TSTP Solution File: SET928+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:29:53 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 12 unt; 5 nHn; 25 RR)
% Number of literals : 41 ( 0 equ; 19 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET928+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ disjoint(u,v)
| equal(set_difference(u,v),u) ),
file('SET928+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(set_difference(u,v),u)
| disjoint(u,v) ),
file('SET928+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| ~ disjoint(unordered_pair(u,w),v) ),
file('SET928+1.p',unknown),
[] ).
cnf(9,axiom,
( in(u,v)
| in(w,v)
| disjoint(unordered_pair(w,u),v) ),
file('SET928+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(skc5,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6)) ),
file('SET928+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(skc6,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6)) ),
file('SET928+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6))
| in(skc6,skc7)
| in(skc5,skc7) ),
file('SET928+1.p',unknown),
[] ).
cnf(13,plain,
equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6)),
inference(spt,[spt(split,[position(s1)])],[11]),
[iquote('1:Spt:11.1')] ).
cnf(14,plain,
( ~ equal(unordered_pair(skc5,skc6),unordered_pair(skc5,skc6))
| in(skc6,skc7)
| in(skc5,skc7) ),
inference(rew,[status(thm),theory(equality)],[13,12]),
[iquote('1:Rew:13.0,12.0')] ).
cnf(15,plain,
( in(skc6,skc7)
| in(skc5,skc7) ),
inference(obv,[status(thm),theory(equality)],[14]),
[iquote('1:Obv:14.0')] ).
cnf(24,plain,
( ~ equal(unordered_pair(skc5,skc6),unordered_pair(skc5,skc6))
| disjoint(unordered_pair(skc5,skc6),skc7) ),
inference(spl,[status(thm),theory(equality)],[13,7]),
[iquote('1:SpL:13.0,7.0')] ).
cnf(26,plain,
disjoint(unordered_pair(skc5,skc6),skc7),
inference(obv,[status(thm),theory(equality)],[24]),
[iquote('1:Obv:24.0')] ).
cnf(27,plain,
( ~ in(u,v)
| ~ disjoint(unordered_pair(w,u),v) ),
inference(spl,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpL:3.0,8.1')] ).
cnf(30,plain,
~ in(skc5,skc7),
inference(res,[status(thm),theory(equality)],[26,8]),
[iquote('1:Res:26.0,8.1')] ).
cnf(31,plain,
in(skc6,skc7),
inference(mrr,[status(thm)],[15,30]),
[iquote('1:MRR:15.1,30.0')] ).
cnf(42,plain,
~ in(skc6,skc7),
inference(res,[status(thm),theory(equality)],[26,27]),
[iquote('1:Res:26.0,27.1')] ).
cnf(43,plain,
$false,
inference(mrr,[status(thm)],[42,31]),
[iquote('1:MRR:42.0,31.0')] ).
cnf(44,plain,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6)),
inference(spt,[spt(split,[position(sa)])],[43,13]),
[iquote('1:Spt:43.0,11.1,13.0')] ).
cnf(45,plain,
~ in(skc6,skc7),
inference(spt,[spt(split,[position(s2)])],[11]),
[iquote('1:Spt:43.0,11.0')] ).
cnf(46,plain,
~ in(skc5,skc7),
inference(mrr,[status(thm)],[10,44]),
[iquote('1:MRR:10.1,44.0')] ).
cnf(47,plain,
( ~ disjoint(unordered_pair(skc5,skc6),skc7)
| ~ equal(unordered_pair(skc5,skc6),unordered_pair(skc5,skc6)) ),
inference(spl,[status(thm),theory(equality)],[6,44]),
[iquote('1:SpL:6.1,44.0')] ).
cnf(48,plain,
~ disjoint(unordered_pair(skc5,skc6),skc7),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('1:Obv:47.1')] ).
cnf(49,plain,
( in(skc6,skc7)
| in(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[9,48]),
[iquote('1:Res:9.2,48.0')] ).
cnf(50,plain,
$false,
inference(mrr,[status(thm)],[49,45,46]),
[iquote('1:MRR:49.0,49.1,45.0,46.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 19:01:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 30 clauses, backtracked 4 clauses, performed 1 splits and kept 28 clauses.
% 0.19/0.44 SPASS allocated 85086 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 3, length 25 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : commutativity_k2_tarski t83_xboole_1 t55_zfmisc_1 t57_zfmisc_1 t72_zfmisc_1
% 0.19/0.44
%------------------------------------------------------------------------------