TSTP Solution File: LCL130-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL130-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 : Sun Jul 17 14:34:49 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 22 ( 14 unt; 0 nHn; 22 RR)
% Number of literals : 31 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL130-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))),u)),
file('LCL130-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('LCL130-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(v,w))),equivalent(equivalent(x,y),equivalent(equivalent(x,z),equivalent(y,z))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(v,w)))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(11,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,w),equivalent(v,w))) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(equivalent(u,x),equivalent(v,x)),w))),
inference(sor,[status(thm)],[11,9]),
[iquote('0:SoR:11.0,9.0')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))),y),equivalent(u,y))),
inference(sor,[status(thm)],[11,2]),
[iquote('0:SoR:11.0,2.0')] ).
cnf(17,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(equivalent(equivalent(u,x),equivalent(v,x)),w)) ),
inference(res,[status(thm),theory(equality)],[12,1]),
[iquote('0:Res:12.0,1.1')] ).
cnf(22,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))),y))
| is_a_theorem(equivalent(u,y)) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.0,1.1')] ).
cnf(26,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(equivalent(u,x),equivalent(w,x)))),
inference(sor,[status(thm)],[17,9]),
[iquote('0:SoR:17.0,9.0')] ).
cnf(31,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(equivalent(equivalent(u,x),equivalent(w,x))) ),
inference(res,[status(thm),theory(equality)],[26,1]),
[iquote('0:Res:26.0,1.1')] ).
cnf(39,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(u,v),w))),
inference(sor,[status(thm)],[31,26]),
[iquote('0:SoR:31.0,26.0')] ).
cnf(52,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(x,w)),equivalent(equivalent(u,v),x))),
inference(sor,[status(thm)],[17,39]),
[iquote('0:SoR:17.0,39.0')] ).
cnf(60,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(x,w)))
| is_a_theorem(equivalent(equivalent(u,v),x)) ),
inference(res,[status(thm),theory(equality)],[52,1]),
[iquote('0:Res:52.0,1.1')] ).
cnf(62,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,v))),
inference(sor,[status(thm)],[60,39]),
[iquote('0:SoR:60.0,39.0')] ).
cnf(70,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(u,w))),
inference(sor,[status(thm)],[17,62]),
[iquote('0:SoR:17.0,62.0')] ).
cnf(86,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(equivalent(u,w)) ),
inference(res,[status(thm),theory(equality)],[70,1]),
[iquote('0:Res:70.0,1.1')] ).
cnf(87,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[86,62]),
[iquote('0:SoR:86.0,62.0')] ).
cnf(119,plain,
is_a_theorem(equivalent(u,equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))))),
inference(sor,[status(thm)],[22,87]),
[iquote('0:SoR:22.0,87.0')] ).
cnf(120,plain,
$false,
inference(unc,[status(thm)],[119,3]),
[iquote('0:UnC:119.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL130-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 04:45:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 113 clauses, backtracked 0 clauses, performed 0 splits and kept 66 clauses.
% 0.20/0.44 SPASS allocated 75908 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.01 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.01 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 16, length 22 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : condensed_detachment p_4 prove_lg_2
% 0.20/0.44
%------------------------------------------------------------------------------