TSTP Solution File: LCL429-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL429-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:36:53 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 27 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lessequals(u,v,tc_set(tc_PropLog_Opl(w)))
| ~ c_in(x,c_PropLog_Othms(c_minus(u,y,tc_set(tc_PropLog_Opl(w))),w),tc_PropLog_Opl(w))
| c_in(x,c_PropLog_Othms(c_minus(v,y,tc_set(tc_PropLog_Opl(w))),w),tc_PropLog_Opl(w)) ),
file('LCL429-2.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(c_PropLog_Ohyps(u,c_minus(v,c_insert(w,c_emptyset,x),tc_set(x)),x),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(w,x),c_PropLog_Opl_Ofalse,x),c_minus(c_PropLog_Ohyps(u,v,x),c_insert(c_PropLog_Opl_Ovar(w,x),c_emptyset,tc_PropLog_Opl(x)),tc_set(tc_PropLog_Opl(x))),tc_PropLog_Opl(x)),tc_set(tc_PropLog_Opl(x))),
file('LCL429-2.p',unknown),
[] ).
cnf(3,axiom,
c_lessequals(c_minus(u,v,tc_set(w)),c_insert(x,c_minus(u,c_insert(x,v,w),tc_set(w)),w),tc_set(w)),
file('LCL429-2.p',unknown),
[] ).
cnf(4,axiom,
c_lessequals(c_minus(c_insert(u,c_minus(v,c_insert(w,c_emptyset,x),tc_set(x)),x),y,tc_set(x)),c_insert(u,c_minus(v,c_insert(w,y,x),tc_set(x)),x),tc_set(x)),
file('LCL429-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,c_PropLog_Othms(c_insert(v,w,tc_PropLog_Opl(x)),x),tc_PropLog_Opl(x))
| ~ c_in(u,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,c_PropLog_Opl_Ofalse,x),w,tc_PropLog_Opl(x)),x),tc_PropLog_Opl(x))
| c_in(u,c_PropLog_Othms(w,x),tc_PropLog_Opl(x)) ),
file('LCL429-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_lessequals(u,v,tc_set(tc_PropLog_Opl(w)))
| ~ c_in(x,c_PropLog_Othms(u,w),tc_PropLog_Opl(w))
| c_in(x,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) ),
file('LCL429-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,u,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('LCL429-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('LCL429-2.p',unknown),
[] ).
cnf(9,plain,
( ~ c_lessequals(c_minus(c_PropLog_Ohyps(v,u,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),v,tc_set(tc_PropLog_Opl(t_a)))
| c_in(v,c_PropLog_Othms(v,t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[7,6]),
[iquote('0:Res:7.0,6.0')] ).
cnf(10,plain,
( ~ c_lessequals(c_PropLog_Ohyps(v,u,t_a),v,tc_set(tc_PropLog_Opl(t_a)))
| c_in(v,c_PropLog_Othms(c_minus(v,v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.0,1.0')] ).
cnf(17,plain,
c_in(v,c_PropLog_Othms(c_insert(u,c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(u,v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(21,plain,
c_in(v,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(u,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(c_PropLog_Opl_Ovar(u,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(22,plain,
( ~ c_lessequals(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(u,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(c_PropLog_Opl_Ovar(u,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),w,tc_set(tc_PropLog_Opl(t_a)))
| c_in(v,c_PropLog_Othms(w,t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[21,6]),
[iquote('0:Res:21.0,6.1')] ).
cnf(25,plain,
c_in(v,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(u,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(c_PropLog_Opl_Ovar(u,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[4,22]),
[iquote('0:Res:4.0,22.0')] ).
cnf(27,plain,
( ~ c_in(v,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(u,t_a),c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(c_PropLog_Opl_Ovar(u,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,v,t_a),c_insert(c_PropLog_Opl_Ovar(u,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[25,5]),
[iquote('0:Res:25.0,5.1')] ).
cnf(28,plain,
c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,u,t_a),c_insert(c_PropLog_Opl_Ovar(v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(mrr,[status(thm)],[27,17]),
[iquote('0:MRR:27.0,17.0')] ).
cnf(29,plain,
$false,
inference(unc,[status(thm)],[28,8]),
[iquote('0:UnC:28.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL429-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 11:46:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.39
% 0.13/0.39 SPASS V 3.9
% 0.13/0.39 SPASS beiseite: Proof found.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.13/0.39 SPASS allocated 63194 KBytes.
% 0.13/0.39 SPASS spent 0:00:00.04 on the problem.
% 0.13/0.39 0:00:00.02 for the input.
% 0.13/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.39 0:00:00.00 for inferences.
% 0.13/0.39 0:00:00.00 for the backtracking.
% 0.13/0.39 0:00:00.00 for the reduction.
% 0.13/0.39
% 0.13/0.39
% 0.13/0.39 Here is a proof with depth 5, length 17 :
% 0.13/0.39 % SZS output start Refutation
% See solution above
% 0.13/0.39 Formulae used in the proof : cls_PropLog_ODiff__weaken__left_0 cls_PropLog_Ohyps__Diff_0 cls_PropLog_Oinsert__Diff__same_0 cls_PropLog_Oinsert__Diff__subset2_0 cls_PropLog_Othms__excluded__middle__rule_0 cls_PropLog_Oweaken__left_0 cls_conjecture_3 cls_conjecture_5
% 0.13/0.39
%------------------------------------------------------------------------------