TSTP Solution File: SET961+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:30:05 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 10 unt; 3 nHn; 23 RR)
% Number of literals : 40 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc5,empty_set),
file('SET961+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(skc5,skc4),
file('SET961+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(skc4,empty_set),
file('SET961+1.p',unknown),
[] ).
cnf(8,axiom,
equal(cartesian_product2(skc5,skc4),cartesian_product2(skc4,skc5)),
file('SET961+1.p',unknown),
[] ).
cnf(10,axiom,
( equal(u,empty_set)
| in(skf2(u),u) ),
file('SET961+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(u,w) ),
file('SET961+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SET961+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(skf3(u,v),u)
| ~ in(skf3(u,v),v) ),
file('SET961+1.p',unknown),
[] ).
cnf(17,axiom,
( equal(u,v)
| in(skf3(v,u),v)
| in(skf3(v,u),u) ),
file('SET961+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ in(w,x)
| in(ordered_pair(u,w),cartesian_product2(v,x)) ),
file('SET961+1.p',unknown),
[] ).
cnf(20,plain,
in(skf2(skc4),skc4),
inference(res,[status(thm),theory(equality)],[10,6]),
[iquote('0:Res:10.1,6.0')] ).
cnf(23,plain,
( in(skf3(skc4,skc5),skc4)
| in(skf3(skc4,skc5),skc5) ),
inference(res,[status(thm),theory(equality)],[17,5]),
[iquote('0:Res:17.2,5.0')] ).
cnf(25,plain,
in(skf2(skc5),skc5),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.1,4.0')] ).
cnf(45,plain,
( ~ in(ordered_pair(u,v),cartesian_product2(skc4,skc5))
| in(v,skc4) ),
inference(spl,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpL:8.0,15.0')] ).
cnf(54,plain,
( ~ in(ordered_pair(u,v),cartesian_product2(skc4,skc5))
| in(u,skc5) ),
inference(spl,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpL:8.0,14.0')] ).
cnf(100,plain,
( ~ in(u,skc4)
| ~ in(v,skc5)
| in(v,skc4) ),
inference(res,[status(thm),theory(equality)],[18,45]),
[iquote('0:Res:18.2,45.0')] ).
cnf(101,plain,
( ~ in(u,skc4)
| ~ in(v,skc5)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[18,54]),
[iquote('0:Res:18.2,54.0')] ).
cnf(102,plain,
( ~ in(u,skc5)
| in(u,skc4) ),
inference(res,[status(thm),theory(equality)],[20,100]),
[iquote('0:Res:20.0,100.0')] ).
cnf(111,plain,
in(skf3(skc4,skc5),skc4),
inference(mrr,[status(thm)],[23,102]),
[iquote('0:MRR:23.1,102.0')] ).
cnf(116,plain,
~ in(skf3(skc4,skc5),skc5),
inference(res,[status(thm),theory(equality)],[111,16]),
[iquote('0:Res:111.0,16.0')] ).
cnf(156,plain,
( ~ in(u,skc5)
| in(skf3(skc4,skc5),skc5) ),
inference(res,[status(thm),theory(equality)],[111,101]),
[iquote('0:Res:111.0,101.0')] ).
cnf(163,plain,
~ in(u,skc5),
inference(mrr,[status(thm)],[156,116]),
[iquote('0:MRR:156.1,116.0')] ).
cnf(164,plain,
$false,
inference(unc,[status(thm)],[163,25]),
[iquote('0:UnC:163.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 22:55:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 133 clauses, backtracked 0 clauses, performed 0 splits and kept 88 clauses.
% 0.18/0.44 SPASS allocated 85219 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.44 0:00:00.03 for the input.
% 0.18/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.01 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 3, length 23 :
% 0.18/0.44 % SZS output start Refutation
% See solution above
% 0.18/0.44 Formulae used in the proof : t114_zfmisc_1 d1_xboole_0 l55_zfmisc_1 t2_tarski antisymmetry_r2_hidden
% 0.18/0.44
%------------------------------------------------------------------------------