TSTP Solution File: LAT359+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT359+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 : Sun Jul 17 06:51:24 EDT 2022

% Result   : Theorem 0.16s 0.49s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   61 (  13 unt;  14 nHn;  61 RR)
%            Number of literals    :  161 (   0 equ;  99 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  10 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    l2_altcat_1(skc14),
    file('LAT359+1.p',unknown),
    [] ).

cnf(5,axiom,
    v1_xboole_0(k1_xboole_0),
    file('LAT359+1.p',unknown),
    [] ).

cnf(20,axiom,
    v1_relat_1(skc25),
    file('LAT359+1.p',unknown),
    [] ).

cnf(21,axiom,
    v1_xboole_0(skc25),
    file('LAT359+1.p',unknown),
    [] ).

cnf(34,axiom,
    m1_subset_1(skf3(u),u),
    file('LAT359+1.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ v1_xboole_0(u)
    | v1_funct_1(u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ l2_altcat_1(u)
    | l1_altcat_1(u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ m1_pboole(u,v)
    | v1_relat_1(u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ m1_pboole(u,v)
    | v1_funct_1(u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ v1_xboole_0(u)
    | equal(u,k1_xboole_0) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(71,axiom,
    r2_hidden(skc17,k1_binop_1(u1_altcat_1(skc14),skc15,skc16)),
    file('LAT359+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ r2_hidden(u,v)
    | m1_subset_1(u,v) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ v1_xboole_0(u)
    | ~ r2_hidden(v,u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(94,axiom,
    ( ~ m1_subset_1(u,v)
    | v1_xboole_0(v)
    | r2_hidden(u,v) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(114,axiom,
    ( ~ l1_altcat_1(u)
    | m1_pboole(u1_altcat_1(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u))) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(115,axiom,
    ( ~ r2_hidden(k4_tarski(u,v),k2_zfmisc_1(w,x))
    | r2_hidden(u,w) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(116,axiom,
    ( ~ r2_hidden(k4_tarski(u,v),k2_zfmisc_1(w,x))
    | r2_hidden(v,x) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(118,axiom,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | ~ m1_pboole(u,v)
    | equal(k1_relat_1(u),v) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(121,axiom,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | equal(k1_funct_1(u,k4_tarski(v,w)),k1_binop_1(u,v,w)) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(123,axiom,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | ~ equal(v,k1_xboole_0)
    | r2_hidden(w,k1_relat_1(u))
    | equal(v,k1_funct_1(u,w)) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(125,axiom,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | ~ r2_hidden(v,k1_relat_1(u))
    | ~ equal(w,k1_funct_1(u,v))
    | r2_hidden(k4_tarski(v,w),u) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(126,axiom,
    ( ~ l1_altcat_1(u)
    | ~ m1_subset_1(v,u1_struct_0(u))
    | ~ m1_subset_1(w,u1_struct_0(u))
    | equal(k1_binop_1(u1_altcat_1(u),w,v),k1_altcat_1(u,w,v)) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(127,axiom,
    ( ~ m1_subset_1(u,u1_struct_0(skc14))
    | ~ equal(u,skc15)
    | ~ r2_hidden(skc17,k1_altcat_1(skc14,u,skc16))
    | ~ m1_subset_1(skc17,k1_altcat_1(skc14,u,skc16))
    | ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
    file('LAT359+1.p',unknown),
    [] ).

cnf(130,plain,
    ( ~ m1_pboole(u,v)
    | equal(k1_relat_1(u),v) ),
    inference(mrr,[status(thm)],[118,53,52]),
    [iquote('0:MRR:118.0,118.1,53.1,52.1')] ).

cnf(131,plain,
    ( ~ equal(u,skc15)
    | ~ m1_subset_1(u,u1_struct_0(skc14))
    | ~ m1_subset_1(skc16,u1_struct_0(skc14))
    | ~ r2_hidden(skc17,k1_altcat_1(skc14,u,skc16)) ),
    inference(mrr,[status(thm)],[127,73]),
    [iquote('0:MRR:127.3,73.1')] ).

cnf(132,plain,
    l1_altcat_1(skc14),
    inference(res,[status(thm),theory(equality)],[1,49]),
    [iquote('0:Res:1.0,49.0')] ).

cnf(142,plain,
    equal(skc25,k1_xboole_0),
    inference(ems,[status(thm)],[70,21]),
    [iquote('0:EmS:70.0,21.0')] ).

cnf(144,plain,
    v1_relat_1(k1_xboole_0),
    inference(rew,[status(thm),theory(equality)],[142,20]),
    [iquote('0:Rew:142.0,20.0')] ).

cnf(235,plain,
    ( v1_xboole_0(u)
    | r2_hidden(skf3(u),u) ),
    inference(res,[status(thm),theory(equality)],[34,94]),
    [iquote('0:Res:34.0,94.0')] ).

cnf(324,plain,
    ( ~ l1_altcat_1(u)
    | equal(k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),k1_relat_1(u1_altcat_1(u))) ),
    inference(res,[status(thm),theory(equality)],[114,130]),
    [iquote('0:Res:114.1,130.0')] ).

cnf(325,plain,
    ( ~ l1_altcat_1(u)
    | v1_relat_1(u1_altcat_1(u)) ),
    inference(res,[status(thm),theory(equality)],[114,52]),
    [iquote('0:Res:114.1,52.0')] ).

cnf(326,plain,
    ( ~ l1_altcat_1(u)
    | v1_funct_1(u1_altcat_1(u)) ),
    inference(res,[status(thm),theory(equality)],[114,53]),
    [iquote('0:Res:114.1,53.0')] ).

cnf(361,plain,
    ( ~ l1_altcat_1(u)
    | ~ r2_hidden(k4_tarski(v,w),k1_relat_1(u1_altcat_1(u)))
    | r2_hidden(v,u1_struct_0(u)) ),
    inference(spl,[status(thm),theory(equality)],[324,115]),
    [iquote('0:SpL:324.1,115.0')] ).

cnf(362,plain,
    ( ~ l1_altcat_1(u)
    | ~ r2_hidden(k4_tarski(v,w),k1_relat_1(u1_altcat_1(u)))
    | r2_hidden(w,u1_struct_0(u)) ),
    inference(spl,[status(thm),theory(equality)],[324,116]),
    [iquote('0:SpL:324.1,116.0')] ).

cnf(397,plain,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | r2_hidden(v,k1_relat_1(u))
    | equal(k1_funct_1(u,v),k1_xboole_0) ),
    inference(eqr,[status(thm),theory(equality)],[123]),
    [iquote('0:EqR:123.2')] ).

cnf(415,plain,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | ~ v1_xboole_0(u)
    | ~ r2_hidden(v,k1_relat_1(u))
    | ~ equal(w,k1_funct_1(u,v)) ),
    inference(res,[status(thm),theory(equality)],[125,74]),
    [iquote('0:Res:125.4,74.1')] ).

cnf(421,plain,
    ( ~ v1_funct_1(u)
    | ~ v1_relat_1(u)
    | ~ v1_xboole_0(u)
    | ~ r2_hidden(v,k1_relat_1(u)) ),
    inference(aed,[status(thm),theory(equality)],[415]),
    [iquote('0:AED:415.4')] ).

cnf(422,plain,
    ( ~ v1_relat_1(u)
    | ~ v1_xboole_0(u)
    | ~ r2_hidden(v,k1_relat_1(u)) ),
    inference(ssi,[status(thm)],[421,43]),
    [iquote('0:SSi:421.0,43.1')] ).

cnf(426,plain,
    ( ~ v1_relat_1(u)
    | ~ v1_xboole_0(u)
    | v1_xboole_0(k1_relat_1(u)) ),
    inference(res,[status(thm),theory(equality)],[235,422]),
    [iquote('0:Res:235.1,422.2')] ).

cnf(431,plain,
    ( ~ v1_xboole_0(u)
    | ~ v1_relat_1(u)
    | equal(k1_relat_1(u),k1_xboole_0) ),
    inference(ems,[status(thm)],[70,426]),
    [iquote('0:EmS:70.0,426.2')] ).

cnf(434,plain,
    ( ~ v1_relat_1(u)
    | ~ v1_xboole_0(u)
    | ~ r2_hidden(v,k1_xboole_0) ),
    inference(rew,[status(thm),theory(equality)],[431,422]),
    [iquote('0:Rew:431.2,422.2')] ).

cnf(448,plain,
    ~ r2_hidden(u,k1_xboole_0),
    inference(ems,[status(thm)],[434,144,5]),
    [iquote('0:EmS:434.0,434.1,144.0,5.0')] ).

cnf(453,plain,
    ( ~ l1_altcat_1(skc14)
    | ~ m1_subset_1(skc16,u1_struct_0(skc14))
    | ~ m1_subset_1(skc15,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_altcat_1(skc14,skc15,skc16)) ),
    inference(spr,[status(thm),theory(equality)],[126,71]),
    [iquote('0:SpR:126.3,71.0')] ).

cnf(457,plain,
    ( ~ m1_subset_1(skc16,u1_struct_0(skc14))
    | ~ m1_subset_1(skc15,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_altcat_1(skc14,skc15,skc16)) ),
    inference(ssi,[status(thm)],[453,1,132]),
    [iquote('0:SSi:453.0,1.0,132.0')] ).

cnf(540,plain,
    ( ~ m1_subset_1(skc16,u1_struct_0(skc14))
    | ~ m1_subset_1(skc15,u1_struct_0(skc14))
    | ~ equal(skc15,skc15)
    | ~ m1_subset_1(skc15,u1_struct_0(skc14))
    | ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
    inference(res,[status(thm),theory(equality)],[457,131]),
    [iquote('0:Res:457.2,131.3')] ).

cnf(559,plain,
    ( ~ m1_subset_1(skc15,u1_struct_0(skc14))
    | ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
    inference(obv,[status(thm),theory(equality)],[540]),
    [iquote('0:Obv:540.2')] ).

cnf(560,plain,
    ( ~ r2_hidden(skc16,u1_struct_0(skc14))
    | ~ m1_subset_1(skc15,u1_struct_0(skc14)) ),
    inference(res,[status(thm),theory(equality)],[73,559]),
    [iquote('0:Res:73.1,559.1')] ).

cnf(561,plain,
    ( ~ r2_hidden(skc15,u1_struct_0(skc14))
    | ~ r2_hidden(skc16,u1_struct_0(skc14)) ),
    inference(res,[status(thm),theory(equality)],[73,560]),
    [iquote('0:Res:73.1,560.1')] ).

cnf(612,plain,
    ( ~ v1_funct_1(u1_altcat_1(u))
    | ~ v1_relat_1(u1_altcat_1(u))
    | ~ l1_altcat_1(u)
    | equal(k1_funct_1(u1_altcat_1(u),k4_tarski(v,w)),k1_xboole_0)
    | r2_hidden(v,u1_struct_0(u)) ),
    inference(res,[status(thm),theory(equality)],[397,361]),
    [iquote('0:Res:397.2,361.1')] ).

cnf(613,plain,
    ( ~ v1_funct_1(u1_altcat_1(u))
    | ~ v1_relat_1(u1_altcat_1(u))
    | ~ l1_altcat_1(u)
    | equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
    | r2_hidden(v,u1_struct_0(u)) ),
    inference(rew,[status(thm),theory(equality)],[121,612]),
    [iquote('0:Rew:121.2,612.3')] ).

cnf(614,plain,
    ( ~ l1_altcat_1(u)
    | equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
    | r2_hidden(v,u1_struct_0(u)) ),
    inference(ssi,[status(thm)],[613,325,326]),
    [iquote('0:SSi:613.1,613.0,325.1,326.1,325.1,326.1')] ).

cnf(616,plain,
    ( ~ l1_altcat_1(skc14)
    | r2_hidden(skc15,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_xboole_0) ),
    inference(spr,[status(thm),theory(equality)],[614,71]),
    [iquote('0:SpR:614.1,71.0')] ).

cnf(622,plain,
    ( r2_hidden(skc15,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_xboole_0) ),
    inference(ssi,[status(thm)],[616,1,132]),
    [iquote('0:SSi:616.0,1.0,132.0')] ).

cnf(623,plain,
    r2_hidden(skc15,u1_struct_0(skc14)),
    inference(mrr,[status(thm)],[622,448]),
    [iquote('0:MRR:622.1,448.0')] ).

cnf(624,plain,
    ~ r2_hidden(skc16,u1_struct_0(skc14)),
    inference(mrr,[status(thm)],[561,623]),
    [iquote('0:MRR:561.0,623.0')] ).

cnf(667,plain,
    ( ~ v1_funct_1(u1_altcat_1(u))
    | ~ v1_relat_1(u1_altcat_1(u))
    | ~ l1_altcat_1(u)
    | equal(k1_funct_1(u1_altcat_1(u),k4_tarski(v,w)),k1_xboole_0)
    | r2_hidden(w,u1_struct_0(u)) ),
    inference(res,[status(thm),theory(equality)],[397,362]),
    [iquote('0:Res:397.2,362.1')] ).

cnf(668,plain,
    ( ~ v1_funct_1(u1_altcat_1(u))
    | ~ v1_relat_1(u1_altcat_1(u))
    | ~ l1_altcat_1(u)
    | equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
    | r2_hidden(w,u1_struct_0(u)) ),
    inference(rew,[status(thm),theory(equality)],[121,667]),
    [iquote('0:Rew:121.2,667.3')] ).

cnf(669,plain,
    ( ~ l1_altcat_1(u)
    | equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
    | r2_hidden(w,u1_struct_0(u)) ),
    inference(ssi,[status(thm)],[668,325,326]),
    [iquote('0:SSi:668.1,668.0,325.1,326.1,325.1,326.1')] ).

cnf(716,plain,
    ( ~ l1_altcat_1(skc14)
    | r2_hidden(skc16,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_xboole_0) ),
    inference(spr,[status(thm),theory(equality)],[669,71]),
    [iquote('0:SpR:669.1,71.0')] ).

cnf(723,plain,
    ( r2_hidden(skc16,u1_struct_0(skc14))
    | r2_hidden(skc17,k1_xboole_0) ),
    inference(ssi,[status(thm)],[716,1,132]),
    [iquote('0:SSi:716.0,1.0,132.0')] ).

cnf(724,plain,
    $false,
    inference(mrr,[status(thm)],[723,624,448]),
    [iquote('0:MRR:723.0,723.1,624.0,448.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LAT359+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.31  % Computer : n018.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 600
% 0.12/0.31  % DateTime : Tue Jun 28 20:02:14 EDT 2022
% 0.12/0.31  % CPUTime  : 
% 0.16/0.49  
% 0.16/0.49  SPASS V 3.9 
% 0.16/0.49  SPASS beiseite: Proof found.
% 0.16/0.49  % SZS status Theorem
% 0.16/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.16/0.49  SPASS derived 524 clauses, backtracked 0 clauses, performed 0 splits and kept 421 clauses.
% 0.16/0.49  SPASS allocated 98282 KBytes.
% 0.16/0.49  SPASS spent	0:00:00.17 on the problem.
% 0.16/0.49  		0:00:00.04 for the input.
% 0.16/0.49  		0:00:00.04 for the FLOTTER CNF translation.
% 0.16/0.49  		0:00:00.01 for inferences.
% 0.16/0.49  		0:00:00.00 for the backtracking.
% 0.16/0.49  		0:00:00.05 for the reduction.
% 0.16/0.49  
% 0.16/0.49  
% 0.16/0.49  Here is a proof with depth 4, length 61 :
% 0.16/0.49  % SZS output start Refutation
% See solution above
% 0.16/0.49  Formulae used in the proof : t12_waybel34 fc6_membered rc2_funct_1 existence_m1_subset_1 cc1_funct_1 dt_l2_altcat_1 dt_m1_pboole t6_boole t1_subset t7_boole t2_subset dt_u1_altcat_1 t106_zfmisc_1 d3_pboole d1_binop_1 d4_funct_1 d2_altcat_1
% 0.16/0.49  
%------------------------------------------------------------------------------