%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL197-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 01:07:00 PM UTC 2026
% Result : Unsatisfiable 64.56s 64.88s
% Output : Refutation 64.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 48 ( 31 unt; 0 nHn; 48 RR)
% Number of literals : 68 ( 0 equ; 21 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(or__dfg(q,or__dfg(p,q)),or__dfg(p,q))),
file('LCL197-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL197-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL197-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL197-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL197-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL197-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL197-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL197-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL197-3.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(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(20,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[19,16]),
[iquote('0:SoR:19.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,15]),
[iquote('0:SoR:19.0,15.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,4]),
[iquote('0:SoR:19.0,4.0')] ).
cnf(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(35,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[19,5]),
[iquote('0:SoR:19.0,5.0')] ).
cnf(36,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(37,plain,
axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(40,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,36]),
[iquote('0:Rew:7.0,36.0')] ).
cnf(41,plain,
axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,37]),
[iquote('0:Rew:7.0,37.0')] ).
cnf(49,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(51,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,49]),
[iquote('0:Rew:7.0,49.0')] ).
cnf(62,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,8]),
[iquote('0:SoR:20.0,8.1')] ).
cnf(63,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,40]),
[iquote('0:SoR:19.0,40.0')] ).
cnf(80,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[62,3]),
[iquote('0:SoR:62.0,3.0')] ).
cnf(81,plain,
theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
inference(sor,[status(thm)],[62,2]),
[iquote('0:SoR:62.0,2.0')] ).
cnf(89,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[19,41]),
[iquote('0:SoR:19.0,41.0')] ).
cnf(95,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,80]),
[iquote('0:SoR:23.0,80.0')] ).
cnf(102,plain,
theorem(implies__dfg(or__dfg(u,u),u)),
inference(sor,[status(thm)],[23,81]),
[iquote('0:SoR:23.0,81.0')] ).
cnf(112,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[19,51]),
[iquote('0:SoR:19.0,51.0')] ).
cnf(138,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[35,26]),
[iquote('0:SoR:35.0,26.1')] ).
cnf(189,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[63,95]),
[iquote('0:SoR:63.0,95.0')] ).
cnf(191,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,189]),
[iquote('0:SoR:27.0,189.0')] ).
cnf(196,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[63,191]),
[iquote('0:SoR:63.0,191.0')] ).
cnf(233,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[112,102]),
[iquote('0:SoR:112.0,102.0')] ).
cnf(247,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[25,196]),
[iquote('0:SoR:25.0,196.0')] ).
cnf(249,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,196]),
[iquote('0:SpR:7.0,196.0')] ).
cnf(251,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,249]),
[iquote('0:Rew:7.0,249.0')] ).
cnf(286,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[251,9]),
[iquote('0:Res:251.0,9.1')] ).
cnf(309,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),or__dfg(w,u))),
inference(sor,[status(thm)],[138,247]),
[iquote('0:SoR:138.0,247.0')] ).
cnf(686,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[286,9]),
[iquote('0:Res:286.1,9.1')] ).
cnf(1945,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,v)))
| theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[686,233]),
[iquote('0:SoR:686.1,233.0')] ).
cnf(2048,plain,
theorem(or__dfg(or__dfg(u,v),implies__dfg(or__dfg(v,w),w))),
inference(sor,[status(thm)],[25,309]),
[iquote('0:SoR:25.0,309.0')] ).
cnf(2804,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(or__dfg(w,u),v))),
inference(sor,[status(thm)],[89,2048]),
[iquote('0:SoR:89.0,2048.0')] ).
cnf(38275,plain,
theorem(implies__dfg(or__dfg(u,or__dfg(v,u)),or__dfg(v,u))),
inference(sor,[status(thm)],[1945,2804]),
[iquote('0:SoR:1945.0,2804.0')] ).
cnf(38403,plain,
$false,
inference(unc,[status(thm)],[38275,1]),
[iquote('0:UnC:38275.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL197-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n028.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 : Sat Sep 5 13:36:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 64.56/64.88
% 64.56/64.88 SPASS V 3.9
% 64.56/64.88 SPASS beiseite: Proof found.
% 64.56/64.88 % SZS status Theorem
% 64.56/64.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.56/64.88 SPASS derived 35593 clauses, backtracked 0 clauses, performed 0 splits and kept 15392 clauses.
% 64.56/64.88 SPASS allocated 121623 KBytes.
% 64.56/64.88 SPASS spent 0:01:03.74 on the problem.
% 64.56/64.88 0:00:00.04 for the input.
% 64.56/64.88 0:00:00.00 for the FLOTTER CNF translation.
% 64.56/64.88 0:00:02.33 for inferences.
% 64.56/64.88 0:00:00.00 for the backtracking.
% 64.56/64.88 0:01:00.57 for the reduction.
% 64.56/64.88
% 64.56/64.88
% 64.56/64.88 Here is a proof with depth 13, length 48 :
% 64.56/64.88 % SZS output start Refutation
% See solution above
% 64.56/64.88 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
% 64.56/64.88
%------------------------------------------------------------------------------