TSTP Solution File: SWV254-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 : Wed Jul 20 21:41:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 14 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| equal(c_SetInterval_OatLeastLessThan(w,v,u),c_emptyset) ),
file('SWV254-2.p',unknown),
[] ).
cnf(2,axiom,
equal(c_SetInterval_OatLeastLessThan(u,c_Suc(u),tc_nat),c_insert(u,c_emptyset,tc_nat)),
file('SWV254-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(c_insert(u,v,w),c_emptyset),
file('SWV254-2.p',unknown),
[] ).
cnf(4,axiom,
class_Orderings_Oorder(tc_nat),
file('SWV254-2.p',unknown),
[] ).
cnf(5,axiom,
c_lessequals(u,v_x(u),tc_nat),
file('SWV254-2.p',unknown),
[] ).
cnf(6,axiom,
equal(v_x(u),v_nat),
file('SWV254-2.p',unknown),
[] ).
cnf(7,plain,
c_lessequals(u,v_nat,tc_nat),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(8,plain,
( ~ class_Orderings_Oorder(tc_nat)
| equal(c_SetInterval_OatLeastLessThan(v_nat,u,tc_nat),c_emptyset) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.0,1.1')] ).
cnf(9,plain,
equal(c_SetInterval_OatLeastLessThan(v_nat,u,tc_nat),c_emptyset),
inference(mrr,[status(thm)],[8,4]),
[iquote('0:MRR:8.0,4.0')] ).
cnf(12,plain,
equal(c_insert(v_nat,c_emptyset,tc_nat),c_emptyset),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(14,plain,
$false,
inference(mrr,[status(thm)],[12,3]),
[iquote('0:MRR:12.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 : Wed Jun 15 20:00:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 8 clauses.
% 0.18/0.41 SPASS allocated 75589 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 2, length 11 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : cls_SetInterval_OatLeastLessThan__empty_0 cls_SetInterval_OatLeastLessThan__singleton_0 cls_Set_Oempty__not__insert_0 clsarity_nat_3 cls_conjecture_0 cls_conjecture_1
% 0.18/0.41
%------------------------------------------------------------------------------