%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV255-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 7 unt; 1 nHn; 14 RR)
% Number of literals : 21 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lessequals(c_plus(u,v,tc_nat),w,tc_nat)
| c_lessequals(v,w,tc_nat) ),
file('SWV255-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(c_plus(u,v,tc_nat),w,tc_nat)
| c_lessequals(u,w,tc_nat) ),
file('SWV255-2.p',unknown),
[] ).
cnf(3,axiom,
c_lessequals(u,v_xb(u),tc_nat),
file('SWV255-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_lessequals(v_x,u,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(u),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('SWV255-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_lessequals(v_xa,u,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(u),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('SWV255-2.p',unknown),
[] ).
cnf(6,axiom,
( c_in(c_Message_Omsg_ONonce(v_xb(u)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(u)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('SWV255-2.p',unknown),
[] ).
cnf(7,plain,
c_lessequals(u,v_xb(c_plus(u,v,tc_nat)),tc_nat),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.0,2.0')] ).
cnf(10,plain,
c_lessequals(u,v_xb(c_plus(v,u,tc_nat)),tc_nat),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.0')] ).
cnf(14,plain,
c_lessequals(u,v_xb(c_plus(v,c_plus(u,w,tc_nat),tc_nat)),tc_nat),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.0,2.0')] ).
cnf(20,plain,
c_lessequals(u,v_xb(c_plus(v,c_plus(c_plus(u,w,tc_nat),x,tc_nat),tc_nat)),tc_nat),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.0,2.0')] ).
cnf(37,plain,
( ~ c_lessequals(v_x,v_xb(u),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(u)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.0,4.1')] ).
cnf(38,plain,
( ~ c_lessequals(v_x,v_xb(u),tc_nat)
| ~ c_lessequals(v_xa,v_xb(u),tc_nat) ),
inference(res,[status(thm),theory(equality)],[37,5]),
[iquote('0:Res:37.1,5.1')] ).
cnf(40,plain,
~ c_lessequals(v_xa,v_xb(c_plus(v_x,u,tc_nat)),tc_nat),
inference(res,[status(thm),theory(equality)],[7,38]),
[iquote('0:Res:7.0,38.0')] ).
cnf(54,plain,
$false,
inference(unc,[status(thm)],[40,20]),
[iquote('0:UnC:40.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV255-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 18:50:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 53 clauses.
% 0.21/0.43 SPASS allocated 63190 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.43 0:00:00.03 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.00 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 3, length 14 :
% 0.21/0.43 % SZS output start Refutation
% See solution above
% 0.21/0.43 Formulae used in the proof : cls_Nat_Oadd__leE_0 cls_Nat_Oadd__leE_1 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.21/0.43
%------------------------------------------------------------------------------