TSTP Solution File: SET984+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 05:30:14 EDT 2022

% Result   : Theorem 49.65s 49.89s
% Output   : Refutation 49.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   42 (  20 unt;   4 nHn;  42 RR)
%            Number of literals    :   75 (   0 equ;  30 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(set_intersection2(u,u),u),
    file('SET984+1.p',unknown),
    [] ).

cnf(6,axiom,
    subset(set_intersection2(u,v),u),
    file('SET984+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(cartesian_product2(skc6,skc7),empty_set),
    file('SET984+1.p',unknown),
    [] ).

cnf(8,axiom,
    subset(cartesian_product2(skc6,skc7),cartesian_product2(skc9,skc8)),
    file('SET984+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET984+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ subset(skc7,skc8)
    | ~ subset(skc6,skc9) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ equal(u,empty_set)
    | equal(cartesian_product2(u,v),empty_set) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ equal(u,empty_set)
    | equal(cartesian_product2(v,u),empty_set) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ subset(u,v)
    | equal(set_intersection2(u,v),u) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,w),cartesian_product2(v,x))),
    file('SET984+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ equal(cartesian_product2(u,v),cartesian_product2(w,x))
    | equal(u,w)
    | equal(v,empty_set)
    | equal(u,empty_set) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(cartesian_product2(u,v),cartesian_product2(w,x))
    | equal(v,x)
    | equal(v,empty_set)
    | equal(u,empty_set) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(19,plain,
    ~ equal(skc6,empty_set),
    inference(res,[status(thm),theory(equality)],[11,7]),
    [iquote('0:Res:11.1,7.0')] ).

cnf(34,plain,
    subset(set_intersection2(u,v),v),
    inference(spr,[status(thm),theory(equality)],[9,6]),
    [iquote('0:SpR:9.0,6.0')] ).

cnf(61,plain,
    ( ~ subset(u,v)
    | equal(set_intersection2(v,u),u) ),
    inference(spr,[status(thm),theory(equality)],[13,9]),
    [iquote('0:SpR:13.1,9.0')] ).

cnf(91,plain,
    ( ~ equal(set_intersection2(u,v),empty_set)
    | equal(set_intersection2(cartesian_product2(w,u),cartesian_product2(x,v)),empty_set) ),
    inference(spr,[status(thm),theory(equality)],[15,12]),
    [iquote('0:SpR:15.0,12.1')] ).

cnf(95,plain,
    ( ~ subset(u,v)
    | equal(set_intersection2(cartesian_product2(w,u),cartesian_product2(x,v)),cartesian_product2(set_intersection2(w,x),u)) ),
    inference(spr,[status(thm),theory(equality)],[13,15]),
    [iquote('0:SpR:13.1,15.0')] ).

cnf(96,plain,
    equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,x),cartesian_product2(v,w))),
    inference(spr,[status(thm),theory(equality)],[9,15]),
    [iquote('0:SpR:9.0,15.0')] ).

cnf(99,plain,
    equal(set_intersection2(cartesian_product2(u,v),cartesian_product2(u,w)),cartesian_product2(u,set_intersection2(v,w))),
    inference(spr,[status(thm),theory(equality)],[5,15]),
    [iquote('0:SpR:5.0,15.0')] ).

cnf(105,plain,
    equal(set_intersection2(cartesian_product2(u,v),cartesian_product2(w,x)),set_intersection2(cartesian_product2(u,x),cartesian_product2(w,v))),
    inference(rew,[status(thm),theory(equality)],[15,96]),
    [iquote('0:Rew:15.0,96.0')] ).

cnf(356,plain,
    ( ~ subset(cartesian_product2(u,v),cartesian_product2(u,w))
    | equal(cartesian_product2(u,set_intersection2(w,v)),cartesian_product2(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[99,61]),
    [iquote('0:SpR:99.0,61.1')] ).

cnf(495,plain,
    ( ~ equal(set_intersection2(u,v),empty_set)
    | ~ subset(cartesian_product2(w,u),cartesian_product2(x,v))
    | equal(cartesian_product2(w,u),empty_set) ),
    inference(spr,[status(thm),theory(equality)],[91,13]),
    [iquote('0:SpR:91.1,13.1')] ).

cnf(726,plain,
    subset(set_intersection2(cartesian_product2(u,v),cartesian_product2(w,x)),cartesian_product2(u,x)),
    inference(spr,[status(thm),theory(equality)],[105,6]),
    [iquote('0:SpR:105.0,6.0')] ).

cnf(1161,plain,
    ( ~ subset(u,v)
    | ~ subset(cartesian_product2(w,u),cartesian_product2(x,v))
    | equal(cartesian_product2(set_intersection2(w,x),u),cartesian_product2(w,u)) ),
    inference(spr,[status(thm),theory(equality)],[95,13]),
    [iquote('0:SpR:95.1,13.1')] ).

cnf(3268,plain,
    ( ~ subset(cartesian_product2(u,v),cartesian_product2(w,x))
    | subset(cartesian_product2(u,v),cartesian_product2(u,x)) ),
    inference(spr,[status(thm),theory(equality)],[13,726]),
    [iquote('0:SpR:13.1,726.0')] ).

cnf(11262,plain,
    ( ~ equal(set_intersection2(skc7,skc8),empty_set)
    | equal(cartesian_product2(skc6,skc7),empty_set) ),
    inference(res,[status(thm),theory(equality)],[8,495]),
    [iquote('0:Res:8.0,495.1')] ).

cnf(11288,plain,
    ~ equal(set_intersection2(skc7,skc8),empty_set),
    inference(mrr,[status(thm)],[11262,7]),
    [iquote('0:MRR:11262.1,7.0')] ).

cnf(40029,plain,
    subset(cartesian_product2(skc6,skc7),cartesian_product2(skc6,skc8)),
    inference(res,[status(thm),theory(equality)],[8,3268]),
    [iquote('0:Res:8.0,3268.0')] ).

cnf(40115,plain,
    equal(cartesian_product2(skc6,set_intersection2(skc8,skc7)),cartesian_product2(skc6,skc7)),
    inference(res,[status(thm),theory(equality)],[40029,356]),
    [iquote('0:Res:40029.0,356.0')] ).

cnf(40118,plain,
    equal(cartesian_product2(skc6,set_intersection2(skc7,skc8)),cartesian_product2(skc6,skc7)),
    inference(rew,[status(thm),theory(equality)],[9,40115]),
    [iquote('0:Rew:9.0,40115.0')] ).

cnf(41018,plain,
    ( ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v))
    | equal(skc6,u)
    | equal(set_intersection2(skc7,skc8),empty_set)
    | equal(skc6,empty_set) ),
    inference(spl,[status(thm),theory(equality)],[40118,16]),
    [iquote('0:SpL:40118.0,16.0')] ).

cnf(41019,plain,
    ( ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v))
    | equal(set_intersection2(skc7,skc8),v)
    | equal(set_intersection2(skc7,skc8),empty_set)
    | equal(skc6,empty_set) ),
    inference(spl,[status(thm),theory(equality)],[40118,17]),
    [iquote('0:SpL:40118.0,17.0')] ).

cnf(41118,plain,
    ( ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v))
    | equal(skc6,u) ),
    inference(mrr,[status(thm)],[41018,11288,19]),
    [iquote('0:MRR:41018.2,41018.3,11288.0,19.0')] ).

cnf(41126,plain,
    ( ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v))
    | equal(set_intersection2(skc7,skc8),v) ),
    inference(mrr,[status(thm)],[41019,11288,19]),
    [iquote('0:MRR:41019.2,41019.3,11288.0,19.0')] ).

cnf(42863,plain,
    ( ~ subset(skc7,skc8)
    | equal(cartesian_product2(set_intersection2(skc6,skc9),skc7),cartesian_product2(skc6,skc7)) ),
    inference(res,[status(thm),theory(equality)],[8,1161]),
    [iquote('0:Res:8.0,1161.1')] ).

cnf(44707,plain,
    ( ~ subset(skc7,skc8)
    | ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(skc6,skc7))
    | equal(set_intersection2(skc6,skc9),skc6) ),
    inference(spl,[status(thm),theory(equality)],[42863,41118]),
    [iquote('0:SpL:42863.1,41118.0')] ).

cnf(44753,plain,
    ( ~ subset(skc7,skc8)
    | equal(set_intersection2(skc6,skc9),skc6) ),
    inference(obv,[status(thm),theory(equality)],[44707]),
    [iquote('0:Obv:44707.1')] ).

cnf(45231,plain,
    ( ~ subset(skc7,skc8)
    | subset(skc6,skc9) ),
    inference(spr,[status(thm),theory(equality)],[44753,34]),
    [iquote('0:SpR:44753.1,34.0')] ).

cnf(45343,plain,
    ~ subset(skc7,skc8),
    inference(mrr,[status(thm)],[45231,10]),
    [iquote('0:MRR:45231.1,10.1')] ).

cnf(64250,plain,
    equal(set_intersection2(skc7,skc8),skc7),
    inference(eqr,[status(thm),theory(equality)],[41126]),
    [iquote('0:EqR:41126.0')] ).

cnf(64905,plain,
    subset(skc7,skc8),
    inference(spr,[status(thm),theory(equality)],[64250,34]),
    [iquote('0:SpR:64250.0,34.0')] ).

cnf(65029,plain,
    $false,
    inference(mrr,[status(thm)],[64905,45343]),
    [iquote('0:MRR:64905.0,45343.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n003.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 : Sun Jul 10 06:36:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 49.65/49.89  
% 49.65/49.89  SPASS V 3.9 
% 49.65/49.89  SPASS beiseite: Proof found.
% 49.65/49.89  % SZS status Theorem
% 49.65/49.89  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 49.65/49.89  SPASS derived 41369 clauses, backtracked 0 clauses, performed 0 splits and kept 8257 clauses.
% 49.65/49.89  SPASS allocated 137627 KBytes.
% 49.65/49.89  SPASS spent	0:0:47.29 on the problem.
% 49.65/49.89  		0:00:00.04 for the input.
% 49.65/49.89  		0:00:00.03 for the FLOTTER CNF translation.
% 49.65/49.89  		0:00:00.44 for inferences.
% 49.65/49.89  		0:00:00.00 for the backtracking.
% 49.65/49.89  		0:0:46.72 for the reduction.
% 49.65/49.89  
% 49.65/49.89  
% 49.65/49.89  Here is a proof with depth 8, length 42 :
% 49.65/49.89  % SZS output start Refutation
% See solution above
% 49.65/49.89  Formulae used in the proof : idempotence_k3_xboole_0 t17_xboole_1 t138_zfmisc_1 commutativity_k3_xboole_0 t113_zfmisc_1 t28_xboole_1 t123_zfmisc_1 t134_zfmisc_1
% 49.65/49.89  
%------------------------------------------------------------------------------