%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL446-2 : TPTP v9.3.1. Released v3.2.0.
% 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 01:07:33 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Oop_A_N_62(v,u,w),w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w)),
file('LCL446-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,x,w),c_PropLog_Othms(v,w),tc_PropLog_Opl(w))
| c_in(x,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) ),
file('LCL446-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Oop_A_N_62(v,w,x),x),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,v,x),c_PropLog_Opl_Oop_A_N_62(u,w,x),x),x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x)),
file('LCL446-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v,v,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('LCL446-2.p',unknown),
[] ).
cnf(7,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Oop_A_N_62(v,w,x),x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,v,x),c_PropLog_Opl_Oop_A_N_62(u,w,x),x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x)) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.0,2.1')] ).
cnf(10,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Oop_A_N_62(v,w,x),x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v,x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x))
| c_in(c_PropLog_Opl_Oop_A_N_62(u,w,x),c_PropLog_Othms(y,x),tc_PropLog_Opl(x)) ),
inference(res,[status(thm),theory(equality)],[7,2]),
[iquote('0:Res:7.1,2.1')] ).
cnf(11,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v,w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w))
| c_in(c_PropLog_Opl_Oop_A_N_62(u,u,w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w)) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(15,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(u,u,v),c_PropLog_Othms(w,v),tc_PropLog_Opl(v)),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(19,plain,
$false,
inference(unc,[status(thm)],[15,4]),
[iquote('0:UnC:15.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL446-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n028.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 5 14:13:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.22/0.49 SPASS allocated 63118 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.00 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 4, length 9 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : cls_PropLog_Othms_OK_0 cls_PropLog_Othms_OMP_0 cls_PropLog_Othms_OS_0 cls_conjecture_0
% 0.22/0.49
%------------------------------------------------------------------------------