%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV578-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 21:44:27 EDT 2022
% Result : Unsatisfiable 0.83s 1.08s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 13 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1075,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v,tc_nat),w))
| equal(hAPP(hAPP(c_HOL_Oplus__class_Oplus(u),hAPP(x,v)),c_Finite__Set_Osetsum(x,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v),w,tc_nat),tc_nat,u)),c_Finite__Set_Osetsum(x,c_SetInterval_Oord__class_OatLeastLessThan(v,w,tc_nat),tc_nat,u)) ),
file('SWV578-1.p',unknown),
[] ).
cnf(1079,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('SWV578-1.p',unknown),
[] ).
cnf(1080,axiom,
equal(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,u),v,tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(u,v,tc_nat)),
file('SWV578-1.p',unknown),
[] ).
cnf(1224,axiom,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('SWV578-1.p',unknown),
[] ).
cnf(1225,axiom,
~ equal(hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v,v_m)),c_Finite__Set_Osetsum(v,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)),c_Finite__Set_Osetsum(v,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a)),
file('SWV578-1.p',unknown),
[] ).
cnf(1311,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v,tc_nat),w))
| equal(hAPP(hAPP(c_HOL_Oplus__class_Oplus(u),hAPP(x,v)),c_Finite__Set_Osetsum(x,c_SetInterval_Oord__class_OgreaterThanLessThan(v,w,tc_nat),tc_nat,u)),c_Finite__Set_Osetsum(x,c_SetInterval_Oord__class_OatLeastLessThan(v,w,tc_nat),tc_nat,u)) ),
inference(rew,[status(thm),theory(equality)],[1080,1075]),
[iquote('0:Rew:1080.0,1075.2')] ).
cnf(1362,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)) ),
inference(res,[status(thm),theory(equality)],[1311,1225]),
[iquote('0:Res:1311.2,1225.0')] ).
cnf(1481,plain,
$false,
inference(mrr,[status(thm)],[1362,1224,1079]),
[iquote('0:MRR:1362.0,1362.1,1224.0,1079.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV578-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 06:28:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.83/1.08
% 0.83/1.08 SPASS V 3.9
% 0.83/1.08 SPASS beiseite: Proof found.
% 0.83/1.08 % SZS status Theorem
% 0.83/1.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/1.08 SPASS derived 69 clauses, backtracked 0 clauses, performed 0 splits and kept 1084 clauses.
% 0.83/1.08 SPASS allocated 78479 KBytes.
% 0.83/1.08 SPASS spent 0:00:00.71 on the problem.
% 0.83/1.08 0:00:00.10 for the input.
% 0.83/1.08 0:00:00.00 for the FLOTTER CNF translation.
% 0.83/1.08 0:00:00.00 for inferences.
% 0.83/1.08 0:00:00.00 for the backtracking.
% 0.83/1.08 0:00:00.48 for the reduction.
% 0.83/1.08
% 0.83/1.08
% 0.83/1.08 Here is a proof with depth 1, length 8 :
% 0.83/1.08 % SZS output start Refutation
% See solution above
% 0.83/1.08 Formulae used in the proof : cls_setsum__head__upt__Suc_0 cls_less_0 cls_atLeastSucLessThan__greaterThanLessThan_0 tfree_tcs cls_conjecture_0
% 0.83/1.08
%------------------------------------------------------------------------------