TSTP Solution File: SET906+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET906+1 : 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 : Tue Jul 19 05:29:42 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 26 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ in(skc5,skc6),
file('SET906+1.p',unknown),
[] ).
cnf(6,axiom,
subset(set_union2(unordered_pair(skc5,skc7),skc6),skc6),
file('SET906+1.p',unknown),
[] ).
cnf(7,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET906+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET906+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SET906+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET906+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SET906+1.p',unknown),
[] ).
cnf(27,plain,
subset(set_union2(skc6,unordered_pair(skc5,skc7)),skc6),
inference(rew,[status(thm),theory(equality)],[8,6]),
[iquote('0:Rew:8.0,6.0')] ).
cnf(35,plain,
( ~ in(u,set_union2(skc6,unordered_pair(skc5,skc7)))
| in(u,skc6) ),
inference(res,[status(thm),theory(equality)],[27,14]),
[iquote('0:Res:27.0,14.0')] ).
cnf(38,plain,
~ in(skc5,set_union2(skc6,unordered_pair(skc5,skc7))),
inference(res,[status(thm),theory(equality)],[35,4]),
[iquote('0:Res:35.1,4.0')] ).
cnf(80,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[16]),
[iquote('0:EqR:16.1')] ).
cnf(83,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[7,80]),
[iquote('0:SpR:7.0,80.1')] ).
cnf(121,plain,
( ~ in(u,v)
| in(u,set_union2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[18]),
[iquote('0:EqR:18.1')] ).
cnf(132,plain,
~ in(skc5,unordered_pair(skc5,skc7)),
inference(res,[status(thm),theory(equality)],[121,38]),
[iquote('0:Res:121.1,38.0')] ).
cnf(141,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[83,132]),
[iquote('0:Res:83.1,132.0')] ).
cnf(142,plain,
$false,
inference(obv,[status(thm),theory(equality)],[141]),
[iquote('0:Obv:141.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 22:46:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 111 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.19/0.45 SPASS allocated 85464 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.01 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 4, length 16 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : t47_zfmisc_1 commutativity_k2_tarski commutativity_k2_xboole_0 d3_tarski d2_tarski idempotence_k2_xboole_0 d2_xboole_0
% 0.19/0.45
%------------------------------------------------------------------------------