TSTP Solution File: LCL108-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL108-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:34:38 EDT 2022
% Result : Unsatisfiable 1.23s 1.44s
% Output : Refutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of clauses : 42 ( 26 unt; 0 nHn; 42 RR)
% Number of literals : 60 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 12 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('LCL108-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,y),equivalent(equivalent(equivalent(z,y),equivalent(z,x)),x1))),equivalent(w,equivalent(equivalent(v,u),x1)))),
file('LCL108-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
file('LCL108-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,y),equivalent(equivalent(equivalent(z,y),equivalent(z,x)),x1))))
| is_a_theorem(equivalent(w,equivalent(equivalent(v,u),x1))) ),
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(equivalent(w,v),equivalent(w,u)),x)),equivalent(equivalent(equivalent(y,z),equivalent(equivalent(x1,y),equivalent(x1,z))),x))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(x,equivalent(equivalent(y,z),equivalent(y,x1))),equivalent(x,equivalent(z,x1))),x2)),equivalent(equivalent(v,w),x2))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x))),equivalent(equivalent(equivalent(y,z),equivalent(y,x1)),x2)),equivalent(equivalent(equivalent(x3,z),equivalent(x3,x1)),x2))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(x,equivalent(equivalent(y,z),equivalent(y,x1))),equivalent(x,equivalent(z,x1))),x2)))
| is_a_theorem(equivalent(equivalent(v,w),x2)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(v,equivalent(w,y)))),equivalent(u,equivalent(x,y))),z),z)),
inference(sor,[status(thm)],[12,9]),
[iquote('0:SoR:12.0,9.0')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x))),equivalent(equivalent(equivalent(y,z),equivalent(y,x1)),x2)),equivalent(equivalent(z,x1),x2))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(17,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(v,equivalent(w,y)))),equivalent(u,equivalent(x,y))),z))
| is_a_theorem(z) ),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.1')] ).
cnf(20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x))),equivalent(equivalent(equivalent(y,z),equivalent(y,x1)),x2)))
| is_a_theorem(equivalent(equivalent(equivalent(x3,z),equivalent(x3,x1)),x2)) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(30,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,equivalent(equivalent(w,x),equivalent(w,y)))),equivalent(v,equivalent(x,y))),z),z)),
inference(sor,[status(thm)],[12,14]),
[iquote('0:SoR:12.0,14.0')] ).
cnf(35,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(v,x))),equivalent(w,x)),y),y)),
inference(sor,[status(thm)],[12,30]),
[iquote('0:SoR:12.0,30.0')] ).
cnf(38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(v,x))),equivalent(w,x)),y))
| is_a_theorem(y) ),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.1')] ).
cnf(41,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,x)),equivalent(equivalent(equivalent(y,v),equivalent(y,w)),x))),
inference(sor,[status(thm)],[20,9]),
[iquote('0:SoR:20.0,9.0')] ).
cnf(44,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,y)),equivalent(equivalent(w,x),y))),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.0,2.0')] ).
cnf(47,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(x,v),equivalent(x,w)))),
inference(sor,[status(thm)],[20,44]),
[iquote('0:SoR:20.0,44.0')] ).
cnf(51,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)],[47,1]),
[iquote('0:Res:47.0,1.1')] ).
cnf(52,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(v,w)))),
inference(sor,[status(thm)],[51,47]),
[iquote('0:SoR:51.0,47.0')] ).
cnf(63,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x))),
inference(sor,[status(thm)],[7,52]),
[iquote('0:SoR:7.0,52.0')] ).
cnf(74,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w))),
inference(sor,[status(thm)],[38,63]),
[iquote('0:SoR:38.0,63.0')] ).
cnf(81,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[74,1]),
[iquote('0:Res:74.0,1.1')] ).
cnf(104,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,u),v),v)),
inference(sor,[status(thm)],[81,41]),
[iquote('0:SoR:81.0,41.0')] ).
cnf(105,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,v),w)),equivalent(u,w))),
inference(sor,[status(thm)],[51,41]),
[iquote('0:SoR:51.0,41.0')] ).
cnf(123,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[104,1]),
[iquote('0:Res:104.0,1.1')] ).
cnf(124,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v)))),
inference(sor,[status(thm)],[123,63]),
[iquote('0:SoR:123.0,63.0')] ).
cnf(149,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,v),w)))
| is_a_theorem(equivalent(u,w)) ),
inference(res,[status(thm),theory(equality)],[105,1]),
[iquote('0:Res:105.0,1.1')] ).
cnf(155,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(equivalent(x,v),y))),equivalent(equivalent(x,w),y))),
inference(sor,[status(thm)],[17,9]),
[iquote('0:SoR:17.0,9.0')] ).
cnf(172,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,u),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[124,1]),
[iquote('0:Res:124.0,1.1')] ).
cnf(231,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(equivalent(x,v),equivalent(x,w))))),
inference(sor,[status(thm)],[172,124]),
[iquote('0:SoR:172.0,124.0')] ).
cnf(442,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[7,231]),
[iquote('0:SoR:7.0,231.0')] ).
cnf(569,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(equivalent(w,v),x))),x)),
inference(sor,[status(thm)],[149,155]),
[iquote('0:SoR:149.0,155.0')] ).
cnf(599,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,v),u))),
inference(sor,[status(thm)],[81,442]),
[iquote('0:SoR:81.0,442.0')] ).
cnf(600,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,equivalent(equivalent(w,w),v)))),
inference(sor,[status(thm)],[51,442]),
[iquote('0:SoR:51.0,442.0')] ).
cnf(626,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,v),u)) ),
inference(res,[status(thm),theory(equality)],[599,1]),
[iquote('0:Res:599.0,1.1')] ).
cnf(677,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(w,w)),equivalent(v,u))) ),
inference(sor,[status(thm)],[172,626]),
[iquote('0:SoR:172.0,626.1')] ).
cnf(829,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,equivalent(w,w)))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[677,1]),
[iquote('0:Res:677.1,1.1')] ).
cnf(1732,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,v),w),w),u)) ),
inference(sor,[status(thm)],[829,600]),
[iquote('0:SoR:829.1,600.0')] ).
cnf(1824,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,u),v),w))
| is_a_theorem(equivalent(v,w)) ),
inference(sor,[status(thm)],[81,1732]),
[iquote('0:SoR:81.0,1732.1')] ).
cnf(2706,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,u),w)),w)),
inference(sor,[status(thm)],[1824,569]),
[iquote('0:SoR:1824.0,569.0')] ).
cnf(2718,plain,
$false,
inference(unc,[status(thm)],[2706,3]),
[iquote('0:UnC:2706.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL108-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 4 07:24:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.23/1.44
% 1.23/1.44 SPASS V 3.9
% 1.23/1.44 SPASS beiseite: Proof found.
% 1.23/1.44 % SZS status Theorem
% 1.23/1.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/1.44 SPASS derived 2711 clauses, backtracked 0 clauses, performed 0 splits and kept 1244 clauses.
% 1.23/1.44 SPASS allocated 80791 KBytes.
% 1.23/1.44 SPASS spent 0:00:01.05 on the problem.
% 1.23/1.44 0:00:00.04 for the input.
% 1.23/1.44 0:00:00.00 for the FLOTTER CNF translation.
% 1.23/1.44 0:00:00.08 for inferences.
% 1.23/1.44 0:00:00.00 for the backtracking.
% 1.23/1.44 0:00:00.90 for the reduction.
% 1.23/1.44
% 1.23/1.44
% 1.23/1.44 Here is a proof with depth 25, length 42 :
% 1.23/1.44 % SZS output start Refutation
% See solution above
% 1.23/1.45 Formulae used in the proof : condensed_detachment lg_27_1690 prove_q_3
% 1.23/1.45
%------------------------------------------------------------------------------