%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL192-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 170.33s 170.64s
% Output : Refutation 170.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 10 unt; 0 nHn; 21 RR)
% Number of literals : 35 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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(or__dfg(p,q),r)),or__dfg(p,or__dfg(q,r)))),
file('LCL192-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL192-1.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('LCL192-1.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('LCL192-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL192-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL192-1.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('LCL192-1.p',unknown),
[] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.1')] ).
cnf(27,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[23,7]),
[iquote('0:SoR:23.0,7.1')] ).
cnf(32,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[27,4]),
[iquote('0:SoR:27.0,4.0')] ).
cnf(50,plain,
( ~ theorem(or__dfg(not__dfg(u),v))
| theorem(or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.1')] ).
cnf(54,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
inference(sor,[status(thm)],[23,32]),
[iquote('0:SoR:23.0,32.0')] ).
cnf(56,plain,
( ~ axiom(or__dfg(not__dfg(u),v))
| ~ theorem(or__dfg(not__dfg(v),w))
| theorem(or__dfg(w,not__dfg(u))) ),
inference(sor,[status(thm)],[23,9]),
[iquote('0:SoR:23.0,9.2')] ).
cnf(114,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[50,54]),
[iquote('0:SoR:50.0,54.0')] ).
cnf(291,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(or__dfg(v,u)))) ),
inference(res,[status(thm),theory(equality)],[4,56]),
[iquote('0:Res:4.0,56.0')] ).
cnf(292,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),x))
| theorem(or__dfg(x,not__dfg(or__dfg(v,or__dfg(u,w))))) ),
inference(res,[status(thm),theory(equality)],[5,56]),
[iquote('0:Res:5.0,56.0')] ).
cnf(786,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(not__dfg(or__dfg(v,u)),w)) ),
inference(sor,[status(thm)],[23,291]),
[iquote('0:SoR:23.0,291.1')] ).
cnf(1297,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),x))
| theorem(or__dfg(not__dfg(or__dfg(v,or__dfg(u,w))),x)) ),
inference(sor,[status(thm)],[23,292]),
[iquote('0:SoR:23.0,292.1')] ).
cnf(21467,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(v,or__dfg(w,u)))),
inference(res,[status(thm),theory(equality)],[114,1297]),
[iquote('0:Res:114.0,1297.0')] ).
cnf(37987,plain,
theorem(or__dfg(not__dfg(or__dfg(or__dfg(u,v),w)),or__dfg(u,or__dfg(v,w)))),
inference(res,[status(thm),theory(equality)],[21467,786]),
[iquote('0:Res:21467.0,786.0')] ).
cnf(37998,plain,
$false,
inference(unc,[status(thm)],[37987,1]),
[iquote('0:UnC:37987.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL192-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 03:34:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 170.33/170.64
% 170.33/170.64 SPASS V 3.9
% 170.33/170.64 SPASS beiseite: Proof found.
% 170.33/170.64 % SZS status Theorem
% 170.33/170.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 170.33/170.64 SPASS derived 37968 clauses, backtracked 0 clauses, performed 0 splits and kept 21829 clauses.
% 170.33/170.64 SPASS allocated 137049 KBytes.
% 170.33/170.64 SPASS spent 0:2:48.30 on the problem.
% 170.33/170.64 0:00:00.06 for the input.
% 170.33/170.64 0:00:00.00 for the FLOTTER CNF translation.
% 170.33/170.64 0:00:02.60 for inferences.
% 170.33/170.64 0:00:00.00 for the backtracking.
% 170.33/170.64 0:2:44.33 for the reduction.
% 170.33/170.64
% 170.33/170.64
% 170.33/170.64 Here is a proof with depth 7, length 21 :
% 170.33/170.64 % SZS output start Refutation
% See solution above
% 170.33/170.64 Formulae used in the proof : prove_this axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 170.33/170.64
%------------------------------------------------------------------------------