%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 40.95s 41.22s
% Output : Refutation 40.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 20 RR)
% Number of literals : 31 ( 0 equ; 12 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 : 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(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL080-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL080-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
file('LCL080-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL080-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),c),implies__dfg(implies__dfg(c,a),implies__dfg(e,a)))),
file('LCL080-1.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(12,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(14,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)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(16,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)],[14,4]),
[iquote('0:SoR:14.0,4.0')] ).
cnf(17,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[14,11]),
[iquote('0:SoR:14.0,11.1')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(u,w),u),v))),
inference(sor,[status(thm)],[14,3]),
[iquote('0:SoR:14.0,3.0')] ).
cnf(28,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(implies__dfg(u,w),x))) ),
inference(sor,[status(thm)],[14,17]),
[iquote('0:SoR:14.0,17.1')] ).
cnf(33,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,w),u),v)) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(55,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)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(98,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(sor,[status(thm)],[33,2]),
[iquote('0:SoR:33.0,2.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[12,28]),
[iquote('0:SoR:12.0,28.1')] ).
cnf(275,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)],[55,175]),
[iquote('0:SoR:55.0,175.1')] ).
cnf(2616,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),v)),implies__dfg(u,implies__dfg(x,v)))),
inference(sor,[status(thm)],[275,98]),
[iquote('0:SoR:275.0,98.0')] ).
cnf(23831,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(w,u),implies__dfg(x,u)))),
inference(sor,[status(thm)],[55,2616]),
[iquote('0:SoR:55.0,2616.0')] ).
cnf(23854,plain,
$false,
inference(unc,[status(thm)],[23831,5]),
[iquote('0:UnC:23831.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 15:17:44 UTC 2026
% 0.08/0.34 % CPUTime :
% 40.95/41.22
% 40.95/41.22 SPASS V 3.9
% 40.95/41.22 SPASS beiseite: Proof found.
% 40.95/41.22 % SZS status Theorem
% 40.95/41.22 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.95/41.22 SPASS derived 23528 clauses, backtracked 0 clauses, performed 0 splits and kept 6403 clauses.
% 40.95/41.22 SPASS allocated 98991 KBytes.
% 40.95/41.22 SPASS spent 0:0:39.70 on the problem.
% 40.95/41.22 0:00:00.06 for the input.
% 40.95/41.22 0:00:00.00 for the FLOTTER CNF translation.
% 40.95/41.22 0:00:00.88 for inferences.
% 40.95/41.22 0:00:00.00 for the backtracking.
% 40.95/41.22 0:0:38.60 for the reduction.
% 40.95/41.22
% 40.95/41.22
% 40.95/41.22 Here is a proof with depth 7, length 20 :
% 40.95/41.22 % SZS output start Refutation
% See solution above
% 40.95/41.22 Formulae used in the proof : condensed_detachment ic_2 ic_3 ic_4 prove_ic_JLukasiewicz
% 40.95/41.22
%------------------------------------------------------------------------------