TSTP Solution File: SET601+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET601+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:27:19 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 27 RR)
% Number of literals : 27 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(intersection(u,u),u),
file('SET601+3.p',unknown),
[] ).
cnf(3,axiom,
equal(union(u,intersection(u,v)),u),
file('SET601+3.p',unknown),
[] ).
cnf(6,axiom,
equal(union(u,v),union(v,u)),
file('SET601+3.p',unknown),
[] ).
cnf(7,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET601+3.p',unknown),
[] ).
cnf(14,axiom,
equal(union(union(u,v),w),union(u,union(v,w))),
file('SET601+3.p',unknown),
[] ).
cnf(15,axiom,
equal(intersection(intersection(u,v),w),intersection(u,intersection(v,w))),
file('SET601+3.p',unknown),
[] ).
cnf(21,axiom,
equal(union(u,intersection(v,w)),intersection(union(u,v),union(u,w))),
file('SET601+3.p',unknown),
[] ).
cnf(25,axiom,
~ equal(union(union(intersection(skc5,skc4),intersection(skc4,skc3)),intersection(skc3,skc5)),intersection(intersection(union(skc5,skc4),union(skc4,skc3)),union(skc3,skc5))),
file('SET601+3.p',unknown),
[] ).
cnf(26,plain,
equal(intersection(union(u,u),union(u,v)),u),
inference(rew,[status(thm),theory(equality)],[21,3]),
[iquote('0:Rew:21.0,3.0')] ).
cnf(27,plain,
~ equal(intersection(union(skc3,union(skc3,skc4)),intersection(union(skc3,skc4),intersection(union(skc3,union(skc3,skc5)),intersection(union(skc5,union(skc3,skc4)),intersection(union(skc4,skc5),union(skc5,union(skc3,skc5))))))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[15,25,21,6,7,26]),
[iquote('0:Rew:15.0,25.0,15.0,25.0,21.0,25.0,21.0,25.0,6.0,25.0,6.0,25.0,21.0,25.0,21.0,25.0,6.0,25.0,21.0,25.0,7.0,25.0,15.0,25.0,21.0,25.0,6.0,25.0,26.0,25.0,21.0,25.0,6.0,25.0,21.0,25.0,7.0,25.0,7.0,25.0,7.0,25.0,15.0,25.0,7.0,25.0,6.0,25.0,6.0,25.0')] ).
cnf(45,plain,
equal(union(u,u),u),
inference(spr,[status(thm),theory(equality)],[26,2]),
[iquote('0:SpR:26.0,2.0')] ).
cnf(49,plain,
equal(intersection(union(u,u),union(v,u)),u),
inference(spr,[status(thm),theory(equality)],[6,26]),
[iquote('0:SpR:6.0,26.0')] ).
cnf(58,plain,
equal(intersection(u,union(v,u)),u),
inference(rew,[status(thm),theory(equality)],[45,49]),
[iquote('0:Rew:45.0,49.0')] ).
cnf(105,plain,
equal(intersection(u,intersection(u,v)),intersection(u,v)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
cnf(106,plain,
equal(intersection(intersection(u,v),w),intersection(v,intersection(u,w))),
inference(spr,[status(thm),theory(equality)],[7,15]),
[iquote('0:SpR:7.0,15.0')] ).
cnf(109,plain,
equal(intersection(u,intersection(union(v,u),w)),intersection(u,w)),
inference(spr,[status(thm),theory(equality)],[58,15]),
[iquote('0:SpR:58.0,15.0')] ).
cnf(112,plain,
equal(intersection(u,intersection(v,w)),intersection(v,intersection(u,w))),
inference(rew,[status(thm),theory(equality)],[15,106]),
[iquote('0:Rew:15.0,106.0')] ).
cnf(113,plain,
~ equal(intersection(union(skc3,skc4),intersection(union(skc3,union(skc3,skc4)),intersection(union(skc3,union(skc3,skc5)),intersection(union(skc5,union(skc3,skc4)),intersection(union(skc4,skc5),union(skc5,union(skc3,skc5))))))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[112,27]),
[iquote('0:Rew:112.0,27.0')] ).
cnf(118,plain,
~ equal(intersection(union(skc3,skc4),intersection(union(skc3,union(skc3,skc5)),intersection(union(skc4,skc5),intersection(union(skc5,union(skc3,skc4)),union(skc5,union(skc3,skc5)))))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[109,113,112]),
[iquote('0:Rew:109.0,113.0,112.0,113.0')] ).
cnf(156,plain,
equal(union(u,union(v,w)),union(v,union(w,u))),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.0,6.0')] ).
cnf(165,plain,
equal(union(union(u,v),w),union(v,union(u,w))),
inference(spr,[status(thm),theory(equality)],[6,14]),
[iquote('0:SpR:6.0,14.0')] ).
cnf(167,plain,
equal(union(u,union(u,v)),union(u,v)),
inference(spr,[status(thm),theory(equality)],[45,14]),
[iquote('0:SpR:45.0,14.0')] ).
cnf(168,plain,
~ equal(intersection(union(skc3,skc4),intersection(union(skc3,skc5),intersection(union(skc4,skc5),intersection(union(skc5,union(skc3,skc4)),union(skc5,union(skc3,skc5)))))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[167,118]),
[iquote('0:Rew:167.0,118.0')] ).
cnf(170,plain,
equal(union(u,union(v,w)),union(v,union(u,w))),
inference(rew,[status(thm),theory(equality)],[14,165]),
[iquote('0:Rew:14.0,165.0')] ).
cnf(173,plain,
~ equal(intersection(union(skc3,skc4),intersection(union(skc3,skc5),intersection(union(skc4,skc5),union(skc3,union(skc5,skc5))))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[109,168,170,156]),
[iquote('0:Rew:109.0,168.0,170.0,168.0,156.0,168.0,170.0,168.0,170.0,168.0')] ).
cnf(174,plain,
~ equal(intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5))),intersection(union(skc3,skc4),intersection(union(skc3,skc5),union(skc4,skc5)))),
inference(rew,[status(thm),theory(equality)],[105,173,7,45]),
[iquote('0:Rew:105.0,173.0,7.0,173.0,45.0,173.0')] ).
cnf(175,plain,
$false,
inference(obv,[status(thm),theory(equality)],[174]),
[iquote('0:Obv:174.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET601+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 : Sun Jul 10 22:23:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 58 clauses.
% 0.18/0.46 SPASS allocated 85375 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.46 0:00:00.03 for the input.
% 0.18/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.00 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.02 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 2, length 27 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : idempotency_of_intersection union_intersection commutativity_of_union commutativity_of_intersection associativity_of_union associativity_of_intersection union_distributes_over_intersection prove_th72
% 0.18/0.46
%------------------------------------------------------------------------------