%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 01:06:55 PM UTC 2026
% Result : Unsatisfiable 0.47s 0.79s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 12 unt; 0 nHn; 17 RR)
% Number of literals : 24 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(implies__dfg(p,q),implies__dfg(implies__dfg(q,r),implies__dfg(p,r)))),
file('LCL174-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL174-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL174-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL174-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL174-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL174-3.p',unknown),
[] ).
cnf(19,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(31,plain,
axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(35,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,31]),
[iquote('0:Rew:7.0,31.0')] ).
cnf(44,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(46,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,44]),
[iquote('0:Rew:7.0,44.0')] ).
cnf(62,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,35]),
[iquote('0:SpR:7.0,35.0')] ).
cnf(64,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,62]),
[iquote('0:Rew:7.0,62.0')] ).
cnf(126,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,64]),
[iquote('0:SoR:19.0,64.0')] ).
cnf(512,plain,
( ~ axiom(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[126,8]),
[iquote('0:SoR:126.0,8.1')] ).
cnf(1401,plain,
theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[512,46]),
[iquote('0:SoR:512.0,46.0')] ).
cnf(1408,plain,
$false,
inference(unc,[status(thm)],[1401,1]),
[iquote('0:UnC:1401.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n005.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 11:33:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.47/0.79
% 0.47/0.79 SPASS V 3.9
% 0.47/0.79 SPASS beiseite: Proof found.
% 0.47/0.79 % SZS status Theorem
% 0.47/0.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.79 SPASS derived 1317 clauses, backtracked 0 clauses, performed 0 splits and kept 655 clauses.
% 0.47/0.79 SPASS allocated 77323 KBytes.
% 0.47/0.79 SPASS spent 0:00:00.40 on the problem.
% 0.47/0.79 0:00:00.06 for the input.
% 0.47/0.79 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.79 0:00:00.06 for inferences.
% 0.47/0.79 0:00:00.00 for the backtracking.
% 0.47/0.79 0:00:00.23 for the reduction.
% 0.47/0.79
% 0.47/0.79
% 0.47/0.79 Here is a proof with depth 5, length 17 :
% 0.47/0.79 % SZS output start Refutation
% See solution above
% 0.47/0.79 Formulae used in the proof : prove_this axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 0.47/0.79
%------------------------------------------------------------------------------