%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET976+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:30:10 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 12 unt; 2 nHn; 25 RR)
% Number of literals : 42 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( in(skc6,skc8)
| in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))) ),
file('SET976+1.p',unknown),
[] ).
cnf(8,axiom,
( equal(skc9,skc7)
| in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))) ),
file('SET976+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(u,w) ),
file('SET976+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SET976+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET976+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SET976+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(u,v)
| ~ in(w,x)
| in(ordered_pair(u,w),cartesian_product2(v,x)) ),
file('SET976+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9)))
| ~ in(skc6,skc8)
| ~ equal(skc9,skc7) ),
file('SET976+1.p',unknown),
[] ).
cnf(18,plain,
in(skc6,skc8),
inference(mrr,[status(thm)],[7,9]),
[iquote('0:MRR:7.1,9.0')] ).
cnf(19,plain,
( ~ equal(skc9,skc7)
| ~ in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))) ),
inference(mrr,[status(thm)],[16,18]),
[iquote('0:MRR:16.1,18.0')] ).
cnf(24,plain,
( ~ in(u,v)
| in(ordered_pair(skc6,u),cartesian_product2(skc8,v)) ),
inference(res,[status(thm),theory(equality)],[18,15]),
[iquote('0:Res:18.0,15.1')] ).
cnf(34,plain,
equal(skc9,skc7),
inference(spt,[spt(split,[position(s1)])],[8]),
[iquote('1:Spt:8.0')] ).
cnf(35,plain,
( ~ equal(skc7,skc7)
| ~ in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))) ),
inference(rew,[status(thm),theory(equality)],[34,19]),
[iquote('1:Rew:34.0,19.0')] ).
cnf(36,plain,
~ in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))),
inference(obv,[status(thm),theory(equality)],[35]),
[iquote('1:Obv:35.0')] ).
cnf(37,plain,
~ in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc7))),
inference(rew,[status(thm),theory(equality)],[34,36]),
[iquote('1:Rew:34.0,36.0')] ).
cnf(50,plain,
~ in(skc7,singleton(skc7)),
inference(res,[status(thm),theory(equality)],[24,37]),
[iquote('1:Res:24.1,37.0')] ).
cnf(56,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.1')] ).
cnf(58,plain,
~ equal(skc7,skc7),
inference(res,[status(thm),theory(equality)],[56,50]),
[iquote('1:Res:56.1,50.0')] ).
cnf(60,plain,
$false,
inference(obv,[status(thm),theory(equality)],[58]),
[iquote('1:Obv:58.0')] ).
cnf(61,plain,
~ equal(skc9,skc7),
inference(spt,[spt(split,[position(sa)])],[60,34]),
[iquote('1:Spt:60.0,8.0,34.0')] ).
cnf(62,plain,
in(ordered_pair(skc6,skc7),cartesian_product2(skc8,singleton(skc9))),
inference(spt,[spt(split,[position(s2)])],[8]),
[iquote('1:Spt:60.0,8.1')] ).
cnf(65,plain,
in(skc7,singleton(skc9)),
inference(res,[status(thm),theory(equality)],[62,10]),
[iquote('1:Res:62.0,10.0')] ).
cnf(67,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(69,plain,
equal(skc9,skc7),
inference(res,[status(thm),theory(equality)],[65,67]),
[iquote('1:Res:65.0,67.0')] ).
cnf(70,plain,
$false,
inference(mrr,[status(thm)],[69,61]),
[iquote('1:MRR:69.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET976+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jul 11 09:46:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 42 clauses, backtracked 3 clauses, performed 1 splits and kept 41 clauses.
% 0.19/0.43 SPASS allocated 85170 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 3, length 25 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : t129_zfmisc_1 l55_zfmisc_1 d1_tarski antisymmetry_r2_hidden
% 0.19/0.43
%------------------------------------------------------------------------------