TSTP Solution File: LCL088-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:34:31 EDT 2022
% Result : Unsatisfiable 0.58s 0.74s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 58 ( 32 unt; 0 nHn; 58 RR)
% Number of literals : 88 ( 0 equ; 31 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 : 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(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL088-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)),implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u))))),
file('LCL088-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
file('LCL088-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u)))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,implies__dfg(w,x)),y),implies__dfg(implies__dfg(implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)),implies__dfg(w,x)),y)))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),implies__dfg(y,implies__dfg(v,x)))),
inference(ems,[status(thm)],[10,8]),
[iquote('0:EmS:10.0,8.0')] ).
cnf(14,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(v,x))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(16,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w))))),
inference(sor,[status(thm)],[14,11]),
[iquote('0:SoR:14.0,11.0')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w))))),
inference(sor,[status(thm)],[14,2]),
[iquote('0:SoR:14.0,2.0')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w)))) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1)))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(23,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,implies__dfg(w,x)),y),implies__dfg(implies__dfg(implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)),implies__dfg(w,x)),y))) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(26,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(u,v)))),
inference(ems,[status(thm)],[20,17]),
[iquote('0:EmS:20.0,17.0')] ).
cnf(33,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[7,27]),
[iquote('0:SoR:7.0,27.0')] ).
cnf(48,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(implies__dfg(implies__dfg(implies__dfg(y,v),implies__dfg(z,v)),implies__dfg(v,w)),x))),
inference(ems,[status(thm)],[23,2]),
[iquote('0:EmS:23.0,2.0')] ).
cnf(52,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[33,1]),
[iquote('0:Res:33.0,1.1')] ).
cnf(53,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(ems,[status(thm)],[26,27]),
[iquote('0:EmS:26.0,27.0')] ).
cnf(63,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[53,1]),
[iquote('0:Res:53.0,1.1')] ).
cnf(67,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[63,1]),
[iquote('0:Res:63.1,1.1')] ).
cnf(71,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1))) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(84,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(v,u))),
inference(ems,[status(thm)],[52,27]),
[iquote('0:EmS:52.0,27.0')] ).
cnf(94,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[14,84]),
[iquote('0:SoR:14.0,84.0')] ).
cnf(100,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,94]),
[iquote('0:SoR:7.0,94.0')] ).
cnf(103,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[94,1]),
[iquote('0:Res:94.0,1.1')] ).
cnf(107,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[103,48]),
[iquote('0:EmS:103.0,48.0')] ).
cnf(119,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v)))),
inference(sor,[status(thm)],[7,107]),
[iquote('0:SoR:7.0,107.0')] ).
cnf(155,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x))) ),
inference(res,[status(thm),theory(equality)],[100,1]),
[iquote('0:Res:100.0,1.1')] ).
cnf(177,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),y),z),implies__dfg(implies__dfg(implies__dfg(x1,implies__dfg(v,x)),y),z))),
inference(ems,[status(thm)],[71,2]),
[iquote('0:EmS:71.0,2.0')] ).
cnf(182,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[119,1]),
[iquote('0:Res:119.0,1.1')] ).
cnf(244,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(ems,[status(thm)],[155,48]),
[iquote('0:EmS:155.0,48.0')] ).
cnf(291,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(x,implies__dfg(v,w))) ),
inference(sor,[status(thm)],[67,244]),
[iquote('0:SoR:67.1,244.0')] ).
cnf(367,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(ems,[status(thm)],[182,244]),
[iquote('0:EmS:182.0,244.0')] ).
cnf(392,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w))))),
inference(sor,[status(thm)],[7,367]),
[iquote('0:SoR:7.0,367.0')] ).
cnf(396,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,u)) ),
inference(res,[status(thm),theory(equality)],[367,1]),
[iquote('0:Res:367.0,1.1')] ).
cnf(406,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[396,367]),
[iquote('0:SoR:396.0,367.0')] ).
cnf(431,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[406,1]),
[iquote('0:Res:406.0,1.1')] ).
cnf(435,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[431,177]),
[iquote('0:EmS:431.0,177.0')] ).
cnf(500,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
inference(sor,[status(thm)],[291,406]),
[iquote('0:SoR:291.0,406.0')] ).
cnf(525,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w)))),
inference(sor,[status(thm)],[7,500]),
[iquote('0:SoR:7.0,500.0')] ).
cnf(596,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w))) ),
inference(res,[status(thm),theory(equality)],[525,1]),
[iquote('0:Res:525.0,1.1')] ).
cnf(672,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(ems,[status(thm)],[596,435]),
[iquote('0:EmS:596.0,435.0')] ).
cnf(1166,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w)))) ),
inference(res,[status(thm),theory(equality)],[392,1]),
[iquote('0:Res:392.0,1.1')] ).
cnf(2163,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(w,implies__dfg(u,v)))),
inference(ems,[status(thm)],[1166,435]),
[iquote('0:EmS:1166.0,435.0')] ).
cnf(2252,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(w,implies__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[2163,1]),
[iquote('0:Res:2163.0,1.1')] ).
cnf(2281,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[2252,672]),
[iquote('0:SoR:2252.0,672.0')] ).
cnf(2283,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),v))),
inference(sor,[status(thm)],[2252,367]),
[iquote('0:SoR:2252.0,367.0')] ).
cnf(2290,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),w))) ),
inference(sor,[status(thm)],[2252,63]),
[iquote('0:SoR:2252.0,63.1')] ).
cnf(2362,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),w)) ),
inference(res,[status(thm),theory(equality)],[2281,1]),
[iquote('0:Res:2281.0,1.1')] ).
cnf(2404,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(implies__dfg(u,w),w)) ),
inference(res,[status(thm),theory(equality)],[2290,1]),
[iquote('0:Res:2290.1,1.1')] ).
cnf(2405,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(con,[status(thm)],[2404]),
[iquote('0:Con:2404.1')] ).
cnf(2503,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2405,1]),
[iquote('0:Res:2405.1,1.1')] ).
cnf(2658,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(ems,[status(thm)],[2362,435]),
[iquote('0:EmS:2362.0,435.0')] ).
cnf(2753,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[2503,2658]),
[iquote('0:SoR:2503.1,2658.0')] ).
cnf(2769,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
inference(sor,[status(thm)],[2753,2283]),
[iquote('0:SoR:2753.0,2283.0')] ).
cnf(2840,plain,
$false,
inference(unc,[status(thm)],[2769,3]),
[iquote('0:UnC:2769.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jul 4 12:06:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.58/0.74
% 0.58/0.74 SPASS V 3.9
% 0.58/0.74 SPASS beiseite: Proof found.
% 0.58/0.74 % SZS status Theorem
% 0.58/0.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.74 SPASS derived 2784 clauses, backtracked 0 clauses, performed 0 splits and kept 449 clauses.
% 0.58/0.74 SPASS allocated 78985 KBytes.
% 0.58/0.74 SPASS spent 0:00:00.37 on the problem.
% 0.58/0.74 0:00:00.04 for the input.
% 0.58/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.74 0:00:00.07 for inferences.
% 0.58/0.74 0:00:00.00 for the backtracking.
% 0.58/0.74 0:00:00.23 for the reduction.
% 0.58/0.74
% 0.58/0.74
% 0.58/0.74 Here is a proof with depth 28, length 58 :
% 0.58/0.74 % SZS output start Refutation
% See solution above
% 0.58/0.74 Formulae used in the proof : condensed_detachment ic_JLukasiewicz_4 prove_ic_3
% 0.58/0.74
%------------------------------------------------------------------------------