%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET872+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 05:29:29 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 6 unt; 3 nHn; 15 RR)
% Number of literals : 27 ( 0 equ; 13 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; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ subset(singleton(skc5),unordered_pair(skc5,skc4)),
file('SET872+1.p',unknown),
[] ).
cnf(5,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET872+1.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| in(skf5(v,u),u) ),
file('SET872+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(skf5(u,v),u)
| subset(w,u) ),
file('SET872+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET872+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET872+1.p',unknown),
[] ).
cnf(20,plain,
~ subset(singleton(skc5),unordered_pair(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(37,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[10]),
[iquote('0:EqR:10.1')] ).
cnf(39,plain,
( subset(singleton(u),v)
| equal(skf5(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[7,37]),
[iquote('0:Res:7.1,37.0')] ).
cnf(43,plain,
( ~ in(u,v)
| subset(singleton(u),v)
| subset(w,v) ),
inference(spl,[status(thm),theory(equality)],[39,8]),
[iquote('0:SpL:39.1,8.0')] ).
cnf(44,plain,
( ~ in(u,v)
| subset(singleton(u),v) ),
inference(con,[status(thm)],[43]),
[iquote('0:Con:43.2')] ).
cnf(47,plain,
~ in(skc5,unordered_pair(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[44,20]),
[iquote('0:Res:44.1,20.0')] ).
cnf(48,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.1')] ).
cnf(74,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[48,47]),
[iquote('0:Res:48.1,47.0')] ).
cnf(75,plain,
$false,
inference(obv,[status(thm),theory(equality)],[74]),
[iquote('0:Obv:74.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 14:04:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.20/0.45 SPASS allocated 85432 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 5, length 15 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : t12_zfmisc_1 commutativity_k2_tarski d3_tarski d1_tarski d2_tarski
% 0.20/0.45
%------------------------------------------------------------------------------