TSTP Solution File: ALG007-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 3.84s 4.02s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 38 ( 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('ALG007-1.p',unknown),
[] ).
cnf(2,axiom,
equal(difference(u,difference(u,v)),difference(v,difference(v,u))),
file('ALG007-1.p',unknown),
[] ).
cnf(3,axiom,
equal(difference(difference(u,v),w),difference(difference(u,w),v)),
file('ALG007-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(difference(difference(a,c),difference(b,c)),difference(difference(a,b),c)),
file('ALG007-1.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(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(25,plain,
equal(difference(u,difference(difference(v,u),w)),u),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(29,plain,
equal(difference(difference(difference(u,v),w),x),difference(difference(difference(u,w),x),v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(43,plain,
equal(difference(difference(u,difference(u,v)),w),difference(difference(v,w),difference(v,u))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(44,plain,
equal(difference(difference(u,v),difference(w,u)),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(84,plain,
equal(difference(difference(difference(u,v),w),difference(difference(u,v),w)),difference(v,v)),
inference(spr,[status(thm),theory(equality)],[25,23]),
[iquote('0:SpR:25.0,23.0')] ).
cnf(96,plain,
equal(difference(u,u),difference(v,v)),
inference(rew,[status(thm),theory(equality)],[23,84]),
[iquote('0:Rew:23.0,84.0')] ).
cnf(99,plain,
equal(difference(u,difference(v,v)),u),
inference(spr,[status(thm),theory(equality)],[96,1]),
[iquote('0:SpR:96.0,1.0')] ).
cnf(103,plain,
equal(difference(difference(u,u),v),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[96,5]),
[iquote('0:SpR:96.0,5.0')] ).
cnf(158,plain,
equal(difference(u,difference(u,difference(u,v))),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[44,2]),
[iquote('0:SpR:44.0,2.0')] ).
cnf(166,plain,
equal(difference(difference(difference(u,v),w),difference(x,u)),difference(difference(u,v),w)),
inference(spr,[status(thm),theory(equality)],[44,3]),
[iquote('0:SpR:44.0,3.0')] ).
cnf(219,plain,
equal(difference(difference(u,v),u),difference(u,u)),
inference(spr,[status(thm),theory(equality)],[103,3]),
[iquote('0:SpR:103.0,3.0')] ).
cnf(244,plain,
equal(difference(difference(difference(u,v),w),u),difference(difference(u,u),w)),
inference(spr,[status(thm),theory(equality)],[219,3]),
[iquote('0:SpR:219.0,3.0')] ).
cnf(272,plain,
equal(difference(difference(difference(u,v),w),u),difference(u,u)),
inference(rew,[status(thm),theory(equality)],[103,244]),
[iquote('0:Rew:103.0,244.0')] ).
cnf(442,plain,
equal(difference(difference(difference(u,v),w),x),difference(difference(difference(u,w),v),x)),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(684,plain,
equal(difference(u,difference(v,difference(v,u))),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[2,158]),
[iquote('0:SpR:2.0,158.0')] ).
cnf(703,plain,
equal(difference(difference(difference(u,v),w),difference(u,u)),difference(u,difference(u,difference(difference(u,v),w)))),
inference(spr,[status(thm),theory(equality)],[272,2]),
[iquote('0:SpR:272.0,2.0')] ).
cnf(797,plain,
equal(difference(u,difference(u,difference(difference(u,v),w))),difference(difference(u,v),w)),
inference(rew,[status(thm),theory(equality)],[99,703]),
[iquote('0:Rew:99.0,703.0')] ).
cnf(926,plain,
equal(difference(difference(u,v),difference(u,w)),difference(difference(w,v),difference(w,u))),
inference(spr,[status(thm),theory(equality)],[43,3]),
[iquote('0:SpR:43.0,3.0')] ).
cnf(930,plain,
equal(difference(difference(u,difference(v,w)),difference(u,w)),difference(w,difference(w,u))),
inference(spr,[status(thm),theory(equality)],[43,44]),
[iquote('0:SpR:43.0,44.0')] ).
cnf(957,plain,
equal(difference(difference(u,v),difference(difference(w,difference(w,u)),v)),difference(difference(u,w),difference(difference(u,w),difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[43,2]),
[iquote('0:SpR:43.0,2.0')] ).
cnf(5692,plain,
equal(difference(u,difference(difference(difference(v,w),x),difference(difference(difference(v,x),w),u))),difference(u,difference(difference(v,w),x))),
inference(spr,[status(thm),theory(equality)],[442,684]),
[iquote('0:SpR:442.0,684.0')] ).
cnf(5700,plain,
equal(difference(u,difference(difference(difference(v,w),x),difference(difference(difference(v,x),w),u))),difference(u,difference(difference(v,x),w))),
inference(spr,[status(thm),theory(equality)],[442,684]),
[iquote('0:SpR:442.0,684.0')] ).
cnf(6081,plain,
equal(difference(u,difference(difference(v,w),x)),difference(u,difference(difference(v,x),w))),
inference(rew,[status(thm),theory(equality)],[5700,5692]),
[iquote('0:Rew:5700.0,5692.0')] ).
cnf(8376,plain,
equal(difference(difference(difference(u,difference(u,v)),w),difference(difference(v,w),u)),difference(u,difference(u,difference(v,w)))),
inference(spr,[status(thm),theory(equality)],[43,930]),
[iquote('0:SpR:43.0,930.0')] ).
cnf(8389,plain,
equal(difference(difference(difference(u,v),difference(u,w)),difference(difference(w,v),u)),difference(u,difference(u,difference(w,v)))),
inference(spr,[status(thm),theory(equality)],[926,930]),
[iquote('0:SpR:926.0,930.0')] ).
cnf(8435,plain,
equal(difference(difference(u,v),difference(u,w)),difference(u,difference(u,difference(w,v)))),
inference(rew,[status(thm),theory(equality)],[166,8389]),
[iquote('0:Rew:166.0,8389.0')] ).
cnf(8502,plain,
equal(difference(difference(u,v),difference(difference(w,difference(w,u)),v)),difference(difference(u,w),difference(u,difference(u,difference(v,w))))),
inference(rew,[status(thm),theory(equality)],[8435,957]),
[iquote('0:Rew:8435.0,957.0')] ).
cnf(8741,plain,
equal(difference(difference(u,difference(u,v)),w),difference(u,difference(u,difference(v,w)))),
inference(rew,[status(thm),theory(equality)],[166,8376]),
[iquote('0:Rew:166.0,8376.0')] ).
cnf(9157,plain,
equal(difference(difference(u,v),difference(w,difference(w,difference(u,v)))),difference(difference(u,w),difference(v,w))),
inference(rew,[status(thm),theory(equality)],[8741,8502,797,6081,8435]),
[iquote('0:Rew:8741.0,8502.0,797.0,8502.0,6081.0,8502.0,8435.0,8502.0')] ).
cnf(9158,plain,
equal(difference(difference(u,v),difference(w,v)),difference(difference(u,w),v)),
inference(rew,[status(thm),theory(equality)],[684,9157]),
[iquote('0:Rew:684.0,9157.0')] ).
cnf(9159,plain,
$false,
inference(unc,[status(thm)],[9158,4]),
[iquote('0:UnC:9158.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Wed Jun 8 12:52:36 EDT 2022
% 0.10/0.30 % CPUTime :
% 3.84/4.02
% 3.84/4.02 SPASS V 3.9
% 3.84/4.02 SPASS beiseite: Proof found.
% 3.84/4.02 % SZS status Theorem
% 3.84/4.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.84/4.02 SPASS derived 7433 clauses, backtracked 0 clauses, performed 0 splits and kept 1114 clauses.
% 3.84/4.02 SPASS allocated 71453 KBytes.
% 3.84/4.02 SPASS spent 0:00:03.67 on the problem.
% 3.84/4.02 0:00:00.02 for the input.
% 3.84/4.02 0:00:00.00 for the FLOTTER CNF translation.
% 3.84/4.02 0:00:00.06 for inferences.
% 3.84/4.02 0:00:00.00 for the backtracking.
% 3.84/4.02 0:00:03.56 for the reduction.
% 3.84/4.02
% 3.84/4.02
% 3.84/4.02 Here is a proof with depth 7, length 38 :
% 3.84/4.02 % SZS output start Refutation
% See solution above
% 3.84/4.02 Formulae used in the proof : set_difference_1 set_difference_2 set_difference_3_simplified prove_set_difference_3
% 3.84/4.02
%------------------------------------------------------------------------------