%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET885+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 05:29:34 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 5 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 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,
~ equal(skc6,skc5),
file('SET885+1.p',unknown),
[] ).
cnf(5,axiom,
subset(unordered_pair(skc5,skc7),singleton(skc6)),
file('SET885+1.p',unknown),
[] ).
cnf(6,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET885+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SET885+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET885+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET885+1.p',unknown),
[] ).
cnf(25,plain,
( ~ equal(u,singleton(skc6))
| ~ in(skc5,u) ),
inference(res,[status(thm),theory(equality)],[11,4]),
[iquote('0:Res:11.2,4.0')] ).
cnf(27,plain,
( ~ in(u,unordered_pair(skc5,skc7))
| in(u,singleton(skc6)) ),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(52,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[11]),
[iquote('0:EqR:11.1')] ).
cnf(62,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[14]),
[iquote('0:EqR:14.1')] ).
cnf(65,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[6,62]),
[iquote('0:SpR:6.0,62.1')] ).
cnf(69,plain,
( ~ equal(u,skc7)
| in(u,singleton(skc6)) ),
inference(res,[status(thm),theory(equality)],[62,27]),
[iquote('0:Res:62.1,27.0')] ).
cnf(78,plain,
( ~ equal(u,skc7)
| equal(u,skc6) ),
inference(res,[status(thm),theory(equality)],[69,52]),
[iquote('0:Res:69.1,52.0')] ).
cnf(84,plain,
equal(skc7,skc6),
inference(eqr,[status(thm),theory(equality)],[78]),
[iquote('0:EqR:78.0')] ).
cnf(86,plain,
( ~ in(u,unordered_pair(skc5,skc6))
| in(u,singleton(skc6)) ),
inference(rew,[status(thm),theory(equality)],[84,27]),
[iquote('0:Rew:84.0,27.0')] ).
cnf(115,plain,
( ~ equal(u,skc5)
| in(u,singleton(skc6)) ),
inference(res,[status(thm),theory(equality)],[65,86]),
[iquote('0:Res:65.1,86.0')] ).
cnf(120,plain,
( ~ equal(skc5,skc5)
| ~ equal(singleton(skc6),singleton(skc6)) ),
inference(res,[status(thm),theory(equality)],[115,25]),
[iquote('0:Res:115.1,25.1')] ).
cnf(123,plain,
$false,
inference(obv,[status(thm),theory(equality)],[120]),
[iquote('0:Obv:120.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET885+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 17:34:56 EDT 2022
% 0.12/0.33 % 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 98 clauses, backtracked 0 clauses, performed 0 splits and kept 77 clauses.
% 0.19/0.45 SPASS allocated 85503 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 18 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : t26_zfmisc_1 commutativity_k2_tarski d3_tarski d1_tarski d2_tarski
% 0.19/0.45
%------------------------------------------------------------------------------