%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 01:06:55 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.49s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 9 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(implies__dfg(q,r),implies__dfg(implies__dfg(p,q),implies__dfg(p,r)))),
file('LCL173-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL173-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL173-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL173-3.p',unknown),
[] ).
cnf(10,plain,
~ axiom(implies__dfg(implies__dfg(q,r),implies__dfg(implies__dfg(p,q),implies__dfg(p,r)))),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.0')] ).
cnf(44,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(46,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,44]),
[iquote('0:Rew:7.0,44.0')] ).
cnf(47,plain,
$false,
inference(unc,[status(thm)],[46,10]),
[iquote('0:UnC:46.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n029.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 03:35:25 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.23/0.49
% 0.23/0.49 SPASS V 3.9
% 0.23/0.49 SPASS beiseite: Proof found.
% 0.23/0.49 % SZS status Theorem
% 0.23/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.49 SPASS derived 31 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.23/0.49 SPASS allocated 75672 KBytes.
% 0.23/0.49 SPASS spent 0:00:00.11 on the problem.
% 0.23/0.49 0:00:00.06 for the input.
% 0.23/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.49 0:00:00.00 for inferences.
% 0.23/0.49 0:00:00.00 for the backtracking.
% 0.23/0.49 0:00:00.00 for the reduction.
% 0.23/0.49
% 0.23/0.49
% 0.23/0.49 Here is a proof with depth 1, length 8 :
% 0.23/0.49 % SZS output start Refutation
% See solution above
% 0.23/0.49 Formulae used in the proof : prove_this axiom_1_6 implies_definition rule_1
% 0.23/0.49
%------------------------------------------------------------------------------