TSTP Solution File: SET980+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:30:12 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of clauses : 42 ( 16 unt; 7 nHn; 42 RR)
% Number of literals : 80 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc7,empty_set),
file('SET980+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(skc6,empty_set),
file('SET980+1.p',unknown),
[] ).
cnf(7,axiom,
equal(cartesian_product2(skc8,skc9),cartesian_product2(skc7,skc6)),
file('SET980+1.p',unknown),
[] ).
cnf(9,axiom,
( equal(u,empty_set)
| in(skf2(u),u) ),
file('SET980+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(skc9,skc6)
| ~ equal(skc8,skc7) ),
file('SET980+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(u,w) ),
file('SET980+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SET980+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(skf3(u,v),u)
| ~ in(skf3(u,v),v) ),
file('SET980+1.p',unknown),
[] ).
cnf(20,axiom,
( equal(u,v)
| in(skf3(v,u),v)
| in(skf3(v,u),u) ),
file('SET980+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ in(u,v)
| ~ in(w,x)
| in(ordered_pair(u,w),cartesian_product2(v,x)) ),
file('SET980+1.p',unknown),
[] ).
cnf(24,plain,
in(skf2(skc6),skc6),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.1,5.0')] ).
cnf(29,plain,
in(skf2(skc7),skc7),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.1,4.0')] ).
cnf(103,plain,
( ~ in(ordered_pair(u,v),cartesian_product2(skc7,skc6))
| in(v,skc9) ),
inference(spl,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpL:7.0,17.0')] ).
cnf(121,plain,
( ~ in(ordered_pair(u,v),cartesian_product2(skc7,skc6))
| in(u,skc8) ),
inference(spl,[status(thm),theory(equality)],[7,16]),
[iquote('0:SpL:7.0,16.0')] ).
cnf(205,plain,
( ~ in(u,skc8)
| ~ in(v,skc9)
| in(ordered_pair(u,v),cartesian_product2(skc7,skc6)) ),
inference(spr,[status(thm),theory(equality)],[7,21]),
[iquote('0:SpR:7.0,21.2')] ).
cnf(214,plain,
( ~ in(u,skc7)
| ~ in(v,skc6)
| in(u,skc8) ),
inference(res,[status(thm),theory(equality)],[21,121]),
[iquote('0:Res:21.2,121.0')] ).
cnf(215,plain,
( ~ in(u,skc7)
| ~ in(v,skc6)
| in(v,skc9) ),
inference(res,[status(thm),theory(equality)],[21,103]),
[iquote('0:Res:21.2,103.0')] ).
cnf(216,plain,
( ~ in(u,skc6)
| in(skf2(skc7),skc8) ),
inference(res,[status(thm),theory(equality)],[29,214]),
[iquote('0:Res:29.0,214.0')] ).
cnf(220,plain,
( ~ in(u,skc6)
| equal(v,skc7)
| in(skf3(skc7,v),v)
| in(skf3(skc7,v),skc8) ),
inference(res,[status(thm),theory(equality)],[20,214]),
[iquote('0:Res:20.1,214.0')] ).
cnf(222,plain,
in(skf2(skc7),skc8),
inference(res,[status(thm),theory(equality)],[24,216]),
[iquote('0:Res:24.0,216.0')] ).
cnf(234,plain,
( ~ in(u,skc6)
| in(u,skc9) ),
inference(res,[status(thm),theory(equality)],[29,215]),
[iquote('0:Res:29.0,215.0')] ).
cnf(243,plain,
( ~ in(skf3(skc9,u),skc6)
| ~ in(skf3(skc9,u),u) ),
inference(res,[status(thm),theory(equality)],[234,19]),
[iquote('0:Res:234.1,19.0')] ).
cnf(327,plain,
( ~ in(u,skc8)
| ~ in(v,skc9)
| in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[205,16]),
[iquote('0:Res:205.2,16.0')] ).
cnf(328,plain,
( ~ in(u,skc8)
| ~ in(v,skc9)
| in(v,skc6) ),
inference(res,[status(thm),theory(equality)],[205,17]),
[iquote('0:Res:205.2,17.0')] ).
cnf(372,plain,
( ~ in(u,skc9)
| in(u,skc6) ),
inference(res,[status(thm),theory(equality)],[222,328]),
[iquote('0:Res:222.0,328.0')] ).
cnf(410,plain,
( equal(u,skc9)
| in(skf3(skc9,u),u)
| in(skf3(skc9,u),skc6) ),
inference(res,[status(thm),theory(equality)],[20,372]),
[iquote('0:Res:20.1,372.0')] ).
cnf(457,plain,
( equal(skc9,skc6)
| in(skf3(skc9,skc6),skc6) ),
inference(fac,[status(thm)],[410]),
[iquote('0:Fac:410.1,410.2')] ).
cnf(468,plain,
equal(skc9,skc6),
inference(spt,[spt(split,[position(s1)])],[457]),
[iquote('1:Spt:457.0')] ).
cnf(470,plain,
( ~ equal(skc6,skc6)
| ~ equal(skc8,skc7) ),
inference(rew,[status(thm),theory(equality)],[468,10]),
[iquote('1:Rew:468.0,10.0')] ).
cnf(473,plain,
( ~ in(u,skc8)
| ~ in(v,skc6)
| in(u,skc7) ),
inference(rew,[status(thm),theory(equality)],[468,327]),
[iquote('1:Rew:468.0,327.1')] ).
cnf(516,plain,
~ equal(skc8,skc7),
inference(obv,[status(thm),theory(equality)],[470]),
[iquote('1:Obv:470.0')] ).
cnf(813,plain,
( equal(u,skc7)
| in(skf3(skc7,u),u)
| in(skf3(skc7,u),skc8) ),
inference(res,[status(thm),theory(equality)],[24,220]),
[iquote('0:Res:24.0,220.0')] ).
cnf(821,plain,
( equal(skc8,skc7)
| in(skf3(skc7,skc8),skc8) ),
inference(fac,[status(thm)],[813]),
[iquote('0:Fac:813.1,813.2')] ).
cnf(827,plain,
in(skf3(skc7,skc8),skc8),
inference(mrr,[status(thm)],[821,516]),
[iquote('1:MRR:821.0,516.0')] ).
cnf(830,plain,
( ~ in(u,skc6)
| in(skf3(skc7,skc8),skc7) ),
inference(res,[status(thm),theory(equality)],[827,473]),
[iquote('1:Res:827.0,473.0')] ).
cnf(831,plain,
in(skf3(skc7,skc8),skc7),
inference(res,[status(thm),theory(equality)],[24,830]),
[iquote('1:Res:24.0,830.0')] ).
cnf(850,plain,
~ in(skf3(skc7,skc8),skc8),
inference(res,[status(thm),theory(equality)],[831,19]),
[iquote('1:Res:831.0,19.0')] ).
cnf(851,plain,
$false,
inference(mrr,[status(thm)],[850,827]),
[iquote('1:MRR:850.0,827.0')] ).
cnf(852,plain,
~ equal(skc9,skc6),
inference(spt,[spt(split,[position(sa)])],[851,468]),
[iquote('1:Spt:851.0,457.0,468.0')] ).
cnf(853,plain,
in(skf3(skc9,skc6),skc6),
inference(spt,[spt(split,[position(s2)])],[457]),
[iquote('1:Spt:851.0,457.1')] ).
cnf(984,plain,
~ in(skf3(skc9,skc6),skc6),
inference(res,[status(thm),theory(equality)],[853,243]),
[iquote('1:Res:853.0,243.0')] ).
cnf(986,plain,
$false,
inference(mrr,[status(thm)],[984,853]),
[iquote('1:MRR:984.0,853.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 20:06:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 831 clauses, backtracked 52 clauses, performed 2 splits and kept 323 clauses.
% 0.20/0.52 SPASS allocated 85893 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.52 0:00:00.03 for the input.
% 0.20/0.52 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.06 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 9, length 42 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : t134_zfmisc_1 d1_xboole_0 l55_zfmisc_1 t2_tarski antisymmetry_r2_hidden
% 0.20/0.52
%------------------------------------------------------------------------------