%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 06:48:43 PM UTC 2026
% Result : Unsatisfiable 1.74s 1.94s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 52 RR)
% Number of literals : 52 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(minus(u,zero),u),
file('NUN135-1.006.p',unknown),
[] ).
cnf(2,axiom,
equal(minus(s(u),s(v)),minus(u,v)),
file('NUN135-1.006.p',unknown),
[] ).
cnf(3,axiom,
equal(a60__a61_(zero,u),true__dfg),
file('NUN135-1.006.p',unknown),
[] ).
cnf(4,axiom,
equal(a60__a61_(s(u),zero),false__dfg),
file('NUN135-1.006.p',unknown),
[] ).
cnf(5,axiom,
equal(a60__a61_(s(u),s(v)),a60__a61_(u,v)),
file('NUN135-1.006.p',unknown),
[] ).
cnf(6,axiom,
equal(if(true__dfg,u,v),u),
file('NUN135-1.006.p',unknown),
[] ).
cnf(7,axiom,
equal(if(false__dfg,u,v),v),
file('NUN135-1.006.p',unknown),
[] ).
cnf(9,axiom,
equal(f(u,s(zero),s(u),s(u)),perfectp(s(u))),
file('NUN135-1.006.p',unknown),
[] ).
cnf(10,axiom,
equal(f(zero,u,zero,v),true__dfg),
file('NUN135-1.006.p',unknown),
[] ).
cnf(12,axiom,
equal(f(u,v,minus(w,s(u)),v),f(s(u),zero,w,v)),
file('NUN135-1.006.p',unknown),
[] ).
cnf(13,axiom,
equal(if(a60__a61_(u,v),f(s(u),minus(v,u),w,x),f(u,x,w,x)),f(s(u),s(v),w,x)),
file('NUN135-1.006.p',unknown),
[] ).
cnf(14,axiom,
~ equal(perfectp(u),true__dfg),
file('NUN135-1.006.p',unknown),
[] ).
cnf(31,plain,
equal(f(u,v,minus(w,u),v),f(s(u),zero,s(w),v)),
inference(spr,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpR:2.0,12.0')] ).
cnf(34,plain,
equal(f(zero,u,v,u),f(s(zero),zero,s(v),u)),
inference(spr,[status(thm),theory(equality)],[1,31]),
[iquote('0:SpR:1.0,31.0')] ).
cnf(35,plain,
equal(f(s(u),v,minus(w,u),v),f(s(s(u)),zero,s(s(w)),v)),
inference(spr,[status(thm),theory(equality)],[2,31]),
[iquote('0:SpR:2.0,31.0')] ).
cnf(36,plain,
equal(f(s(zero),zero,s(zero),u),true__dfg),
inference(spr,[status(thm),theory(equality)],[34,10]),
[iquote('0:SpR:34.0,10.0')] ).
cnf(68,plain,
equal(if(true__dfg,f(s(zero),minus(u,zero),v,w),f(zero,w,v,w)),f(s(zero),s(u),v,w)),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(69,plain,
equal(if(false__dfg,f(s(s(u)),minus(zero,s(u)),v,w),f(s(u),w,v,w)),f(s(s(u)),s(zero),v,w)),
inference(spr,[status(thm),theory(equality)],[4,13]),
[iquote('0:SpR:4.0,13.0')] ).
cnf(70,plain,
equal(if(a60__a61_(u,v),f(s(s(u)),minus(s(v),s(u)),w,x),f(s(u),x,w,x)),f(s(s(u)),s(s(v)),w,x)),
inference(spr,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpR:5.0,13.0')] ).
cnf(72,plain,
equal(f(s(zero),s(u),v,w),f(s(zero),u,v,w)),
inference(rew,[status(thm),theory(equality)],[6,68,1]),
[iquote('0:Rew:6.0,68.0,1.0,68.0')] ).
cnf(75,plain,
equal(f(s(u),v,w,v),f(s(s(u)),s(zero),w,v)),
inference(rew,[status(thm),theory(equality)],[7,69]),
[iquote('0:Rew:7.0,69.0')] ).
cnf(78,plain,
equal(if(a60__a61_(u,v),f(s(s(u)),minus(v,u),w,x),f(s(u),x,w,x)),f(s(s(u)),s(s(v)),w,x)),
inference(rew,[status(thm),theory(equality)],[2,70]),
[iquote('0:Rew:2.0,70.0')] ).
cnf(94,plain,
equal(f(s(s(zero)),s(zero),u,s(v)),f(s(zero),v,u,s(v))),
inference(spr,[status(thm),theory(equality)],[75,72]),
[iquote('0:SpR:75.0,72.0')] ).
cnf(123,plain,
equal(if(true__dfg,f(s(s(zero)),minus(u,zero),v,w),f(s(zero),w,v,w)),f(s(s(zero)),s(s(u)),v,w)),
inference(spr,[status(thm),theory(equality)],[3,78]),
[iquote('0:SpR:3.0,78.0')] ).
cnf(124,plain,
equal(if(false__dfg,f(s(s(s(u))),minus(zero,s(u)),v,w),f(s(s(u)),w,v,w)),f(s(s(s(u))),s(s(zero)),v,w)),
inference(spr,[status(thm),theory(equality)],[4,78]),
[iquote('0:SpR:4.0,78.0')] ).
cnf(125,plain,
equal(if(a60__a61_(u,v),f(s(s(s(u))),minus(s(v),s(u)),w,x),f(s(s(u)),x,w,x)),f(s(s(s(u))),s(s(s(v))),w,x)),
inference(spr,[status(thm),theory(equality)],[5,78]),
[iquote('0:SpR:5.0,78.0')] ).
cnf(127,plain,
equal(f(s(s(zero)),s(s(u)),v,w),f(s(s(zero)),u,v,w)),
inference(rew,[status(thm),theory(equality)],[6,123,1]),
[iquote('0:Rew:6.0,123.0,1.0,123.0')] ).
cnf(131,plain,
equal(f(s(s(u)),v,w,v),f(s(s(s(u))),s(s(zero)),w,v)),
inference(rew,[status(thm),theory(equality)],[7,124]),
[iquote('0:Rew:7.0,124.0')] ).
cnf(133,plain,
equal(if(a60__a61_(u,v),f(s(s(s(u))),minus(v,u),w,x),f(s(s(u)),x,w,x)),f(s(s(s(u))),s(s(s(v))),w,x)),
inference(rew,[status(thm),theory(equality)],[2,125]),
[iquote('0:Rew:2.0,125.0')] ).
cnf(145,plain,
equal(f(s(s(zero)),s(zero),u,s(s(v))),f(s(zero),v,u,s(s(v)))),
inference(spr,[status(thm),theory(equality)],[94,72]),
[iquote('0:SpR:94.0,72.0')] ).
cnf(158,plain,
equal(f(s(s(s(u))),s(s(zero)),v,w),f(s(s(s(u))),s(zero),v,w)),
inference(spr,[status(thm),theory(equality)],[131,75]),
[iquote('0:SpR:131.0,75.0')] ).
cnf(219,plain,
equal(f(s(s(s(zero))),zero,s(s(u)),s(s(v))),f(s(s(zero)),v,minus(u,s(zero)),s(s(v)))),
inference(spr,[status(thm),theory(equality)],[35,127]),
[iquote('0:SpR:35.0,127.0')] ).
cnf(226,plain,
equal(f(s(zero),u,v,u),f(s(s(zero)),zero,s(s(v)),u)),
inference(spr,[status(thm),theory(equality)],[1,35]),
[iquote('0:SpR:1.0,35.0')] ).
cnf(238,plain,
equal(f(s(s(zero)),zero,s(s(u)),v),f(s(s(zero)),s(zero),u,v)),
inference(spr,[status(thm),theory(equality)],[226,75]),
[iquote('0:SpR:226.0,75.0')] ).
cnf(310,plain,
equal(f(s(s(zero)),s(zero),u,s(s(s(v)))),f(s(zero),v,u,s(s(s(v))))),
inference(spr,[status(thm),theory(equality)],[145,72]),
[iquote('0:SpR:145.0,72.0')] ).
cnf(406,plain,
equal(f(s(s(zero)),s(zero),u,s(s(s(s(v))))),f(s(zero),v,u,s(s(s(s(v)))))),
inference(spr,[status(thm),theory(equality)],[310,72]),
[iquote('0:SpR:310.0,72.0')] ).
cnf(630,plain,
equal(f(s(s(zero)),s(zero),u,s(s(s(s(s(v)))))),f(s(zero),v,u,s(s(s(s(s(v))))))),
inference(spr,[status(thm),theory(equality)],[406,72]),
[iquote('0:SpR:406.0,72.0')] ).
cnf(835,plain,
equal(f(s(s(s(zero))),zero,s(s(u)),s(s(s(s(v))))),f(s(s(zero)),v,minus(u,s(zero)),s(s(s(s(v)))))),
inference(spr,[status(thm),theory(equality)],[219,127]),
[iquote('0:SpR:219.0,127.0')] ).
cnf(941,plain,
equal(f(s(s(zero)),s(zero),u,s(s(s(s(s(s(v))))))),f(s(zero),v,u,s(s(s(s(s(s(v)))))))),
inference(spr,[status(thm),theory(equality)],[630,72]),
[iquote('0:SpR:630.0,72.0')] ).
cnf(1068,plain,
equal(if(true__dfg,f(s(s(s(zero))),minus(u,zero),v,w),f(s(s(zero)),w,v,w)),f(s(s(s(zero))),s(s(s(u))),v,w)),
inference(spr,[status(thm),theory(equality)],[3,133]),
[iquote('0:SpR:3.0,133.0')] ).
cnf(1070,plain,
equal(if(a60__a61_(u,v),f(s(s(s(s(u)))),minus(s(v),s(u)),w,x),f(s(s(s(u))),x,w,x)),f(s(s(s(s(u)))),s(s(s(s(v)))),w,x)),
inference(spr,[status(thm),theory(equality)],[5,133]),
[iquote('0:SpR:5.0,133.0')] ).
cnf(1071,plain,
equal(f(s(s(s(zero))),s(s(s(u))),v,w),f(s(s(s(zero))),u,v,w)),
inference(rew,[status(thm),theory(equality)],[6,1068,1]),
[iquote('0:Rew:6.0,1068.0,1.0,1068.0')] ).
cnf(1076,plain,
equal(if(a60__a61_(u,v),f(s(s(s(s(u)))),minus(v,u),w,x),f(s(s(s(u))),x,w,x)),f(s(s(s(s(u)))),s(s(s(s(v)))),w,x)),
inference(rew,[status(thm),theory(equality)],[2,1070]),
[iquote('0:Rew:2.0,1070.0')] ).
cnf(1091,plain,
equal(f(s(s(s(zero))),u,v,s(s(s(u)))),f(s(s(s(s(zero)))),s(zero),v,s(s(s(u))))),
inference(spr,[status(thm),theory(equality)],[1071,75]),
[iquote('0:SpR:1071.0,75.0')] ).
cnf(1183,plain,
equal(f(s(s(s(s(zero)))),s(zero),u,s(s(s(s(s(s(v))))))),f(s(s(s(zero))),v,u,s(s(s(s(s(s(v)))))))),
inference(spr,[status(thm),theory(equality)],[1091,1071]),
[iquote('0:SpR:1091.0,1071.0')] ).
cnf(1572,plain,
equal(f(s(s(s(zero))),zero,s(s(u)),s(s(s(s(s(s(v))))))),f(s(s(zero)),v,minus(u,s(zero)),s(s(s(s(s(s(v)))))))),
inference(spr,[status(thm),theory(equality)],[835,127]),
[iquote('0:SpR:835.0,127.0')] ).
cnf(3407,plain,
equal(if(true__dfg,f(s(s(s(s(zero)))),minus(u,zero),v,w),f(s(s(s(zero))),w,v,w)),f(s(s(s(s(zero)))),s(s(s(s(u)))),v,w)),
inference(spr,[status(thm),theory(equality)],[3,1076]),
[iquote('0:SpR:3.0,1076.0')] ).
cnf(3410,plain,
equal(f(s(s(s(s(zero)))),s(s(s(s(u)))),v,w),f(s(s(s(s(zero)))),u,v,w)),
inference(rew,[status(thm),theory(equality)],[6,3407,1]),
[iquote('0:Rew:6.0,3407.0,1.0,3407.0')] ).
cnf(3442,plain,
equal(f(s(s(s(s(zero)))),u,v,s(s(s(s(u))))),f(s(s(s(s(s(zero))))),s(zero),v,s(s(s(s(u)))))),
inference(spr,[status(thm),theory(equality)],[3410,75]),
[iquote('0:SpR:3410.0,75.0')] ).
cnf(3589,plain,
equal(f(s(s(s(s(zero)))),s(s(zero)),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))),perfectp(s(s(s(s(s(s(zero)))))))),
inference(spr,[status(thm),theory(equality)],[3442,9]),
[iquote('0:SpR:3442.0,9.0')] ).
cnf(3599,plain,
equal(perfectp(s(s(s(s(s(s(zero))))))),true__dfg),
inference(rew,[status(thm),theory(equality)],[36,3589,941,238,1,2,1572,1183,158]),
[iquote('0:Rew:36.0,3589.0,941.0,3589.0,238.0,3589.0,1.0,3589.0,2.0,3589.0,1572.0,3589.0,1183.0,3589.0,158.0,3589.0')] ).
cnf(3600,plain,
$false,
inference(mrr,[status(thm)],[3599,14]),
[iquote('0:MRR:3599.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:48:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 1.74/1.94
% 1.74/1.94 SPASS V 3.9
% 1.74/1.94 SPASS beiseite: Proof found.
% 1.74/1.94 % SZS status Theorem
% 1.74/1.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.74/1.94 SPASS derived 2241 clauses, backtracked 0 clauses, performed 0 splits and kept 574 clauses.
% 1.74/1.94 SPASS allocated 70602 KBytes.
% 1.74/1.94 SPASS spent 0:00:01.56 on the problem.
% 1.74/1.94 0:00:00.03 for the input.
% 1.74/1.94 0:00:00.00 for the FLOTTER CNF translation.
% 1.74/1.94 0:00:00.08 for inferences.
% 1.74/1.94 0:00:00.00 for the backtracking.
% 1.74/1.94 0:00:01.41 for the reduction.
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94 Here is a proof with depth 7, length 52 :
% 1.74/1.94 % SZS output start Refutation
% See solution above
% 1.74/1.94 Formulae used in the proof : rule1 rule2 rule3 rule4 rule5 rule6 rule7 rule9 rule10 rule12 rule13 goal
% 1.74/1.94
%------------------------------------------------------------------------------