%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:27:32 EDT 2022
% Result : Theorem 0.56s 0.75s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(union(u,intersection(u,v)),u),
file('SET619+3.p',unknown),
[] ).
cnf(5,axiom,
equal(union(u,v),union(v,u)),
file('SET619+3.p',unknown),
[] ).
cnf(6,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET619+3.p',unknown),
[] ).
cnf(7,axiom,
equal(symmetric_difference(u,v),symmetric_difference(v,u)),
file('SET619+3.p',unknown),
[] ).
cnf(9,axiom,
equal(union(intersection(u,v),difference(u,v)),u),
file('SET619+3.p',unknown),
[] ).
cnf(15,axiom,
equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
file('SET619+3.p',unknown),
[] ).
cnf(16,axiom,
equal(union(union(u,v),w),union(u,union(v,w))),
file('SET619+3.p',unknown),
[] ).
cnf(21,axiom,
~ equal(union(symmetric_difference(skc3,skc2),intersection(skc3,skc2)),union(skc3,skc2)),
file('SET619+3.p',unknown),
[] ).
cnf(26,plain,
equal(union(difference(u,v),intersection(u,v)),u),
inference(rew,[status(thm),theory(equality)],[5,9]),
[iquote('0:Rew:5.0,9.0')] ).
cnf(27,plain,
~ equal(union(symmetric_difference(skc2,skc3),intersection(skc2,skc3)),union(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[7,21,6,5]),
[iquote('0:Rew:7.0,21.0,6.0,21.0,5.0,21.0')] ).
cnf(54,plain,
equal(union(difference(u,v),intersection(v,u)),u),
inference(spr,[status(thm),theory(equality)],[6,26]),
[iquote('0:SpR:6.0,26.0')] ).
cnf(100,plain,
equal(union(u,union(intersection(u,v),w)),union(u,w)),
inference(spr,[status(thm),theory(equality)],[2,16]),
[iquote('0:SpR:2.0,16.0')] ).
cnf(106,plain,
equal(union(difference(u,v),union(difference(v,u),w)),union(symmetric_difference(u,v),w)),
inference(spr,[status(thm),theory(equality)],[15,16]),
[iquote('0:SpR:15.0,16.0')] ).
cnf(209,plain,
equal(union(u,union(v,intersection(u,w))),union(u,v)),
inference(spr,[status(thm),theory(equality)],[5,100]),
[iquote('0:SpR:5.0,100.0')] ).
cnf(715,plain,
equal(union(u,difference(v,u)),union(u,v)),
inference(spr,[status(thm),theory(equality)],[54,209]),
[iquote('0:SpR:54.0,209.0')] ).
cnf(2454,plain,
equal(union(symmetric_difference(u,v),intersection(u,v)),union(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[54,106]),
[iquote('0:SpR:54.0,106.0')] ).
cnf(2465,plain,
equal(union(symmetric_difference(u,v),intersection(u,v)),union(v,u)),
inference(rew,[status(thm),theory(equality)],[715,2454,5]),
[iquote('0:Rew:715.0,2454.0,5.0,2454.0')] ).
cnf(2466,plain,
~ equal(union(skc3,skc2),union(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[2465,27]),
[iquote('0:Rew:2465.0,27.0')] ).
cnf(2468,plain,
~ equal(union(skc2,skc3),union(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[5,2466]),
[iquote('0:Rew:5.0,2466.0')] ).
cnf(2469,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2468]),
[iquote('0:Obv:2468.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 21:02:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.75
% 0.56/0.75 SPASS V 3.9
% 0.56/0.75 SPASS beiseite: Proof found.
% 0.56/0.75 % SZS status Theorem
% 0.56/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.75 SPASS derived 1969 clauses, backtracked 0 clauses, performed 0 splits and kept 736 clauses.
% 0.56/0.75 SPASS allocated 87180 KBytes.
% 0.56/0.75 SPASS spent 0:00:00.40 on the problem.
% 0.56/0.75 0:00:00.03 for the input.
% 0.56/0.75 0:00:00.03 for the FLOTTER CNF translation.
% 0.56/0.75 0:00:00.02 for inferences.
% 0.56/0.75 0:00:00.00 for the backtracking.
% 0.56/0.75 0:00:00.29 for the reduction.
% 0.56/0.75
% 0.56/0.75
% 0.56/0.75 Here is a proof with depth 3, length 20 :
% 0.56/0.75 % SZS output start Refutation
% See solution above
% 0.56/0.75 Formulae used in the proof : union_intersection commutativity_of_union commutativity_of_intersection commutativity_of_symmetric_difference union_intersection_difference symmetric_difference_defn associativity_of_union prove_th95
% 0.56/0.75
%------------------------------------------------------------------------------