TSTP Solution File: PHI012+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PHI012+1 : TPTP v8.1.0. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 : Mon Jul 18 16:48:54 EDT 2022
% Result : Theorem 0.17s 0.43s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 8 unt; 4 nHn; 27 RR)
% Number of literals : 74 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
object(skc1),
file('PHI012+1.p',unknown),
[] ).
cnf(2,axiom,
object(skf2(u)),
file('PHI012+1.p',unknown),
[] ).
cnf(3,axiom,
exemplifies_property(none_greater,skc1),
file('PHI012+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ object(u)
| ~ exemplifies_property(none_greater,u)
| exemplifies_property(conceivable,u) ),
file('PHI012+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ object(u)
| ~ exemplifies_property(none_greater,u)
| exemplifies_property(none_greater,skf2(u)) ),
file('PHI012+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ object(u)
| ~ exemplifies_property(none_greater,u)
| ~ equal(skf2(u),u) ),
file('PHI012+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ object(u)
| ~ object(v)
| equal(v,u)
| exemplifies_relation(greater_than,u,v)
| exemplifies_relation(greater_than,v,u) ),
file('PHI012+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ object(u)
| ~ object(v)
| ~ exemplifies_property(none_greater,u)
| ~ exemplifies_property(conceivable,v)
| ~ exemplifies_relation(greater_than,v,u) ),
file('PHI012+1.p',unknown),
[] ).
cnf(12,plain,
( ~ object(u)
| ~ exemplifies_property(conceivable,skc1)
| ~ exemplifies_property(none_greater,u)
| ~ exemplifies_relation(greater_than,skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(13,plain,
( ~ object(u)
| equal(skc1,u)
| exemplifies_relation(greater_than,u,skc1)
| exemplifies_relation(greater_than,skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(21,plain,
( ~ object(skc1)
| ~ equal(skf2(skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.0,7.2')] ).
cnf(22,plain,
( ~ object(skc1)
| exemplifies_property(none_greater,skf2(skc1)) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.1')] ).
cnf(23,plain,
( ~ object(skc1)
| exemplifies_property(conceivable,skc1) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.0,5.1')] ).
cnf(24,plain,
( ~ object(u)
| ~ object(skc1)
| ~ exemplifies_property(conceivable,u)
| ~ exemplifies_relation(greater_than,u,skc1) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.3')] ).
cnf(25,plain,
exemplifies_property(conceivable,skc1),
inference(mrr,[status(thm)],[23,1]),
[iquote('0:MRR:23.0,1.0')] ).
cnf(26,plain,
exemplifies_property(none_greater,skf2(skc1)),
inference(mrr,[status(thm)],[22,1]),
[iquote('0:MRR:22.0,1.0')] ).
cnf(27,plain,
~ equal(skf2(skc1),skc1),
inference(mrr,[status(thm)],[21,1]),
[iquote('0:MRR:21.0,1.0')] ).
cnf(28,plain,
( ~ object(u)
| ~ exemplifies_property(conceivable,u)
| ~ exemplifies_relation(greater_than,u,skc1) ),
inference(mrr,[status(thm)],[24,1]),
[iquote('0:MRR:24.1,1.0')] ).
cnf(29,plain,
( ~ object(u)
| ~ exemplifies_property(none_greater,u)
| ~ exemplifies_relation(greater_than,skc1,u) ),
inference(mrr,[status(thm)],[12,25]),
[iquote('0:MRR:12.1,25.0')] ).
cnf(40,plain,
( ~ object(u)
| ~ object(u)
| ~ exemplifies_property(conceivable,u)
| equal(skc1,u)
| exemplifies_relation(greater_than,skc1,u) ),
inference(res,[status(thm),theory(equality)],[13,28]),
[iquote('0:Res:13.2,28.2')] ).
cnf(42,plain,
( ~ object(u)
| ~ exemplifies_property(conceivable,u)
| equal(skc1,u)
| exemplifies_relation(greater_than,skc1,u) ),
inference(obv,[status(thm),theory(equality)],[40]),
[iquote('0:Obv:40.0')] ).
cnf(44,plain,
( ~ object(u)
| ~ object(u)
| ~ exemplifies_property(conceivable,u)
| ~ exemplifies_property(none_greater,u)
| equal(skc1,u) ),
inference(res,[status(thm),theory(equality)],[42,29]),
[iquote('0:Res:42.3,29.2')] ).
cnf(46,plain,
( ~ object(u)
| ~ exemplifies_property(conceivable,u)
| ~ exemplifies_property(none_greater,u)
| equal(skc1,u) ),
inference(obv,[status(thm),theory(equality)],[44]),
[iquote('0:Obv:44.0')] ).
cnf(47,plain,
( ~ object(u)
| ~ exemplifies_property(none_greater,u)
| equal(skc1,u) ),
inference(mrr,[status(thm)],[46,5]),
[iquote('0:MRR:46.1,5.2')] ).
cnf(49,plain,
( ~ object(skf2(skc1))
| equal(skf2(skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[26,47]),
[iquote('0:Res:26.0,47.1')] ).
cnf(51,plain,
equal(skf2(skc1),skc1),
inference(ssi,[status(thm)],[49,2,1]),
[iquote('0:SSi:49.0,2.0,1.0')] ).
cnf(52,plain,
$false,
inference(mrr,[status(thm)],[51,27]),
[iquote('0:MRR:51.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PHI012+1 : TPTP v8.1.0. Released v7.2.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 2 01:44:59 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.43
% 0.17/0.43 SPASS V 3.9
% 0.17/0.43 SPASS beiseite: Proof found.
% 0.17/0.43 % SZS status Theorem
% 0.17/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 SPASS derived 28 clauses, backtracked 0 clauses, performed 0 splits and kept 25 clauses.
% 0.17/0.43 SPASS allocated 103901 KBytes.
% 0.17/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.17/0.43 0:00:00.04 for the input.
% 0.17/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.17/0.43 0:00:00.00 for inferences.
% 0.17/0.43 0:00:00.00 for the backtracking.
% 0.17/0.43 0:00:00.00 for the reduction.
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 Here is a proof with depth 4, length 27 :
% 0.17/0.43 % SZS output start Refutation
% See solution above
% 0.17/0.43 Formulae used in the proof : lemma_2 definition_none_greater connectedness_of_greater_than
% 0.17/0.43
%------------------------------------------------------------------------------