TSTP Solution File: SET993+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET993+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 05:30:17 EDT 2022
% Result : Theorem 3.54s 3.76s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 9 unt; 12 nHn; 39 RR)
% Number of literals : 104 ( 0 equ; 56 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
~ equal(skc8,empty_set),
file('SET993+1.p',unknown),
[] ).
cnf(20,axiom,
element(skf13(u),u),
file('SET993+1.p',unknown),
[] ).
cnf(23,axiom,
relation(skf16(u,v)),
file('SET993+1.p',unknown),
[] ).
cnf(24,axiom,
function(skf16(u,v)),
file('SET993+1.p',unknown),
[] ).
cnf(34,axiom,
equal(relation_dom(skf16(u,v)),v),
file('SET993+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SET993+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SET993+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ in(u,v)
| equal(apply(skf16(w,v),u),w) ),
file('SET993+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET993+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SET993+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc8)
| ~ equal(relation_rng(u),singleton(skc9)) ),
file('SET993+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ in(u,relation_dom(v))
| ~ in(skf11(v,w),w)
| ~ equal(skf11(v,w),apply(v,u)) ),
file('SET993+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_rng(u))
| in(skf11(u,v),v)
| in(skf12(u,w),relation_dom(u)) ),
file('SET993+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_rng(u))
| in(skf11(u,v),v)
| equal(apply(u,skf12(u,v)),skf11(u,v)) ),
file('SET993+1.p',unknown),
[] ).
cnf(59,plain,
~ empty(skc8),
inference(res,[status(thm),theory(equality)],[35,19]),
[iquote('0:Res:35.1,19.0')] ).
cnf(72,plain,
( ~ relation(skf16(u,skc8))
| ~ function(skf16(u,skc8))
| ~ equal(relation_rng(skf16(u,skc8)),singleton(skc9)) ),
inference(res,[status(thm),theory(equality)],[34,52]),
[iquote('0:Res:34.0,52.2')] ).
cnf(74,plain,
~ equal(relation_rng(skf16(u,skc8)),singleton(skc9)),
inference(mrr,[status(thm)],[72,23,24]),
[iquote('0:MRR:72.0,72.1,23.0,24.0')] ).
cnf(127,plain,
( empty(u)
| in(skf13(u),u) ),
inference(res,[status(thm),theory(equality)],[20,43]),
[iquote('0:Res:20.0,43.0')] ).
cnf(176,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.1')] ).
cnf(211,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[48]),
[iquote('0:EqR:48.1')] ).
cnf(267,plain,
( ~ in(u,v)
| ~ in(u,relation_dom(skf16(w,v)))
| ~ in(skf11(skf16(w,v),x),x)
| ~ equal(skf11(skf16(w,v),x),w) ),
inference(spl,[status(thm),theory(equality)],[45,53]),
[iquote('0:SpL:45.1,53.2')] ).
cnf(268,plain,
( ~ in(u,v)
| ~ in(u,v)
| ~ in(skf11(skf16(w,v),x),x)
| ~ equal(skf11(skf16(w,v),x),w) ),
inference(rew,[status(thm),theory(equality)],[34,267]),
[iquote('0:Rew:34.0,267.1')] ).
cnf(269,plain,
( ~ in(u,v)
| ~ in(skf11(skf16(w,v),x),x)
| ~ equal(skf11(skf16(w,v),x),w) ),
inference(obv,[status(thm),theory(equality)],[268]),
[iquote('0:Obv:268.0')] ).
cnf(320,plain,
( ~ function(skf16(u,v))
| ~ relation(skf16(u,v))
| equal(w,relation_rng(skf16(u,v)))
| in(skf11(skf16(u,v),w),w)
| in(skf12(skf16(u,v),x),v) ),
inference(spr,[status(thm),theory(equality)],[34,54]),
[iquote('0:SpR:34.0,54.4')] ).
cnf(337,plain,
( equal(u,relation_rng(skf16(v,w)))
| in(skf11(skf16(v,w),u),u)
| in(skf12(skf16(v,w),x),w) ),
inference(ssi,[status(thm)],[320,24,23]),
[iquote('0:SSi:320.1,320.0,24.0,23.0,24.0,23.0')] ).
cnf(379,plain,
( ~ function(skf16(u,v))
| ~ relation(skf16(u,v))
| ~ in(skf12(skf16(u,v),w),v)
| equal(w,relation_rng(skf16(u,v)))
| in(skf11(skf16(u,v),w),w)
| equal(skf11(skf16(u,v),w),u) ),
inference(spr,[status(thm),theory(equality)],[57,45]),
[iquote('0:SpR:57.4,45.1')] ).
cnf(389,plain,
( ~ in(skf12(skf16(u,v),w),v)
| equal(w,relation_rng(skf16(u,v)))
| in(skf11(skf16(u,v),w),w)
| equal(skf11(skf16(u,v),w),u) ),
inference(ssi,[status(thm)],[379,24,23]),
[iquote('0:SSi:379.1,379.0,24.0,23.0,24.0,23.0')] ).
cnf(390,plain,
( equal(u,relation_rng(skf16(v,w)))
| in(skf11(skf16(v,w),u),u)
| equal(skf11(skf16(v,w),u),v) ),
inference(mrr,[status(thm)],[389,337]),
[iquote('0:MRR:389.0,337.2')] ).
cnf(849,plain,
( ~ equal(skf11(skf16(u,v),singleton(w)),w)
| ~ in(x,v)
| ~ equal(skf11(skf16(u,v),singleton(w)),u) ),
inference(res,[status(thm),theory(equality)],[211,269]),
[iquote('0:Res:211.1,269.1')] ).
cnf(939,plain,
( equal(singleton(u),relation_rng(skf16(v,w)))
| equal(skf11(skf16(v,w),singleton(u)),v)
| equal(skf11(skf16(v,w),singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[390,176]),
[iquote('0:Res:390.1,176.0')] ).
cnf(3243,plain,
( equal(relation_rng(skf16(u,v)),singleton(u))
| equal(skf11(skf16(u,v),singleton(u)),u) ),
inference(fac,[status(thm)],[939]),
[iquote('0:Fac:939.1,939.2')] ).
cnf(9450,plain,
( ~ equal(u,u)
| ~ in(v,w)
| ~ equal(skf11(skf16(u,w),singleton(u)),u)
| equal(relation_rng(skf16(u,w)),singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[3243,849]),
[iquote('0:SpL:3243.1,849.0')] ).
cnf(9453,plain,
( ~ in(u,v)
| ~ equal(skf11(skf16(w,v),singleton(w)),w)
| equal(relation_rng(skf16(w,v)),singleton(w)) ),
inference(obv,[status(thm),theory(equality)],[9450]),
[iquote('0:Obv:9450.0')] ).
cnf(9454,plain,
( ~ in(u,v)
| ~ equal(w,w)
| equal(relation_rng(skf16(w,v)),singleton(w)) ),
inference(rew,[status(thm),theory(equality)],[3243,9453]),
[iquote('0:Rew:3243.1,9453.1')] ).
cnf(9455,plain,
( ~ in(u,v)
| equal(relation_rng(skf16(w,v)),singleton(w)) ),
inference(obv,[status(thm),theory(equality)],[9454]),
[iquote('0:Obv:9454.1')] ).
cnf(9777,plain,
( empty(u)
| equal(relation_rng(skf16(v,u)),singleton(v)) ),
inference(res,[status(thm),theory(equality)],[127,9455]),
[iquote('0:Res:127.1,9455.0')] ).
cnf(10455,plain,
( ~ equal(singleton(u),singleton(skc9))
| empty(skc8) ),
inference(spl,[status(thm),theory(equality)],[9777,74]),
[iquote('0:SpL:9777.1,74.0')] ).
cnf(10457,plain,
~ equal(singleton(u),singleton(skc9)),
inference(mrr,[status(thm)],[10455,59]),
[iquote('0:MRR:10455.1,59.0')] ).
cnf(10470,plain,
$false,
inference(eqr,[status(thm),theory(equality)],[10457]),
[iquote('0:EqR:10457.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET993+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Sun Jul 10 03:25:57 EDT 2022
% 0.16/0.36 % CPUTime :
% 3.54/3.76
% 3.54/3.76 SPASS V 3.9
% 3.54/3.76 SPASS beiseite: Proof found.
% 3.54/3.76 % SZS status Theorem
% 3.54/3.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.54/3.76 SPASS derived 8032 clauses, backtracked 0 clauses, performed 3 splits and kept 2927 clauses.
% 3.54/3.76 SPASS allocated 107012 KBytes.
% 3.54/3.76 SPASS spent 0:00:03.28 on the problem.
% 3.54/3.76 0:00:00.03 for the input.
% 3.54/3.76 0:00:00.04 for the FLOTTER CNF translation.
% 3.54/3.76 0:00:00.15 for inferences.
% 3.54/3.76 0:00:00.13 for the backtracking.
% 3.54/3.76 0:00:02.85 for the reduction.
% 3.54/3.76
% 3.54/3.76
% 3.54/3.76 Here is a proof with depth 7, length 39 :
% 3.54/3.76 % SZS output start Refutation
% See solution above
% 3.54/3.76 Formulae used in the proof : t15_funct_1 existence_m1_subset_1 s3_funct_1__e2_13__funct_1 t6_boole t2_subset d1_tarski antisymmetry_r2_hidden d5_funct_1
% 3.54/3.76
%------------------------------------------------------------------------------