%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 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 : 300s
% DateTime : Tue May 5 07:07:24 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(aux2(u,v,w,bfalse),bfalse),
file('SWX200-1.p',unknown),
[] ).
cnf(6,axiom,
equal(leqNat(s(u),z__dfg),bfalse),
file('SWX200-1.p',unknown),
[] ).
cnf(8,axiom,
equal(merge(nil,u),u),
file('SWX200-1.p',unknown),
[] ).
cnf(11,axiom,
equal(ord(nil),btrue),
file('SWX200-1.p',unknown),
[] ).
cnf(13,axiom,
equal(aux2(u,v,w,leqNat(u,v)),ord(cons(u,cons(v,w)))),
file('SWX200-1.p',unknown),
[] ).
cnf(14,axiom,
equal(impl(btrue,u),u),
file('SWX200-1.p',unknown),
[] ).
cnf(16,axiom,
equal(impl(eq2(ord(u),btrue),impl(eq2(ord(v),bfalse),eq2(ord(merge(u,v)),btrue))),prop_merge_ord_not3(u,v)),
file('SWX200-1.p',unknown),
[] ).
cnf(17,axiom,
equal(eq2(bfalse,btrue),bfalse),
file('SWX200-1.p',unknown),
[] ).
cnf(23,axiom,
equal(eq2(u,u),btrue),
file('SWX200-1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(eq2(prop_merge_ord_not3(u,v),bfalse),btrue),
file('SWX200-1.p',unknown),
[] ).
cnf(46,plain,
equal(ord(cons(s(u),cons(z__dfg,v))),aux2(s(u),z__dfg,v,bfalse)),
inference(spr,[status(thm),theory(equality)],[6,13]),
[iquote('0:SpR:6.0,13.0')] ).
cnf(49,plain,
equal(ord(cons(s(u),cons(z__dfg,v))),bfalse),
inference(rew,[status(thm),theory(equality)],[4,46]),
[iquote('0:Rew:4.0,46.0')] ).
cnf(102,plain,
equal(impl(eq2(ord(nil),btrue),impl(eq2(ord(u),bfalse),eq2(ord(u),btrue))),prop_merge_ord_not3(nil,u)),
inference(spr,[status(thm),theory(equality)],[8,16]),
[iquote('0:SpR:8.0,16.0')] ).
cnf(122,plain,
equal(impl(eq2(ord(u),bfalse),eq2(ord(u),btrue)),prop_merge_ord_not3(nil,u)),
inference(rew,[status(thm),theory(equality)],[14,102,23,11]),
[iquote('0:Rew:14.0,102.0,23.0,102.0,11.0,102.0')] ).
cnf(160,plain,
equal(prop_merge_ord_not3(nil,cons(s(u),cons(z__dfg,v))),impl(eq2(bfalse,bfalse),eq2(bfalse,btrue))),
inference(spr,[status(thm),theory(equality)],[49,122]),
[iquote('0:SpR:49.0,122.0')] ).
cnf(176,plain,
equal(prop_merge_ord_not3(nil,cons(s(u),cons(z__dfg,v))),bfalse),
inference(rew,[status(thm),theory(equality)],[14,160,23,17]),
[iquote('0:Rew:14.0,160.0,23.0,160.0,17.0,160.0')] ).
cnf(192,plain,
~ equal(eq2(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[176,24]),
[iquote('0:SpL:176.0,24.0')] ).
cnf(193,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[23,192]),
[iquote('0:Rew:23.0,192.0')] ).
cnf(194,plain,
$false,
inference(obv,[status(thm),theory(equality)],[193]),
[iquote('0:Obv:193.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 11:15:59 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 124 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.18/0.42 SPASS allocated 63486 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.02 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 19 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : axiom_003 axiom_005 axiom_007 axiom_010 axiom_012 axiom_013 axiom_015 axiom_016 axiom_022 goal
% 0.18/0.42
%------------------------------------------------------------------------------