,[status(thm),theory(equality)],[67,315]),
    [iquote('0:Res:67.0,315.0')] ).

cnf(355,plain,
    equal(skf14(u,skf13(v)),skf16(u,v)),
    inference(res,[status(thm),theory(equality)],[120,315]),
    [iquote('0:Res:120.0,315.0')] ).

cnf(360,plain,
    equal(skf19(u,skc1),skf14(skc1,u)),
    inference(res,[status(thm),theory(equality)],[306,315]),
    [iquote('0:Res:306.0,315.0')] ).

cnf(363,plain,
    r2(skf14(u,v),skf16(u,v)),
    inference(rew,[status(thm),theory(equality)],[353,14]),
    [iquote('0:Rew:353.0,14.0')] ).

cnf(392,plain,
    r2(u,skf16(u,skc1)),
    inference(spr,[status(thm),theory(equality)],[354,363]),
    [iquote('0:SpR:354.0,363.0')] ).

cnf(401,plain,
    equal(skf16(u,skc1),skf13(u)),
    inference(res,[status(thm),theory(equality)],[392,104]),
    [iquote('0:Res:392.0,104.0')] ).

cnf(420,plain,
    r3(skf14(skc1,u),u,skf19(u,skf13(skc1))),
    inference(spr,[status(thm),theory(equality)],[360,318]),
    [iquote('0:SpR:360.0,318.0')] ).

cnf(613,plain,
    equal(skf14(skf14(skc1,u),u),skf19(u,skf13(skc1))),
    inference(res,[status(thm),theory(equality)],[420,315]),
    [iquote('0:Res:420.0,315.0')] ).

cnf(788,plain,
    equal(skf16(skf14(skc1,skf13(u)),u),skf19(skf13(u),skf13(skc1))),
    inference(spr,[status(thm),theory(equality)],[613,355]),
    [iquote('0:SpR:613.0,355.0')] ).

cnf(797,plain,
    equal(skf16(skf16(skc1,u),u),skf19(skf13(u),skf13(skc1))),
    inference(rew,[status(thm),theory(equality)],[355,788]),
    [iquote('0:Rew:355.0,788.0')] ).

cnf(1089,plain,
    r4(skf13(u),skf13(skf13(skc1)),skf16(skf16(skc1,u),u)),
    inference(spr,[status(thm),theory(equality)],[797,111]),
    [iquote('0:SpR:797.0,111.0')] ).

cnf(1190,plain,
    r4(skf13(skc1),skf13(skf13(skc1)),skf16(skf13(skc1),skc1)),
    inference(spr,[status(thm),theory(equality)],[401,1089]),
    [iquote('0:SpR:401.0,1089.0')] ).

cnf(1205,plain,
    r4(skf13(skc1),skf13(skf13(skc1)),skf13(skf13(skc1))),
    inference(rew,[status(thm),theory(equality)],[401,1190]),
    [iquote('0:Rew:401.0,1190.0')] ).

cnf(1223,plain,
    ( ~ r1(u)
    | ~ r1(skc1)
    | ~ r1(v)
    | ~ r2(u,w)
    | ~ r2(v,x)
    | ~ r2(w,skf13(skf13(skc1)))
    | ~ r2(x,skf13(skf13(skc1))) ),
    inference(res,[status(thm),theory(equality)],[1205,117]),
    [iquote('0:Res:1205.0,117.7')] ).

cnf(1225,plain,
    ( ~ r1(u)
    | ~ r1(skc1)
    | ~ r2(u,v)
    | ~ r2(v,skf13(skf13(skc1))) ),
    inference(con,[status(thm)],[1223]),
    [iquote('0:Con:1223.2')] ).

cnf(1226,plain,
    ( ~ r1(u)
    | ~ r2(u,v)
    | ~ r2(v,skf13(skf13(skc1))) ),
    inference(ssi,[status(thm)],[1225,66]),
    [iquote('0:SSi:1225.1,66.0')] ).

cnf(13543,plain,
    ( ~ r1(u)
    | ~ r2(u,skf13(skc1)) ),
    inference(res,[status(thm),theory(equality)],[112,1226]),
    [iquote('0:Res:112.0,1226.2')] ).

cnf(13552,plain,
    ~ r1(skc1),
    inference(res,[status(thm),theory(equality)],[112,13543]),
    [iquote('0:Res:112.0,13543.1')] ).

cnf(13560,plain,
    $false,
    inference(ssi,[status(thm)],[13552,66]),
    [iquote('0:SSi:13552.0,66.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem  : NUN072+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.15  % Command  : run_spass %d %s
% 0.14/0.37  % Computer : n025.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 600
% 0.14/0.37  % DateTime : Thu Jun  2 10:12:14 EDT 2022
% 0.14/0.37  % CPUTime  : 
% 11.61/11.85  
% 11.61/11.85  SPASS V 3.9 
% 11.61/11.85  SPASS beiseite: Proof found.
% 11.61/11.85  % SZS status Theorem
% 11.61/11.85  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 11.61/11.85  SPASS derived 10249 clauses, backtracked 0 clauses, performed 0 splits and kept 3892 clauses.
% 11.61/11.85  SPASS allocated 111847 KBytes.
% 11.61/11.85  SPASS spent	0:0:11.28 on the problem.
% 11.61/11.85  		0:00:00.03 for the input.
% 11.61/11.85  		0:00:00.03 for the FLOTTER CNF translation.
% 11.61/11.85  		0:00:00.17 for inferences.
% 11.61/11.85  		0:00:00.00 for the backtracking.
% 11.61/11.85  		0:0:10.93 for the reduction.
% 11.61/11.85  
% 11.61/11.85  
% 11.61/11.85  Here is a proof with depth 12, length 66 :
% 11.61/11.85  % SZS output start Refutation
% See solution above
% 11.61/11.85  Formulae used in the proof : axiom_4a axiom_5a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 axiom_4 onetimestwoeqtwo
% 11.61/11.85  
%------------------------------------------------------------------------------