%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 01:06:42 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.58s
% Output : Refutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 20 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 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; 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('LCL075-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(w),not__dfg(x))),w),y),implies__dfg(implies__dfg(y,u),implies__dfg(x,u)))),
file('LCL075-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(not__dfg(a),b))),
file('LCL075-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(w),not__dfg(x))),w),y))
| is_a_theorem(implies__dfg(implies__dfg(y,u),implies__dfg(x,u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,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(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x),implies__dfg(v,x))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(14,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
inference(sor,[status(thm)],[14,11]),
[iquote('0:SoR:14.0,11.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,v)),w),implies__dfg(x,w))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(221,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[7,18]),
[iquote('0:SoR:7.0,18.0')] ).
cnf(233,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),u),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[7,221]),
[iquote('0:SoR:7.0,221.0')] ).
cnf(905,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),u),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[233,1]),
[iquote('0:Res:233.0,1.1')] ).
cnf(5216,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[905,221]),
[iquote('0:SoR:905.0,221.0')] ).
cnf(5305,plain,
$false,
inference(unc,[status(thm)],[5216,3]),
[iquote('0:UnC:5216.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n010.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 : Fri Sep 4 18:06:53 UTC 2026
% 0.08/0.34 % CPUTime :
% 1.24/1.58
% 1.24/1.58 SPASS V 3.9
% 1.24/1.58 SPASS beiseite: Proof found.
% 1.24/1.58 % SZS status Theorem
% 1.24/1.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.24/1.58 SPASS derived 5095 clauses, backtracked 0 clauses, performed 0 splits and kept 810 clauses.
% 1.24/1.58 SPASS allocated 80333 KBytes.
% 1.24/1.58 SPASS spent 0:00:01.13 on the problem.
% 1.24/1.58 0:00:00.06 for the input.
% 1.24/1.58 0:00:00.00 for the FLOTTER CNF translation.
% 1.24/1.58 0:00:00.19 for inferences.
% 1.24/1.58 0:00:00.00 for the backtracking.
% 1.24/1.58 0:00:00.82 for the reduction.
% 1.24/1.58
% 1.24/1.58
% 1.24/1.58 Here is a proof with depth 11, length 15 :
% 1.24/1.58 % SZS output start Refutation
% See solution above
% 1.24/1.58 Formulae used in the proof : condensed_detachment cn_CAMeredith prove_cn_3
% 1.24/1.58
%------------------------------------------------------------------------------