%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL368+2 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:07:20 PM UTC 2026
% Result : Theorem 46.15s 46.42s
% Output : Refutation 46.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 20 unt; 0 nHn; 30 RR)
% Number of literals : 41 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 21 ( 21 usr; 19 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('LCL368+2.p',unknown),
[] ).
cnf(2,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(x__dfg,implies__dfg(y__dfg,z__dfg)),u__dfg),implies__dfg(implies__dfg(y__dfg,implies__dfg(x__dfg,z__dfg)),u__dfg))),
file('LCL368+2.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,u)),implies__dfg(implies__dfg(w,implies__dfg(x,implies__dfg(y,x))),z)),z),implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(x1,x2),implies__dfg(implies__dfg(x2,x3),implies__dfg(x1,x3))),implies__dfg(implies__dfg(implies__dfg(n(x4),x4),x4),x5)),x5),implies__dfg(implies__dfg(x6,implies__dfg(n(x6),x7)),x8)),x8),x9)),x9)),
file('LCL368+2.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,u)),implies__dfg(implies__dfg(w,implies__dfg(x,implies__dfg(y,x))),z)),z),implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(x1,x2),implies__dfg(implies__dfg(x2,x3),implies__dfg(x1,x3))),implies__dfg(implies__dfg(implies__dfg(n(x4),x4),x4),x5)),x5),implies__dfg(implies__dfg(x6,implies__dfg(n(x6),x7)),x8)),x8),x9)))
| is_a_theorem(x9) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[7,3]),
[iquote('0:SoR:7.0,3.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,u)),implies__dfg(implies__dfg(w,implies__dfg(x,implies__dfg(y,x))),z)),z)),
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(v,u)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(16,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,u)),implies__dfg(implies__dfg(w,implies__dfg(x,implies__dfg(y,x))),z)))
| is_a_theorem(z) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(w,x),implies__dfg(v,x))),implies__dfg(implies__dfg(implies__dfg(n(y),y),y),z)),z),implies__dfg(implies__dfg(x1,implies__dfg(n(x1),x2)),x3)),x3))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(19,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,v))),x))
| is_a_theorem(x) ),
inference(sor,[status(thm)],[16,10]),
[iquote('0:SoR:16.0,10.1')] ).
cnf(34,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),implies__dfg(implies__dfg(implies__dfg(n(x),x),x),y)),y),implies__dfg(implies__dfg(z,implies__dfg(n(z),x1)),x2)),x2)),
inference(sor,[status(thm)],[19,17]),
[iquote('0:SoR:19.0,17.0')] ).
cnf(70,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),implies__dfg(implies__dfg(implies__dfg(n(x),x),x),y)),y),implies__dfg(implies__dfg(z,implies__dfg(n(z),x1)),x2)))
| is_a_theorem(x2) ),
inference(res,[status(thm),theory(equality)],[34,1]),
[iquote('0:Res:34.0,1.1')] ).
cnf(79,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),implies__dfg(implies__dfg(implies__dfg(n(x),x),x),y)),y)),
inference(sor,[status(thm)],[70,8]),
[iquote('0:SoR:70.0,8.0')] ).
cnf(98,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,u)),w),implies__dfg(x,w))),
inference(sor,[status(thm)],[16,79]),
[iquote('0:SoR:16.0,79.0')] ).
cnf(100,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),implies__dfg(implies__dfg(implies__dfg(n(x),x),x),y)))
| is_a_theorem(y) ),
inference(res,[status(thm),theory(equality)],[79,1]),
[iquote('0:Res:79.0,1.1')] ).
cnf(103,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[70,98]),
[iquote('0:SoR:70.0,98.0')] ).
cnf(114,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[103,1]),
[iquote('0:Res:103.0,1.1')] ).
cnf(125,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[100,98]),
[iquote('0:SoR:100.0,98.0')] ).
cnf(140,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[125,1]),
[iquote('0:Res:125.0,1.1')] ).
cnf(243,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(n(u),u),u),v),v)),
inference(sor,[status(thm)],[140,79]),
[iquote('0:SoR:140.0,79.0')] ).
cnf(420,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[114,103]),
[iquote('0:SoR:114.0,103.0')] ).
cnf(1826,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[420,1]),
[iquote('0:Res:420.0,1.1')] ).
cnf(22163,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(n(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[1826,243]),
[iquote('0:SoR:1826.0,243.0')] ).
cnf(22750,plain,
is_a_theorem(implies__dfg(implies__dfg(n(u),v),implies__dfg(implies__dfg(v,u),u))),
inference(sor,[status(thm)],[1826,22163]),
[iquote('0:SoR:1826.0,22163.0')] ).
cnf(23985,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[140,22750]),
[iquote('0:SoR:140.0,22750.0')] ).
cnf(24012,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[114,23985]),
[iquote('0:SoR:114.0,23985.0')] ).
cnf(32705,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[1826,24012]),
[iquote('0:SoR:1826.0,24012.0')] ).
cnf(33836,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(implies__dfg(v,implies__dfg(u,w)),x))),
inference(sor,[status(thm)],[114,32705]),
[iquote('0:SoR:114.0,32705.0')] ).
cnf(33895,plain,
$false,
inference(unc,[status(thm)],[33836,2]),
[iquote('0:UnC:33836.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL368+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Fri Sep 4 14:13:35 UTC 2026
% 0.02/0.36 % CPUTime :
% 46.15/46.42
% 46.15/46.42 SPASS V 3.9
% 46.15/46.42 SPASS beiseite: Proof found.
% 46.15/46.42 % SZS status Theorem
% 46.15/46.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.15/46.42 SPASS derived 33776 clauses, backtracked 0 clauses, performed 0 splits and kept 7722 clauses.
% 46.15/46.42 SPASS allocated 132684 KBytes.
% 46.15/46.42 SPASS spent 0:0:44.92 on the problem.
% 46.15/46.42 0:00:00.06 for the input.
% 46.15/46.42 0:00:00.05 for the FLOTTER CNF translation.
% 46.15/46.42 0:00:01.66 for inferences.
% 46.15/46.42 0:00:00.00 for the backtracking.
% 46.15/46.42 0:0:42.91 for the reduction.
% 46.15/46.42
% 46.15/46.42
% 46.15/46.42 Here is a proof with depth 19, length 30 :
% 46.15/46.42 % SZS output start Refutation
% See solution above
% 46.15/46.42 Formulae used in the proof : condensed_detachment f3 f2
% 46.15/46.42
%------------------------------------------------------------------------------