%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL064-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 01:06:41 PM UTC 2026
% Result : Unsatisfiable 122.63s 122.95s
% Output : Refutation 122.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 31 ( 16 unt; 0 nHn; 31 RR)
% Number of literals : 49 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 7 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('LCL064-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL064-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
file('LCL064-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(a,b),implies__dfg(implies__dfg(b,c),implies__dfg(a,c)))),
file('LCL064-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(18,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(19,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[18,11]),
[iquote('0:SoR:18.0,11.1')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)),implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w)))),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(24,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[24,2]),
[iquote('0:SoR:24.0,2.0')] ).
cnf(32,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x))))),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(34,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(35,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[18,29]),
[iquote('0:SoR:18.0,29.0')] ).
cnf(41,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[34,1]),
[iquote('0:Res:34.0,1.1')] ).
cnf(46,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
inference(sor,[status(thm)],[41,11]),
[iquote('0:SoR:41.0,11.1')] ).
cnf(52,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[41,2]),
[iquote('0:SoR:41.0,2.0')] ).
cnf(57,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,u)))),
inference(sor,[status(thm)],[18,52]),
[iquote('0:SoR:18.0,52.0')] ).
cnf(79,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)))
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(128,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.1')] ).
cnf(151,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
| is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x)))) ),
inference(res,[status(thm),theory(equality)],[32,1]),
[iquote('0:Res:32.0,1.1')] ).
cnf(193,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,u),w)),implies__dfg(u,w))),
inference(sor,[status(thm)],[79,57]),
[iquote('0:SoR:79.0,57.0')] ).
cnf(279,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[128,11]),
[iquote('0:SoR:128.0,11.1')] ).
cnf(282,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),w)) ),
inference(sor,[status(thm)],[128,46]),
[iquote('0:SoR:128.0,46.1')] ).
cnf(303,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[279,1]),
[iquote('0:Res:279.1,1.1')] ).
cnf(645,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(sor,[status(thm)],[151,2]),
[iquote('0:SoR:151.0,2.0')] ).
cnf(1747,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,u)),implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[18,645]),
[iquote('0:SoR:18.0,645.0')] ).
cnf(7175,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| ~ is_a_theorem(v)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[303,282]),
[iquote('0:SoR:303.1,282.1')] ).
cnf(27817,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[7175,193]),
[iquote('0:SoR:7175.0,193.0')] ).
cnf(35674,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[27817,1747]),
[iquote('0:SoR:27817.0,1747.0')] ).
cnf(35677,plain,
$false,
inference(unc,[status(thm)],[35674,5]),
[iquote('0:UnC:35674.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL064-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 09:33:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 122.63/122.95
% 122.63/122.95 SPASS V 3.9
% 122.63/122.95 SPASS beiseite: Proof found.
% 122.63/122.95 % SZS status Theorem
% 122.63/122.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 122.63/122.95 SPASS derived 35522 clauses, backtracked 0 clauses, performed 0 splits and kept 16692 clauses.
% 122.63/122.95 SPASS allocated 137649 KBytes.
% 122.63/122.95 SPASS spent 0:02:00.77 on the problem.
% 122.63/122.95 0:00:00.06 for the input.
% 122.63/122.95 0:00:00.00 for the FLOTTER CNF translation.
% 122.63/122.95 0:00:01.89 for inferences.
% 122.63/122.95 0:00:00.00 for the backtracking.
% 122.63/122.95 0:1:58.14 for the reduction.
% 122.63/122.95
% 122.63/122.95
% 122.63/122.95 Here is a proof with depth 11, length 31 :
% 122.63/122.95 % SZS output start Refutation
% See solution above
% 122.63/122.95 Formulae used in the proof : condensed_detachment cn_18 cn_35 prove_cn_1
% 122.63/122.95
%------------------------------------------------------------------------------