%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL194-1 : TPTP v9.3.1. Released v1.1.0.
% 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 01:07:00 PM UTC 2026
% Result : Unsatisfiable 23.36s 23.69s
% Output : Refutation 23.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 7 unt; 0 nHn; 14 RR)
% Number of literals : 24 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 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,
~ theorem(or__dfg(not__dfg(or__dfg(not__dfg(q),r)),or__dfg(not__dfg(or__dfg(q,p)),or__dfg(p,r)))),
file('LCL194-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL194-1.p',unknown),
[] ).
cnf(5,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(v,or__dfg(u,w)))),
file('LCL194-1.p',unknown),
[] ).
cnf(6,axiom,
axiom(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v)))),
file('LCL194-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL194-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL194-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(or__dfg(not__dfg(u),v))
| ~ axiom(or__dfg(not__dfg(w),u))
| theorem(or__dfg(not__dfg(w),v)) ),
file('LCL194-1.p',unknown),
[] ).
cnf(30,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.1')] ).
cnf(48,plain,
( ~ axiom(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[30,7]),
[iquote('0:SoR:30.0,7.1')] ).
cnf(61,plain,
( ~ axiom(or__dfg(not__dfg(u),v))
| ~ theorem(or__dfg(not__dfg(v),or__dfg(w,x)))
| theorem(or__dfg(w,or__dfg(not__dfg(u),x))) ),
inference(sor,[status(thm)],[30,9]),
[iquote('0:SoR:30.0,9.2')] ).
cnf(198,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(or__dfg(not__dfg(v),w)),or__dfg(u,w)))),
inference(sor,[status(thm)],[48,6]),
[iquote('0:SoR:48.0,6.0')] ).
cnf(741,plain,
( ~ axiom(or__dfg(not__dfg(u),or__dfg(v,w)))
| theorem(or__dfg(not__dfg(or__dfg(not__dfg(w),x)),or__dfg(not__dfg(u),or__dfg(v,x)))) ),
inference(res,[status(thm),theory(equality)],[198,61]),
[iquote('0:Res:198.0,61.1')] ).
cnf(14500,plain,
~ axiom(or__dfg(not__dfg(or__dfg(q,p)),or__dfg(p,q))),
inference(res,[status(thm),theory(equality)],[741,1]),
[iquote('0:Res:741.1,1.0')] ).
cnf(14518,plain,
$false,
inference(mrr,[status(thm)],[14500,4]),
[iquote('0:MRR:14500.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL194-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 18:04:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 23.36/23.69
% 23.36/23.69 SPASS V 3.9
% 23.36/23.69 SPASS beiseite: Proof found.
% 23.36/23.69 % SZS status Theorem
% 23.36/23.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.36/23.69 SPASS derived 14494 clauses, backtracked 0 clauses, performed 0 splits and kept 8180 clauses.
% 23.36/23.69 SPASS allocated 98425 KBytes.
% 23.36/23.69 SPASS spent 0:0:22.63 on the problem.
% 23.36/23.69 0:00:00.06 for the input.
% 23.36/23.69 0:00:00.00 for the FLOTTER CNF translation.
% 23.36/23.69 0:00:00.75 for inferences.
% 23.36/23.69 0:00:00.00 for the backtracking.
% 23.36/23.69 0:0:21.43 for the reduction.
% 23.36/23.69
% 23.36/23.69
% 23.36/23.69 Here is a proof with depth 5, length 14 :
% 23.36/23.69 % SZS output start Refutation
% See solution above
% 23.36/23.69 Formulae used in the proof : prove_this axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 23.36/23.69
%------------------------------------------------------------------------------