TSTP Solution File: PUZ064-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ064-2 : TPTP v8.1.0. Released v3.2.0.
% 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 18:27:26 EDT 2022
% Result : Unsatisfiable 1.09s 1.33s
% Output : Refutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of clauses : 106 ( 94 unt; 0 nHn; 106 RR)
% Number of literals : 127 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(c_inter(u,v,w),c_emptyset)
| ~ c_in(u,x,tc_set(w))
| ~ c_in(v,c_Mutil_Otiling(x,w),tc_set(w))
| c_in(c_union(u,v,w),c_Mutil_Otiling(x,w),tc_set(w)) ),
file('PUZ064-2.p',unknown),
[] ).
cnf(3,axiom,
equal(c_uminus(c_minus(u,v,tc_set(w)),tc_set(w)),c_union(c_uminus(u,tc_set(w)),v,w)),
file('PUZ064-2.p',unknown),
[] ).
cnf(4,axiom,
equal(c_uminus(c_UNIV,tc_set(u)),c_emptyset),
file('PUZ064-2.p',unknown),
[] ).
cnf(5,axiom,
equal(c_minus(u,c_uminus(v,tc_set(w)),tc_set(w)),c_inter(u,v,w)),
file('PUZ064-2.p',unknown),
[] ).
cnf(6,axiom,
equal(c_inter(c_UNIV,u,v),u),
file('PUZ064-2.p',unknown),
[] ).
cnf(8,axiom,
equal(c_union(c_minus(u,v,tc_set(w)),v,w),c_union(u,v,w)),
file('PUZ064-2.p',unknown),
[] ).
cnf(9,axiom,
equal(c_union(u,c_minus(v,u,tc_set(w)),w),c_union(u,v,w)),
file('PUZ064-2.p',unknown),
[] ).
cnf(10,axiom,
equal(c_union(c_UNIV,u,v),c_UNIV),
file('PUZ064-2.p',unknown),
[] ).
cnf(11,axiom,
equal(c_union(u,u,v),u),
file('PUZ064-2.p',unknown),
[] ).
cnf(12,axiom,
equal(c_union(c_union(u,v,w),x,w),c_union(u,c_union(v,x,w),w)),
file('PUZ064-2.p',unknown),
[] ).
cnf(13,axiom,
equal(c_union(c_emptyset,u,v),u),
file('PUZ064-2.p',unknown),
[] ).
cnf(14,axiom,
equal(c_union(u,c_emptyset,v),u),
file('PUZ064-2.p',unknown),
[] ).
cnf(15,axiom,
( ~ c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_lessequals(u,x,tc_set(w)) ),
file('PUZ064-2.p',unknown),
[] ).
cnf(16,axiom,
( ~ c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_lessequals(v,x,tc_set(w)) ),
file('PUZ064-2.p',unknown),
[] ).
cnf(18,axiom,
equal(c_uminus(c_uminus(u,tc_set(v)),tc_set(v)),u),
file('PUZ064-2.p',unknown),
[] ).
cnf(22,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('PUZ064-2.p',unknown),
[] ).
cnf(23,axiom,
c_lessequals(u,u,tc_set(v)),
file('PUZ064-2.p',unknown),
[] ).
cnf(24,axiom,
c_in(v_a,v_A,tc_set(t_a)),
file('PUZ064-2.p',unknown),
[] ).
cnf(25,axiom,
equal(c_inter(v_a,v_t,t_a),c_emptyset),
file('PUZ064-2.p',unknown),
[] ).
cnf(26,axiom,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('PUZ064-2.p',unknown),
[] ).
cnf(27,axiom,
equal(c_inter(c_union(v_a,v_t,t_a),v_u,t_a),c_emptyset),
file('PUZ064-2.p',unknown),
[] ).
cnf(28,axiom,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('PUZ064-2.p',unknown),
[] ).
cnf(29,axiom,
( ~ equal(c_inter(v_t,v_u,t_a),c_emptyset)
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
file('PUZ064-2.p',unknown),
[] ).
cnf(30,plain,
~ c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(rew,[status(thm),theory(equality)],[12,28]),
[iquote('0:Rew:12.0,28.0')] ).
cnf(31,plain,
( ~ equal(c_inter(v_t,v_u,t_a),c_emptyset)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(mrr,[status(thm)],[29,26]),
[iquote('0:MRR:29.1,26.0')] ).
cnf(74,plain,
equal(c_minus(u,c_emptyset,tc_set(v)),c_inter(u,c_UNIV,v)),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(76,plain,
equal(c_inter(u,c_uminus(v,tc_set(w)),w),c_minus(u,v,tc_set(w))),
inference(spr,[status(thm),theory(equality)],[18,5]),
[iquote('0:SpR:18.0,5.0')] ).
cnf(79,plain,
equal(c_minus(c_UNIV,u,tc_set(v)),c_uminus(u,tc_set(v))),
inference(spr,[status(thm),theory(equality)],[76,6]),
[iquote('0:SpR:76.0,6.0')] ).
cnf(92,plain,
equal(c_minus(u,c_emptyset,tc_set(v)),c_union(u,c_emptyset,v)),
inference(spr,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpR:8.0,14.0')] ).
cnf(97,plain,
equal(c_union(c_uminus(u,tc_set(v)),u,v),c_union(c_UNIV,u,v)),
inference(spr,[status(thm),theory(equality)],[79,8]),
[iquote('0:SpR:79.0,8.0')] ).
cnf(98,plain,
equal(c_inter(u,c_UNIV,v),u),
inference(rew,[status(thm),theory(equality)],[74,92,14]),
[iquote('0:Rew:74.0,92.0,14.0,92.0')] ).
cnf(99,plain,
equal(c_minus(u,c_emptyset,tc_set(v)),u),
inference(rew,[status(thm),theory(equality)],[98,74]),
[iquote('0:Rew:98.0,74.0')] ).
cnf(101,plain,
equal(c_union(c_uminus(u,tc_set(v)),u,v),c_UNIV),
inference(rew,[status(thm),theory(equality)],[10,97]),
[iquote('0:Rew:10.0,97.0')] ).
cnf(122,plain,
equal(c_union(c_uminus(u,tc_set(v)),c_inter(w,u,v),v),c_union(c_uminus(u,tc_set(v)),w,v)),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(172,plain,
c_lessequals(u,c_union(u,v,w),tc_set(w)),
inference(res,[status(thm),theory(equality)],[23,15]),
[iquote('0:Res:23.0,15.0')] ).
cnf(281,plain,
c_lessequals(c_union(u,v,w),c_union(u,c_union(v,x,w),w),tc_set(w)),
inference(spr,[status(thm),theory(equality)],[12,172]),
[iquote('0:SpR:12.0,172.0')] ).
cnf(293,plain,
equal(c_union(u,c_union(u,v,w),w),c_union(u,v,w)),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(391,plain,
equal(c_uminus(c_union(c_uminus(u,tc_set(v)),w,v),tc_set(v)),c_minus(u,w,tc_set(v))),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(392,plain,
equal(c_union(c_union(c_uminus(u,tc_set(v)),w,v),c_minus(u,w,tc_set(v)),v),c_UNIV),
inference(spr,[status(thm),theory(equality)],[3,101]),
[iquote('0:SpR:3.0,101.0')] ).
cnf(397,plain,
equal(c_minus(u,c_union(c_uminus(v,tc_set(w)),x,w),tc_set(w)),c_inter(u,c_minus(v,x,tc_set(w)),w)),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(400,plain,
equal(c_union(c_uminus(u,tc_set(v)),c_uminus(w,tc_set(v)),v),c_uminus(c_inter(u,w,v),tc_set(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(406,plain,
equal(c_union(c_uminus(u,tc_set(v)),c_union(w,u,v),v),c_UNIV),
inference(rew,[status(thm),theory(equality)],[9,392,12]),
[iquote('0:Rew:9.0,392.0,12.0,392.0')] ).
cnf(470,plain,
equal(c_union(u,c_union(v,c_uminus(u,tc_set(w)),w),w),c_UNIV),
inference(spr,[status(thm),theory(equality)],[18,406]),
[iquote('0:SpR:18.0,406.0')] ).
cnf(789,plain,
( ~ equal(c_inter(c_minus(u,v,tc_set(w)),v,w),c_emptyset)
| ~ c_in(c_minus(u,v,tc_set(w)),x,tc_set(w))
| ~ c_in(v,c_Mutil_Otiling(x,w),tc_set(w))
| c_in(c_union(u,v,w),c_Mutil_Otiling(x,w),tc_set(w)) ),
inference(spr,[status(thm),theory(equality)],[8,1]),
[iquote('0:SpR:8.0,1.3')] ).
cnf(818,plain,
c_lessequals(c_union(c_union(u,v,w),u,w),c_union(u,v,w),tc_set(w)),
inference(spr,[status(thm),theory(equality)],[11,281]),
[iquote('0:SpR:11.0,281.0')] ).
cnf(855,plain,
c_lessequals(c_union(u,c_union(v,u,w),w),c_union(u,v,w),tc_set(w)),
inference(rew,[status(thm),theory(equality)],[12,818]),
[iquote('0:Rew:12.0,818.0')] ).
cnf(906,plain,
c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w)),
inference(res,[status(thm),theory(equality)],[855,16]),
[iquote('0:Res:855.0,16.0')] ).
cnf(965,plain,
( ~ c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w))
| equal(c_union(v,u,w),c_union(u,v,w)) ),
inference(res,[status(thm),theory(equality)],[906,22]),
[iquote('0:Res:906.0,22.0')] ).
cnf(983,plain,
equal(c_union(u,v,w),c_union(v,u,w)),
inference(mrr,[status(thm)],[965,906]),
[iquote('0:MRR:965.0,906.0')] ).
cnf(1121,plain,
equal(c_minus(c_uminus(u,tc_set(v)),w,tc_set(v)),c_uminus(c_union(u,w,v),tc_set(v))),
inference(spr,[status(thm),theory(equality)],[18,391]),
[iquote('0:SpR:18.0,391.0')] ).
cnf(1122,plain,
equal(c_uminus(c_union(c_union(c_uminus(u,tc_set(v)),w,v),x,v),tc_set(v)),c_minus(c_minus(u,w,tc_set(v)),x,tc_set(v))),
inference(spr,[status(thm),theory(equality)],[3,391]),
[iquote('0:SpR:3.0,391.0')] ).
cnf(1129,plain,
equal(c_minus(u,c_minus(v,c_uminus(u,tc_set(w)),tc_set(w)),tc_set(w)),c_uminus(c_union(c_uminus(u,tc_set(w)),v,w),tc_set(w))),
inference(spr,[status(thm),theory(equality)],[9,391]),
[iquote('0:SpR:9.0,391.0')] ).
cnf(1130,plain,
equal(c_minus(u,c_union(v,c_uminus(c_uminus(u,tc_set(w)),tc_set(w)),w),tc_set(w)),c_uminus(c_UNIV,tc_set(w))),
inference(spr,[status(thm),theory(equality)],[470,391]),
[iquote('0:SpR:470.0,391.0')] ).
cnf(1131,plain,
equal(c_minus(u,c_union(c_uminus(u,tc_set(v)),w,v),tc_set(v)),c_uminus(c_union(c_uminus(u,tc_set(v)),w,v),tc_set(v))),
inference(spr,[status(thm),theory(equality)],[293,391]),
[iquote('0:SpR:293.0,391.0')] ).
cnf(1154,plain,
equal(c_minus(u,c_union(v,u,w),tc_set(w)),c_emptyset),
inference(rew,[status(thm),theory(equality)],[18,1130,4]),
[iquote('0:Rew:18.0,1130.0,4.0,1130.0')] ).
cnf(1157,plain,
equal(c_minus(u,c_union(c_uminus(u,tc_set(v)),w,v),tc_set(v)),c_minus(u,w,tc_set(v))),
inference(rew,[status(thm),theory(equality)],[391,1131]),
[iquote('0:Rew:391.0,1131.0')] ).
cnf(1158,plain,
equal(c_inter(u,c_minus(u,v,tc_set(w)),w),c_minus(u,v,tc_set(w))),
inference(rew,[status(thm),theory(equality)],[397,1157]),
[iquote('0:Rew:397.0,1157.0')] ).
cnf(1160,plain,
equal(c_minus(u,c_inter(v,u,w),tc_set(w)),c_minus(u,v,tc_set(w))),
inference(rew,[status(thm),theory(equality)],[5,1129,391]),
[iquote('0:Rew:5.0,1129.0,391.0,1129.0')] ).
cnf(1161,plain,
equal(c_minus(c_minus(u,v,tc_set(w)),x,tc_set(w)),c_minus(u,c_union(v,x,w),tc_set(w))),
inference(rew,[status(thm),theory(equality)],[391,1122,12]),
[iquote('0:Rew:391.0,1122.0,12.0,1122.0')] ).
cnf(1322,plain,
equal(c_minus(u,c_union(v,c_union(w,u,x),x),tc_set(x)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[12,1154]),
[iquote('0:SpR:12.0,1154.0')] ).
cnf(1422,plain,
equal(c_minus(u,c_union(v,c_union(u,w,x),x),tc_set(x)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[983,1322]),
[iquote('0:SpR:983.0,1322.0')] ).
cnf(1543,plain,
equal(c_inter(u,c_inter(u,v,w),w),c_inter(u,v,w)),
inference(spr,[status(thm),theory(equality)],[5,1158]),
[iquote('0:SpR:5.0,1158.0')] ).
cnf(1578,plain,
equal(c_minus(c_uminus(u,tc_set(v)),c_uminus(c_inter(w,u,v),tc_set(v)),tc_set(v)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[400,1154]),
[iquote('0:SpR:400.0,1154.0')] ).
cnf(1610,plain,
equal(c_inter(c_uminus(u,tc_set(v)),c_inter(w,u,v),v),c_emptyset),
inference(rew,[status(thm),theory(equality)],[5,1578]),
[iquote('0:Rew:5.0,1578.0')] ).
cnf(1850,plain,
equal(c_minus(c_inter(u,v,w),c_union(c_uminus(v,tc_set(w)),u,w),tc_set(w)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[122,1154]),
[iquote('0:SpR:122.0,1154.0')] ).
cnf(1861,plain,
equal(c_union(c_uminus(v_t,tc_set(t_a)),c_emptyset,t_a),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a)),
inference(spr,[status(thm),theory(equality)],[25,122]),
[iquote('0:SpR:25.0,122.0')] ).
cnf(1862,plain,
equal(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a)),
inference(spr,[status(thm),theory(equality)],[27,122]),
[iquote('0:SpR:27.0,122.0')] ).
cnf(1883,plain,
equal(c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[13,1861,983]),
[iquote('0:Rew:13.0,1861.0,983.0,1861.0,983.0,1861.0')] ).
cnf(1887,plain,
equal(c_inter(c_inter(u,v,w),c_minus(v,u,tc_set(w)),w),c_emptyset),
inference(rew,[status(thm),theory(equality)],[397,1850]),
[iquote('0:Rew:397.0,1850.0')] ).
cnf(1888,plain,
equal(c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),c_uminus(v_u,tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[12,1862,983,13]),
[iquote('0:Rew:12.0,1862.0,983.0,1862.0,13.0,1862.0,983.0,1862.0')] ).
cnf(2339,plain,
equal(c_inter(c_inter(u,v,w),c_minus(c_inter(u,v,w),u,tc_set(w)),w),c_emptyset),
inference(spr,[status(thm),theory(equality)],[1543,1887]),
[iquote('0:SpR:1543.0,1887.0')] ).
cnf(2347,plain,
equal(c_minus(c_inter(u,v,w),u,tc_set(w)),c_emptyset),
inference(rew,[status(thm),theory(equality)],[1158,2339]),
[iquote('0:Rew:1158.0,2339.0')] ).
cnf(2364,plain,
equal(c_union(u,c_inter(u,v,w),w),c_union(u,c_emptyset,w)),
inference(spr,[status(thm),theory(equality)],[2347,9]),
[iquote('0:SpR:2347.0,9.0')] ).
cnf(2391,plain,
equal(c_union(u,c_inter(u,v,w),w),u),
inference(rew,[status(thm),theory(equality)],[14,2364]),
[iquote('0:Rew:14.0,2364.0')] ).
cnf(2569,plain,
equal(c_union(u,c_minus(u,v,tc_set(w)),w),u),
inference(spr,[status(thm),theory(equality)],[76,2391]),
[iquote('0:SpR:76.0,2391.0')] ).
cnf(2625,plain,
equal(c_minus(u,c_minus(c_uminus(u,tc_set(v)),w,tc_set(v)),tc_set(v)),c_uminus(c_uminus(u,tc_set(v)),tc_set(v))),
inference(spr,[status(thm),theory(equality)],[2569,391]),
[iquote('0:SpR:2569.0,391.0')] ).
cnf(2676,plain,
equal(c_minus(u,c_minus(c_uminus(u,tc_set(v)),w,tc_set(v)),tc_set(v)),u),
inference(rew,[status(thm),theory(equality)],[18,2625]),
[iquote('0:Rew:18.0,2625.0')] ).
cnf(2677,plain,
equal(c_minus(u,c_uminus(c_union(u,v,w),tc_set(w)),tc_set(w)),u),
inference(rew,[status(thm),theory(equality)],[1121,2676]),
[iquote('0:Rew:1121.0,2676.0')] ).
cnf(2678,plain,
equal(c_inter(u,c_union(u,v,w),w),u),
inference(rew,[status(thm),theory(equality)],[5,2677]),
[iquote('0:Rew:5.0,2677.0')] ).
cnf(2728,plain,
equal(c_minus(u,c_union(v,c_uminus(w,tc_set(x)),x),tc_set(x)),c_inter(u,c_minus(w,v,tc_set(x)),x)),
inference(spr,[status(thm),theory(equality)],[983,397]),
[iquote('0:SpR:983.0,397.0')] ).
cnf(2771,plain,
equal(c_inter(c_uminus(c_union(u,v,w),tc_set(w)),u,w),c_emptyset),
inference(spr,[status(thm),theory(equality)],[2678,1610]),
[iquote('0:SpR:2678.0,1610.0')] ).
cnf(2794,plain,
equal(c_inter(v_a,c_uminus(v_t,tc_set(t_a)),t_a),v_a),
inference(spr,[status(thm),theory(equality)],[1883,2678]),
[iquote('0:SpR:1883.0,2678.0')] ).
cnf(2795,plain,
equal(c_inter(u,c_union(v,u,w),w),u),
inference(spr,[status(thm),theory(equality)],[983,2678]),
[iquote('0:SpR:983.0,2678.0')] ).
cnf(2809,plain,
equal(c_minus(v_a,v_t,tc_set(t_a)),v_a),
inference(rew,[status(thm),theory(equality)],[76,2794]),
[iquote('0:Rew:76.0,2794.0')] ).
cnf(2855,plain,
equal(c_inter(c_uminus(c_union(u,v,w),tc_set(w)),v,w),c_emptyset),
inference(spr,[status(thm),theory(equality)],[2795,1610]),
[iquote('0:SpR:2795.0,1610.0')] ).
cnf(3686,plain,
equal(c_inter(c_minus(u,v,tc_set(w)),v,w),c_emptyset),
inference(spr,[status(thm),theory(equality)],[391,2855]),
[iquote('0:SpR:391.0,2855.0')] ).
cnf(3694,plain,
( ~ equal(c_emptyset,c_emptyset)
| ~ c_in(c_minus(u,v,tc_set(w)),x,tc_set(w))
| ~ c_in(v,c_Mutil_Otiling(x,w),tc_set(w))
| c_in(c_union(u,v,w),c_Mutil_Otiling(x,w),tc_set(w)) ),
inference(rew,[status(thm),theory(equality)],[3686,789]),
[iquote('0:Rew:3686.0,789.0')] ).
cnf(3707,plain,
( ~ c_in(c_minus(u,v,tc_set(w)),x,tc_set(w))
| ~ c_in(v,c_Mutil_Otiling(x,w),tc_set(w))
| c_in(c_union(u,v,w),c_Mutil_Otiling(x,w),tc_set(w)) ),
inference(obv,[status(thm),theory(equality)],[3694]),
[iquote('0:Obv:3694.0')] ).
cnf(5733,plain,
( ~ c_in(c_minus(v_a,c_union(v_t,v_u,t_a),tc_set(t_a)),v_A,tc_set(t_a))
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[3707,30]),
[iquote('0:Res:3707.2,30.0')] ).
cnf(7684,plain,
equal(c_inter(c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),v_a,t_a),c_emptyset),
inference(spr,[status(thm),theory(equality)],[1888,2771]),
[iquote('0:SpR:1888.0,2771.0')] ).
cnf(7714,plain,
equal(c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[1888,1422]),
[iquote('0:SpR:1888.0,1422.0')] ).
cnf(7736,plain,
equal(c_inter(v_t,v_u,t_a),c_emptyset),
inference(rew,[status(thm),theory(equality)],[5,7714]),
[iquote('0:Rew:5.0,7714.0')] ).
cnf(7737,plain,
( ~ equal(c_emptyset,c_emptyset)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rew,[status(thm),theory(equality)],[7736,31]),
[iquote('0:Rew:7736.0,31.0')] ).
cnf(7741,plain,
equal(c_inter(v_u,v_a,t_a),c_emptyset),
inference(rew,[status(thm),theory(equality)],[18,7684]),
[iquote('0:Rew:18.0,7684.0')] ).
cnf(7745,plain,
c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[7737]),
[iquote('0:Obv:7737.0')] ).
cnf(7747,plain,
~ c_in(c_minus(v_a,c_union(v_t,v_u,t_a),tc_set(t_a)),v_A,tc_set(t_a)),
inference(mrr,[status(thm)],[5733,7745]),
[iquote('0:MRR:5733.1,7745.0')] ).
cnf(7917,plain,
equal(c_union(c_uminus(v_a,tc_set(t_a)),c_emptyset,t_a),c_union(c_uminus(v_a,tc_set(t_a)),v_u,t_a)),
inference(spr,[status(thm),theory(equality)],[7741,122]),
[iquote('0:SpR:7741.0,122.0')] ).
cnf(7973,plain,
equal(c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a),c_uminus(v_a,tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[13,7917,983]),
[iquote('0:Rew:13.0,7917.0,983.0,7917.0,983.0,7917.0')] ).
cnf(9071,plain,
equal(c_minus(v_u,c_union(u,c_uminus(v_a,tc_set(t_a)),t_a),tc_set(t_a)),c_emptyset),
inference(spr,[status(thm),theory(equality)],[7973,1422]),
[iquote('0:SpR:7973.0,1422.0')] ).
cnf(9088,plain,
equal(c_inter(v_u,c_minus(v_a,u,tc_set(t_a)),t_a),c_emptyset),
inference(rew,[status(thm),theory(equality)],[2728,9071]),
[iquote('0:Rew:2728.0,9071.0')] ).
cnf(9111,plain,
equal(c_minus(c_minus(v_a,u,tc_set(t_a)),c_emptyset,tc_set(t_a)),c_minus(c_minus(v_a,u,tc_set(t_a)),v_u,tc_set(t_a))),
inference(spr,[status(thm),theory(equality)],[9088,1160]),
[iquote('0:SpR:9088.0,1160.0')] ).
cnf(9170,plain,
equal(c_minus(c_minus(v_a,u,tc_set(t_a)),v_u,tc_set(t_a)),c_minus(v_a,u,tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[99,9111]),
[iquote('0:Rew:99.0,9111.0')] ).
cnf(9171,plain,
equal(c_minus(v_a,c_union(u,v_u,t_a),tc_set(t_a)),c_minus(v_a,u,tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[1161,9170]),
[iquote('0:Rew:1161.0,9170.0')] ).
cnf(9172,plain,
~ c_in(c_minus(v_a,v_t,tc_set(t_a)),v_A,tc_set(t_a)),
inference(rew,[status(thm),theory(equality)],[9171,7747]),
[iquote('0:Rew:9171.0,7747.0')] ).
cnf(9173,plain,
~ c_in(v_a,v_A,tc_set(t_a)),
inference(rew,[status(thm),theory(equality)],[2809,9172]),
[iquote('0:Rew:2809.0,9172.0')] ).
cnf(9174,plain,
$false,
inference(mrr,[status(thm)],[9173,24]),
[iquote('0:MRR:9173.0,24.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ064-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat May 28 22:41:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.09/1.33
% 1.09/1.33 SPASS V 3.9
% 1.09/1.33 SPASS beiseite: Proof found.
% 1.09/1.33 % SZS status Theorem
% 1.09/1.33 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.09/1.33 SPASS derived 7033 clauses, backtracked 0 clauses, performed 0 splits and kept 1079 clauses.
% 1.09/1.33 SPASS allocated 69639 KBytes.
% 1.09/1.33 SPASS spent 0:00:00.98 on the problem.
% 1.09/1.33 0:00:00.03 for the input.
% 1.09/1.33 0:00:00.00 for the FLOTTER CNF translation.
% 1.09/1.33 0:00:00.06 for inferences.
% 1.09/1.33 0:00:00.00 for the backtracking.
% 1.09/1.33 0:00:00.85 for the reduction.
% 1.09/1.33
% 1.09/1.33
% 1.09/1.33 Here is a proof with depth 16, length 106 :
% 1.09/1.33 % SZS output start Refutation
% See solution above
% 1.17/1.35 Formulae used in the proof : cls_Mutil_Otiling_OUn_0 cls_Set_OCompl__Diff__eq_0 cls_Set_OCompl__UNIV__eq_0 cls_Set_ODiff__Compl_0 cls_Set_OInt__UNIV__left_0 cls_Set_OUn__Diff__cancel2_0 cls_Set_OUn__Diff__cancel_0 cls_Set_OUn__UNIV__left_0 cls_Set_OUn__absorb_0 cls_Set_OUn__assoc_0 cls_Set_OUn__empty__left_0 cls_Set_OUn__empty__right_0 cls_Set_OUn__subset__iff_0 cls_Set_OUn__subset__iff_1 cls_Set_Odouble__complement_0 cls_Set_Osubset__antisym_0 cls_Set_Osubset__refl_0 cls_conjecture_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6
% 1.17/1.35
%------------------------------------------------------------------------------