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
%------------------------------------------------------------------------------