TSTP Solution File: ALG006-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 18:01:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 1 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(difference(u,difference(v,u)),u),
file('ALG006-1.p',unknown),
[] ).
cnf(2,axiom,
equal(difference(u,difference(u,v)),difference(v,difference(v,u))),
file('ALG006-1.p',unknown),
[] ).
cnf(3,axiom,
equal(difference(difference(u,v),difference(w,v)),difference(difference(u,w),v)),
file('ALG006-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(difference(difference(a,b),c),difference(difference(a,c),b)),
file('ALG006-1.p',unknown),
[] ).
cnf(5,plain,
equal(difference(difference(u,v),v),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(11,plain,
equal(difference(difference(u,v),difference(v,difference(v,u))),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(21,plain,
equal(difference(difference(u,v),difference(u,v)),difference(v,difference(v,difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(23,plain,
equal(difference(difference(u,v),difference(u,v)),difference(v,v)),
inference(rew,[status(thm),theory(equality)],[1,21]),
[iquote('0:Rew:1.0,21.0')] ).
cnf(24,plain,
equal(difference(difference(u,u),v),difference(v,v)),
inference(rew,[status(thm),theory(equality)],[3,23]),
[iquote('0:Rew:3.0,23.0')] ).
cnf(37,plain,
equal(difference(difference(u,u),v),difference(difference(w,w),v)),
inference(spr,[status(thm),theory(equality)],[24]),
[iquote('0:SpR:24.0,24.0')] ).
cnf(40,plain,
equal(difference(difference(difference(u,u),v),w),difference(w,w)),
inference(spr,[status(thm),theory(equality)],[24]),
[iquote('0:SpR:24.0,24.0')] ).
cnf(136,plain,
equal(difference(difference(difference(u,v),u),w),difference(w,w)),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(144,plain,
equal(difference(difference(u,v),difference(difference(w,w),v)),difference(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[24,3]),
[iquote('0:SpR:24.0,3.0')] ).
cnf(155,plain,
equal(difference(difference(u,v),difference(w,u)),difference(u,difference(v,difference(w,u)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(169,plain,
equal(difference(difference(u,difference(v,v)),w),difference(u,w)),
inference(rew,[status(thm),theory(equality)],[3,144,5]),
[iquote('0:Rew:3.0,144.0,5.0,144.0')] ).
cnf(201,plain,
equal(difference(difference(u,v),u),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[136,5]),
[iquote('0:SpR:136.0,5.0')] ).
cnf(224,plain,
equal(difference(difference(difference(u,v),u),difference(difference(w,w),x)),difference(difference(difference(w,w),x),difference(difference(w,w),x))),
inference(spr,[status(thm),theory(equality)],[136,40]),
[iquote('0:SpR:136.0,40.0')] ).
cnf(292,plain,
equal(difference(difference(difference(u,v),u),difference(difference(w,w),x)),difference(difference(w,w),x)),
inference(rew,[status(thm),theory(equality)],[24,224,3]),
[iquote('0:Rew:24.0,224.0,3.0,224.0,3.0,224.0')] ).
cnf(293,plain,
equal(difference(difference(u,u),difference(difference(v,v),w)),difference(difference(v,v),w)),
inference(rew,[status(thm),theory(equality)],[201,292]),
[iquote('0:Rew:201.0,292.0')] ).
cnf(322,plain,
equal(difference(difference(u,difference(v,v)),difference(difference(w,w),difference(difference(v,v),u))),difference(u,difference(v,v))),
inference(spr,[status(thm),theory(equality)],[37,11]),
[iquote('0:SpR:37.0,11.0')] ).
cnf(354,plain,
equal(difference(u,difference(difference(v,v),u)),difference(u,difference(v,v))),
inference(rew,[status(thm),theory(equality)],[169,322,293]),
[iquote('0:Rew:169.0,322.0,293.0,322.0')] ).
cnf(355,plain,
equal(difference(u,difference(v,v)),u),
inference(rew,[status(thm),theory(equality)],[1,354]),
[iquote('0:Rew:1.0,354.0')] ).
cnf(396,plain,
equal(difference(u,difference(difference(v,v),w)),u),
inference(spr,[status(thm),theory(equality)],[3,355]),
[iquote('0:SpR:3.0,355.0')] ).
cnf(405,plain,
equal(difference(difference(u,v),difference(u,u)),difference(u,difference(u,difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[201,2]),
[iquote('0:SpR:201.0,2.0')] ).
cnf(420,plain,
equal(difference(difference(u,v),difference(v,v)),difference(difference(u,difference(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[201,3]),
[iquote('0:SpR:201.0,3.0')] ).
cnf(434,plain,
equal(difference(u,difference(u,difference(u,v))),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[355,405]),
[iquote('0:Rew:355.0,405.0')] ).
cnf(440,plain,
equal(difference(difference(u,difference(v,w)),v),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5,420,3]),
[iquote('0:Rew:5.0,420.0,3.0,420.0')] ).
cnf(856,plain,
equal(difference(difference(u,difference(v,w)),difference(u,difference(v,w))),difference(difference(u,v),difference(u,difference(v,w)))),
inference(spr,[status(thm),theory(equality)],[440,201]),
[iquote('0:SpR:440.0,201.0')] ).
cnf(930,plain,
equal(difference(difference(u,v),difference(u,difference(v,w))),difference(difference(u,u),difference(v,w))),
inference(rew,[status(thm),theory(equality)],[3,856]),
[iquote('0:Rew:3.0,856.0')] ).
cnf(952,plain,
equal(difference(difference(u,v),difference(difference(u,v),difference(u,difference(v,difference(w,u))))),difference(u,difference(v,difference(w,u)))),
inference(spr,[status(thm),theory(equality)],[155,434]),
[iquote('0:SpR:155.0,434.0')] ).
cnf(1040,plain,
equal(difference(difference(u,v),difference(difference(u,u),difference(v,difference(w,u)))),difference(u,difference(v,difference(w,u)))),
inference(rew,[status(thm),theory(equality)],[930,952]),
[iquote('0:Rew:930.0,952.0')] ).
cnf(1041,plain,
equal(difference(u,difference(v,difference(w,u))),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[396,1040]),
[iquote('0:Rew:396.0,1040.0')] ).
cnf(1238,plain,
equal(difference(difference(u,v),difference(w,v)),difference(difference(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,1041]),
[iquote('0:SpR:1.0,1041.0')] ).
cnf(1280,plain,
equal(difference(difference(u,v),w),difference(difference(u,w),v)),
inference(rew,[status(thm),theory(equality)],[3,1238]),
[iquote('0:Rew:3.0,1238.0')] ).
cnf(1281,plain,
$false,
inference(unc,[status(thm)],[1280,4]),
[iquote('0:UnC:1280.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.20/0.34 % DateTime : Thu Jun 9 06:30:04 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 891 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.20/0.52 SPASS allocated 64047 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.52 0:00:00.04 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.08 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 8, length 35 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : set_difference_1 set_difference_2 set_difference_3 prove_set_difference_3_simplified
% 0.20/0.52
%------------------------------------------------------------------------------