TSTP Solution File: PUZ062-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Mon Jul 18 18:27:26 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 34 ( 18 unt; 4 nHn; 34 RR)
% Number of literals : 64 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,c_Finite__Set_OFinites,tc_set(v))
| equal(c_Finite__Set_Ocard(c_insert(w,u,v),v),c_Suc(c_Finite__Set_Ocard(u,v)))
| c_in(w,u,v) ),
file('PUZ062-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_Finite__Set_OFinites,tc_set(v))
| c_in(c_inter(w,u,v),c_Finite__Set_OFinites,tc_set(v)) ),
file('PUZ062-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(u,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('PUZ062-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_inter(v,w,x),x)
| c_in(u,w,x) ),
file('PUZ062-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,v,w)
| ~ c_in(u,x,w)
| c_in(u,c_inter(v,x,w),w) ),
file('PUZ062-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(u,c_insert(u,v,w),w),
file('PUZ062-2.p',unknown),
[] ).
cnf(7,axiom,
~ c_in(u,c_emptyset,v),
file('PUZ062-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('PUZ062-2.p',unknown),
[] ).
cnf(9,axiom,
equal(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
file('PUZ062-2.p',unknown),
[] ).
cnf(10,axiom,
equal(c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),c_emptyset),
file('PUZ062-2.p',unknown),
[] ).
cnf(11,axiom,
equal(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat))),
file('PUZ062-2.p',unknown),
[] ).
cnf(12,axiom,
equal(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat))),
file('PUZ062-2.p',unknown),
[] ).
cnf(13,axiom,
~ equal(c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
file('PUZ062-2.p',unknown),
[] ).
cnf(16,plain,
c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(res,[status(thm),theory(equality)],[8,3]),
[iquote('0:Res:8.0,3.0')] ).
cnf(21,plain,
( ~ c_in(u,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(u,v_t,tc_prod(tc_nat,tc_nat))
| c_in(u,c_emptyset,tc_prod(tc_nat,tc_nat)) ),
inference(spr,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpR:10.0,5.2')] ).
cnf(23,plain,
( ~ c_in(u,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(u,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(mrr,[status(thm)],[21,7]),
[iquote('0:MRR:21.2,7.0')] ).
cnf(24,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(spr,[status(thm),theory(equality)],[11,6]),
[iquote('0:SpR:11.0,6.0')] ).
cnf(26,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(res,[status(thm),theory(equality)],[24,4]),
[iquote('0:Res:24.0,4.0')] ).
cnf(27,plain,
~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(res,[status(thm),theory(equality)],[26,23]),
[iquote('0:Res:26.0,23.0')] ).
cnf(28,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(spr,[status(thm),theory(equality)],[12,6]),
[iquote('0:SpR:12.0,6.0')] ).
cnf(30,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(res,[status(thm),theory(equality)],[28,4]),
[iquote('0:Res:28.0,4.0')] ).
cnf(31,plain,
~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(res,[status(thm),theory(equality)],[30,23]),
[iquote('0:Res:30.0,23.0')] ).
cnf(41,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ equal(c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))))
| c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spl,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpL:1.1,13.0')] ).
cnf(42,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ equal(c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))))
| c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(rew,[status(thm),theory(equality)],[9,41]),
[iquote('0:Rew:9.0,41.1')] ).
cnf(43,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ equal(c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spl,[status(thm),theory(equality)],[1,42]),
[iquote('0:SpL:1.1,42.1')] ).
cnf(44,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(obv,[status(thm),theory(equality)],[43]),
[iquote('0:Obv:43.2')] ).
cnf(45,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
inference(res,[status(thm),theory(equality)],[44,4]),
[iquote('0:Res:44.3,4.0')] ).
cnf(46,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(mrr,[status(thm)],[45,31]),
[iquote('0:MRR:45.3,31.0')] ).
cnf(47,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
inference(res,[status(thm),theory(equality)],[46,4]),
[iquote('0:Res:46.2,4.0')] ).
cnf(48,plain,
( ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(mrr,[status(thm)],[47,27]),
[iquote('0:MRR:47.2,27.0')] ).
cnf(49,plain,
( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(res,[status(thm),theory(equality)],[2,48]),
[iquote('0:Res:2.1,48.1')] ).
cnf(50,plain,
~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(mrr,[status(thm)],[49,16]),
[iquote('0:MRR:49.0,16.0')] ).
cnf(51,plain,
~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(res,[status(thm),theory(equality)],[2,50]),
[iquote('0:Res:2.1,50.0')] ).
cnf(52,plain,
$false,
inference(mrr,[status(thm)],[51,16]),
[iquote('0:MRR:51.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % 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 : Sat May 28 22:54:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.20/0.42 SPASS allocated 63168 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.00 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 6, length 34 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : cls_Finite__Set_Ocard__insert__disjoint_0 cls_Finite__Set_Ofinite__Int_1 cls_Mutil_Otiling__domino__finite_0 cls_Set_OInt__iff_1 cls_Set_OInt__iff_2 cls_Set_Oinsert__iff_1 cls_Set_Oempty__iff_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.20/0.42
%------------------------------------------------------------------------------