TSTP Solution File: LCL102-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL102-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:34:36 EDT 2022
% Result : Unsatisfiable 43.45s 43.66s
% Output : Refutation 43.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 16 unt; 0 nHn; 24 RR)
% Number of literals : 33 ( 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 : 10 ( 10 usr; 9 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('LCL102-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),
file('LCL102-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),u)))),
file('LCL102-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v)))),
file('LCL102-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('LCL102-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,u),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(equivalent(x,v),equivalent(x,w))))),
inference(sor,[status(thm)],[11,4]),
[iquote('0:SoR:11.0,4.0')] ).
cnf(15,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),y)),equivalent(u,y))),
inference(sor,[status(thm)],[11,2]),
[iquote('0:SoR:11.0,2.0')] ).
cnf(16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x))
| is_a_theorem(x) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(28,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(u,equivalent(equivalent(x,v),equivalent(x,w)))) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.0,1.1')] ).
cnf(29,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(x,v),equivalent(x,w)))),
inference(sor,[status(thm)],[16,14]),
[iquote('0:SoR:16.0,14.0')] ).
cnf(33,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x)))),
inference(sor,[status(thm)],[16,4]),
[iquote('0:SoR:16.0,4.0')] ).
cnf(36,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(equivalent(x,v),equivalent(x,w))) ),
inference(res,[status(thm),theory(equality)],[29,1]),
[iquote('0:Res:29.0,1.1')] ).
cnf(37,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,equivalent(equivalent(w,x),equivalent(w,y)))),equivalent(u,equivalent(v,equivalent(x,y))))),
inference(sor,[status(thm)],[11,33]),
[iquote('0:SoR:11.0,33.0')] ).
cnf(77,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(v,equivalent(equivalent(x,w),u))))),
inference(sor,[status(thm)],[28,3]),
[iquote('0:SoR:28.0,3.0')] ).
cnf(98,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(v,w)))),
inference(sor,[status(thm)],[36,29]),
[iquote('0:SoR:36.0,29.0')] ).
cnf(110,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w))),
inference(sor,[status(thm)],[16,98]),
[iquote('0:SoR:16.0,98.0')] ).
cnf(120,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),y)))
| is_a_theorem(equivalent(u,y)) ),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.0,1.1')] ).
cnf(125,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[110,1]),
[iquote('0:Res:110.0,1.1')] ).
cnf(803,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,equivalent(equivalent(w,x),equivalent(w,y)))))
| is_a_theorem(equivalent(u,equivalent(v,equivalent(x,y)))) ),
inference(res,[status(thm),theory(equality)],[37,1]),
[iquote('0:Res:37.0,1.1')] ).
cnf(1931,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(equivalent(x,w),u)))),
inference(sor,[status(thm)],[120,77]),
[iquote('0:SoR:120.0,77.0')] ).
cnf(9138,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(equivalent(x,w),equivalent(x,v)),u)))),
inference(sor,[status(thm)],[125,1931]),
[iquote('0:SoR:125.0,1931.0')] ).
cnf(15832,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[803,9138]),
[iquote('0:SoR:803.0,9138.0')] ).
cnf(15861,plain,
$false,
inference(unc,[status(thm)],[15832,5]),
[iquote('0:UnC:15832.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : LCL102-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 14:23:29 EDT 2022
% 0.14/0.36 % CPUTime :
% 43.45/43.66
% 43.45/43.66 SPASS V 3.9
% 43.45/43.66 SPASS beiseite: Proof found.
% 43.45/43.66 % SZS status Theorem
% 43.45/43.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.45/43.66 SPASS derived 15849 clauses, backtracked 0 clauses, performed 0 splits and kept 7228 clauses.
% 43.45/43.66 SPASS allocated 98838 KBytes.
% 43.45/43.66 SPASS spent 0:0:42.97 on the problem.
% 43.45/43.66 0:00:00.03 for the input.
% 43.45/43.66 0:00:00.00 for the FLOTTER CNF translation.
% 43.45/43.66 0:00:00.52 for inferences.
% 43.45/43.66 0:00:00.00 for the backtracking.
% 43.45/43.66 0:0:42.28 for the reduction.
% 43.45/43.66
% 43.45/43.66
% 43.45/43.66 Here is a proof with depth 9, length 24 :
% 43.45/43.66 % SZS output start Refutation
% See solution above
% 43.45/43.66 Formulae used in the proof : condensed_detachment lg_2 q_1 q_2 prove_p_1
% 43.45/43.66
%------------------------------------------------------------------------------