%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL014-1 : TPTP v9.3.1. 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:06:36 PM UTC 2026
% Result : Unsatisfiable 12.44s 12.74s
% Output : Refutation 12.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of clauses : 45 ( 19 unt; 0 nHn; 45 RR)
% Number of literals : 84 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 8 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('LCL014-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(w,equivalent(u,v)))),
file('LCL014-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
file('LCL014-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(w,equivalent(u,v))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,equivalent(v,w)),w))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(v,equivalent(w,u))))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),w)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(12,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,w),equivalent(v,equivalent(w,u)))) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(15,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(w,equivalent(u,v)),x)),x)),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(16,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(v,w),equivalent(equivalent(v,equivalent(w,u)),x)),x)) ),
inference(sor,[status(thm)],[10,12]),
[iquote('0:SoR:10.0,12.1')] ).
cnf(17,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,u),equivalent(equivalent(w,v),w))) ),
inference(sor,[status(thm)],[7,12]),
[iquote('0:SoR:7.0,12.1')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(equivalent(w,u),equivalent(v,w)))) ),
inference(sor,[status(thm)],[7,17]),
[iquote('0:SoR:7.0,17.1')] ).
cnf(21,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,u))
| is_a_theorem(equivalent(equivalent(w,v),w)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.1,1.1')] ).
cnf(27,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(w,u),equivalent(v,w))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.1,1.1')] ).
cnf(43,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(equivalent(w,v),u))) ),
inference(sor,[status(thm)],[7,27]),
[iquote('0:SoR:7.0,27.2')] ).
cnf(53,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(v,equivalent(w,equivalent(w,u)))) ),
inference(sor,[status(thm)],[7,43]),
[iquote('0:SoR:7.0,43.2')] ).
cnf(61,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(w,u))) ),
inference(res,[status(thm),theory(equality)],[53,1]),
[iquote('0:Res:53.2,1.1')] ).
cnf(62,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(w,u))) ),
inference(obv,[status(thm),theory(equality)],[61]),
[iquote('0:Obv:61.1')] ).
cnf(63,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(v,u))) ),
inference(con,[status(thm)],[62]),
[iquote('0:Con:62.1')] ).
cnf(66,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(u,equivalent(v,v))) ),
inference(sor,[status(thm)],[7,63]),
[iquote('0:SoR:7.0,63.1')] ).
cnf(69,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[63,1]),
[iquote('0:Res:63.1,1.1')] ).
cnf(74,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,v)) ),
inference(res,[status(thm),theory(equality)],[66,1]),
[iquote('0:Res:66.1,1.1')] ).
cnf(75,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,v)) ),
inference(obv,[status(thm),theory(equality)],[74]),
[iquote('0:Obv:74.0')] ).
cnf(77,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(v,equivalent(w,x)),equivalent(equivalent(x,equivalent(v,w)),equivalent(y,u))),y))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(84,plain,
is_a_theorem(equivalent(u,u)),
inference(ems,[status(thm)],[75,15]),
[iquote('0:EmS:75.0,15.0')] ).
cnf(98,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(u,v)),v)),
inference(sor,[status(thm)],[10,84]),
[iquote('0:SoR:10.0,84.0')] ).
cnf(99,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,u),v))),
inference(sor,[status(thm)],[7,84]),
[iquote('0:SoR:7.0,84.0')] ).
cnf(101,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,u),v)) ),
inference(sor,[status(thm)],[21,84]),
[iquote('0:SoR:21.1,84.0')] ).
cnf(103,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(u,v)),equivalent(v,w)),w)),
inference(sor,[status(thm)],[10,98]),
[iquote('0:SoR:10.0,98.0')] ).
cnf(107,plain,
( ~ is_a_theorem(equivalent(u,equivalent(u,v)))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[98,1]),
[iquote('0:Res:98.0,1.1')] ).
cnf(117,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,w),equivalent(equivalent(v,equivalent(w,u)),x)))
| is_a_theorem(x) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.1,1.1')] ).
cnf(132,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,u))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[101,1]),
[iquote('0:Res:101.1,1.1')] ).
cnf(153,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[107,69]),
[iquote('0:SoR:107.0,69.2')] ).
cnf(173,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),u))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[132,99]),
[iquote('0:SoR:132.1,99.0')] ).
cnf(358,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(v,u)))),
inference(sor,[status(thm)],[173,103]),
[iquote('0:SoR:173.0,103.0')] ).
cnf(366,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
inference(sor,[status(thm)],[7,358]),
[iquote('0:SoR:7.0,358.0')] ).
cnf(376,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(sor,[status(thm)],[153,366]),
[iquote('0:SoR:153.1,366.0')] ).
cnf(377,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,u),w)),w)),
inference(sor,[status(thm)],[10,366]),
[iquote('0:SoR:10.0,366.0')] ).
cnf(699,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),u)))),
inference(sor,[status(thm)],[376,377]),
[iquote('0:SoR:376.0,377.0')] ).
cnf(1025,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(x,equivalent(v,w)))))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[117,77]),
[iquote('0:SoR:117.1,77.0')] ).
cnf(1265,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(w,equivalent(v,u)))),
inference(sor,[status(thm)],[7,699]),
[iquote('0:SoR:7.0,699.0')] ).
cnf(2323,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(w,v),u))),
inference(sor,[status(thm)],[376,1265]),
[iquote('0:SoR:376.0,1265.0')] ).
cnf(4375,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(w,u),v))),
inference(sor,[status(thm)],[1025,2323]),
[iquote('0:SoR:1025.0,2323.0')] ).
cnf(7502,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(u,w)),equivalent(w,v)))),
inference(sor,[status(thm)],[7,4375]),
[iquote('0:SoR:7.0,4375.0')] ).
cnf(7512,plain,
$false,
inference(unc,[status(thm)],[7502,3]),
[iquote('0:UnC:7502.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 00:56:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 12.44/12.74
% 12.44/12.74 SPASS V 3.9
% 12.44/12.74 SPASS beiseite: Proof found.
% 12.44/12.74 % SZS status Theorem
% 12.44/12.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.44/12.74 SPASS derived 7438 clauses, backtracked 0 clauses, performed 0 splits and kept 3516 clauses.
% 12.44/12.74 SPASS allocated 85870 KBytes.
% 12.44/12.74 SPASS spent 0:0:12.15 on the problem.
% 12.44/12.74 0:00:00.06 for the input.
% 12.44/12.74 0:00:00.00 for the FLOTTER CNF translation.
% 12.44/12.74 0:00:00.51 for inferences.
% 12.44/12.74 0:00:00.00 for the backtracking.
% 12.44/12.74 0:0:11.46 for the reduction.
% 12.44/12.74
% 12.44/12.74
% 12.44/12.74 Here is a proof with depth 24, length 45 :
% 12.44/12.74 % SZS output start Refutation
% See solution above
% 12.44/12.74 Formulae used in the proof : condensed_detachment wn prove_xgf
% 12.44/12.74
%------------------------------------------------------------------------------