%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL238-3 : TPTP v9.3.1. Released v2.3.0.
% 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 01:07:08 PM UTC 2026
% Result : Unsatisfiable 16.55s 16.84s
% Output : Refutation 16.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 29 unt; 0 nHn; 41 RR)
% Number of literals : 55 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(and__dfg(p,q),and__dfg(q,p))),
file('LCL238-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL238-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL238-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL238-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL238-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL238-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL238-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL238-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL238-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL238-3.p',unknown),
[] ).
cnf(11,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(17,plain,
axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(18,plain,
axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(20,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(30,plain,
axiom(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(31,plain,
axiom(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[20,30]),
[iquote('0:Rew:20.0,30.0')] ).
cnf(38,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(39,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[38,17]),
[iquote('0:SoR:38.0,17.0')] ).
cnf(41,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[38,18]),
[iquote('0:SoR:38.0,18.0')] ).
cnf(42,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[38,4]),
[iquote('0:SoR:38.0,4.0')] ).
cnf(44,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[38,2]),
[iquote('0:SoR:38.0,2.0')] ).
cnf(49,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(53,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,49]),
[iquote('0:Rew:7.0,49.0')] ).
cnf(61,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[42,8]),
[iquote('0:SoR:42.0,8.1')] ).
cnf(62,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[38,6]),
[iquote('0:SoR:38.0,6.0')] ).
cnf(71,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),and__dfg(v,u))),
inference(sor,[status(thm)],[61,31]),
[iquote('0:SoR:61.0,31.0')] ).
cnf(100,plain,
theorem(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[42,71]),
[iquote('0:SoR:42.0,71.0')] ).
cnf(110,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[38,53]),
[iquote('0:SoR:38.0,53.0')] ).
cnf(124,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[41,8]),
[iquote('0:SoR:41.0,8.1')] ).
cnf(149,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[124,3]),
[iquote('0:SoR:124.0,3.0')] ).
cnf(161,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[39,149]),
[iquote('0:SoR:39.0,149.0')] ).
cnf(356,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[110,161]),
[iquote('0:SoR:110.0,161.0')] ).
cnf(358,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[44,356]),
[iquote('0:SoR:44.0,356.0')] ).
cnf(363,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[41,358]),
[iquote('0:SoR:41.0,358.0')] ).
cnf(370,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,363]),
[iquote('0:SpR:7.0,363.0')] ).
cnf(372,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[62,370]),
[iquote('0:SoR:62.0,370.0')] ).
cnf(680,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[372,9]),
[iquote('0:Res:372.0,9.1')] ).
cnf(13541,plain,
theorem(or__dfg(and__dfg(u,v),not__dfg(not__dfg(implies__dfg(v,not__dfg(u)))))),
inference(sor,[status(thm)],[680,100]),
[iquote('0:SoR:680.0,100.0')] ).
cnf(13644,plain,
theorem(or__dfg(and__dfg(u,v),not__dfg(and__dfg(v,u)))),
inference(rew,[status(thm),theory(equality)],[11,13541]),
[iquote('0:Rew:11.0,13541.0')] ).
cnf(20843,plain,
theorem(implies__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(sor,[status(thm)],[39,13644]),
[iquote('0:SoR:39.0,13644.0')] ).
cnf(20865,plain,
$false,
inference(unc,[status(thm)],[20843,1]),
[iquote('0:UnC:20843.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL238-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n026.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 : Fri Sep 4 22:19:40 UTC 2026
% 0.13/0.36 % CPUTime :
% 16.55/16.84
% 16.55/16.84 SPASS V 3.9
% 16.55/16.84 SPASS beiseite: Proof found.
% 16.55/16.84 % SZS status Theorem
% 16.55/16.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.55/16.84 SPASS derived 15884 clauses, backtracked 0 clauses, performed 0 splits and kept 5741 clauses.
% 16.55/16.84 SPASS allocated 123611 KBytes.
% 16.55/16.84 SPASS spent 0:0:16.16 on the problem.
% 16.55/16.84 0:00:00.03 for the input.
% 16.55/16.84 0:00:00.00 for the FLOTTER CNF translation.
% 16.55/16.84 0:00:00.35 for inferences.
% 16.55/16.84 0:00:00.00 for the backtracking.
% 16.55/16.84 0:0:15.68 for the reduction.
% 16.55/16.84
% 16.55/16.84
% 16.55/16.84 Here is a proof with depth 13, length 41 :
% 16.55/16.84 % SZS output start Refutation
% See solution above
% 16.55/16.84 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2 and_defn
% 16.55/16.84
%------------------------------------------------------------------------------