%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL188-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 01:06:59 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 16 unt; 0 nHn; 24 RR)
% Number of literals : 34 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(p,implies__dfg(or__dfg(p,q),q))),
file('LCL188-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL188-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL188-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL188-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL188-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL188-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL188-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL188-3.p',unknown),
[] ).
cnf(15,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(16,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(18,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(21,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[18,16]),
[iquote('0:SoR:18.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,15]),
[iquote('0:SoR:18.0,15.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(30,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(34,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,30]),
[iquote('0:Rew:7.0,30.0')] ).
cnf(52,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[18,34]),
[iquote('0:SoR:18.0,34.0')] ).
cnf(73,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[21,8]),
[iquote('0:SoR:21.0,8.1')] ).
cnf(87,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[73,3]),
[iquote('0:SoR:73.0,3.0')] ).
cnf(99,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,87]),
[iquote('0:SoR:23.0,87.0')] ).
cnf(150,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[52,99]),
[iquote('0:SoR:52.0,99.0')] ).
cnf(152,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,150]),
[iquote('0:SoR:27.0,150.0')] ).
cnf(157,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[52,152]),
[iquote('0:SoR:52.0,152.0')] ).
cnf(159,plain,
$false,
inference(unc,[status(thm)],[157,1]),
[iquote('0:UnC:157.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL188-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 19:25:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.20/0.51
% 0.20/0.51 SPASS V 3.9
% 0.20/0.51 SPASS beiseite: Proof found.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51 SPASS derived 129 clauses, backtracked 0 clauses, performed 0 splits and kept 95 clauses.
% 0.20/0.51 SPASS allocated 75823 KBytes.
% 0.20/0.51 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.51 0:00:00.06 for the input.
% 0.20/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.51 0:00:00.00 for inferences.
% 0.20/0.51 0:00:00.00 for the backtracking.
% 0.20/0.51 0:00:00.01 for the reduction.
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 Here is a proof with depth 8, length 24 :
% 0.20/0.51 % SZS output start Refutation
% See solution above
% 0.20/0.51 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 implies_definition rule_1 rule_2
% 0.20/0.51
%------------------------------------------------------------------------------