TSTP Solution File: SET918+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:29:47 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 30 ( 0 equ; 14 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
in(skc5,skc6),
file('SET918+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(skc7,skc5),
file('SET918+1.p',unknown),
[] ).
cnf(6,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET918+1.p',unknown),
[] ).
cnf(7,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SET918+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_intersection2(unordered_pair(skc7,skc5),skc6),singleton(skc7)),
file('SET918+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET918+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(v,x))
| in(u,w) ),
file('SET918+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SET918+1.p',unknown),
[] ).
cnf(26,plain,
equal(set_intersection2(skc6,unordered_pair(skc5,skc7)),singleton(skc7)),
inference(rew,[status(thm),theory(equality)],[7,8,6]),
[iquote('0:Rew:7.0,8.0,6.0,8.0')] ).
cnf(51,plain,
( ~ in(u,skc6)
| ~ in(u,unordered_pair(skc5,skc7))
| in(u,singleton(skc7)) ),
inference(res,[status(thm),theory(equality)],[26,19]),
[iquote('0:Res:26.0,19.2')] ).
cnf(62,plain,
( ~ in(skc5,unordered_pair(skc5,skc7))
| in(skc5,singleton(skc7)) ),
inference(res,[status(thm),theory(equality)],[2,51]),
[iquote('0:Res:2.0,51.0')] ).
cnf(113,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[11]),
[iquote('0:EqR:11.1')] ).
cnf(135,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.1')] ).
cnf(154,plain,
( ~ equal(skc5,skc5)
| in(skc5,singleton(skc7)) ),
inference(res,[status(thm),theory(equality)],[135,62]),
[iquote('0:Res:135.1,62.0')] ).
cnf(155,plain,
in(skc5,singleton(skc7)),
inference(obv,[status(thm),theory(equality)],[154]),
[iquote('0:Obv:154.0')] ).
cnf(158,plain,
equal(skc7,skc5),
inference(res,[status(thm),theory(equality)],[155,113]),
[iquote('0:Res:155.0,113.0')] ).
cnf(160,plain,
$false,
inference(mrr,[status(thm)],[158,4]),
[iquote('0:MRR:158.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 23:01:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.21/0.47 SPASS allocated 85367 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.03 for the input.
% 0.21/0.47 0:00:00.05 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.00 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 4, length 17 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : t59_zfmisc_1 commutativity_k2_tarski commutativity_k3_xboole_0 d1_tarski idempotence_k3_xboole_0 d2_tarski d3_xboole_0
% 0.21/0.48
%------------------------------------------------------------------------------