TSTP Solution File: LAT269-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 06:49:56 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 6 unt; 3 nHn; 11 RR)
% Number of literals : 22 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file('LAT269-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v_A,t_a)
| ~ c_in(v,v_A,t_a)
| equal(c_Tarski_Ointerval(v_r,u,v,t_a),c_emptyset)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,u,v,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,u,v,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
file('LAT269-2.p',unknown),
[] ).
cnf(3,axiom,
equal(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_intY1),
file('LAT269-2.p',unknown),
[] ).
cnf(4,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file('LAT269-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(c_Tarski_Ointerval(v_r,u,c_Tarski_OTop(v_cl,t_a),t_a),c_emptyset)
| ~ c_in(u,v_A,t_a) ),
file('LAT269-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT269-2.p',unknown),
[] ).
cnf(8,plain,
( ~ equal(c_emptyset,v_intY1)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a) ),
inference(spl,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpL:3.0,5.0')] ).
cnf(9,plain,
~ equal(c_emptyset,v_intY1),
inference(mrr,[status(thm)],[8,4]),
[iquote('0:MRR:8.1,4.0')] ).
cnf(11,plain,
( ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| equal(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_emptyset)
| c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.3')] ).
cnf(12,plain,
( ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| equal(c_emptyset,v_intY1)
| c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rew,[status(thm),theory(equality)],[3,11]),
[iquote('0:Rew:3.0,11.2')] ).
cnf(13,plain,
$false,
inference(mrr,[status(thm)],[12,4,1,9,6]),
[iquote('0:MRR:12.0,12.1,12.2,12.3,4.0,1.0,9.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 30 14:01:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.41
% 0.13/0.41 SPASS V 3.9
% 0.13/0.41 SPASS beiseite: Proof found.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.13/0.41 SPASS allocated 63105 KBytes.
% 0.13/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.13/0.41 0:00:00.04 for the input.
% 0.13/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.41 0:00:00.00 for inferences.
% 0.13/0.41 0:00:00.00 for the backtracking.
% 0.13/0.41 0:00:00.00 for the reduction.
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41 Here is a proof with depth 1, length 11 :
% 0.13/0.41 % SZS output start Refutation
% See solution above
% 0.13/0.41 Formulae used in the proof : cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0 cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0 cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0 cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0 cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0 cls_conjecture_0
% 0.13/0.41
%------------------------------------------------------------------------------