TSTP Solution File: LAT263-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 06:49:52 EDT 2022
% Result : Unsatisfiable 0.14s 0.35s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 9 unt; 0 nHn; 15 RR)
% Number of literals : 31 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A),
file('LAT263-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_in(u,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_lessequals(w,c_Tarski_Opotype_Opset(u,v,tc_Product__Type_Ounit),tc_set(v))
| c_in(c_Tarski_Olub(w,u,v),c_Tarski_Opotype_Opset(u,v,tc_Product__Type_Ounit),v) ),
file('LAT263-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT263-2.p',unknown),
[] ).
cnf(4,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT263-2.p',unknown),
[] ).
cnf(5,axiom,
equal(c_Tarski_Olub(u,c_Tarski_Odual(v,w),w),c_Tarski_Oglb(u,v,w)),
file('LAT263-2.p',unknown),
[] ).
cnf(6,axiom,
equal(c_Tarski_Opotype_Opset(c_Tarski_Odual(u,v),v,tc_Product__Type_Ounit),c_Tarski_Opotype_Opset(u,v,tc_Product__Type_Ounit)),
file('LAT263-2.p',unknown),
[] ).
cnf(7,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('LAT263-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
file('LAT263-2.p',unknown),
[] ).
cnf(14,plain,
( ~ c_in(c_Tarski_Odual(u,v),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(u,v),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_lessequals(w,c_Tarski_Opotype_Opset(c_Tarski_Odual(u,v),v,tc_Product__Type_Ounit),tc_set(v))
| c_in(c_Tarski_Oglb(w,u,v),c_Tarski_Opotype_Opset(c_Tarski_Odual(u,v),v,tc_Product__Type_Ounit),v) ),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.3')] ).
cnf(16,plain,
( ~ c_in(c_Tarski_Odual(u,v),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(u,v),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(v,tc_Product__Type_Ounit))
| ~ c_lessequals(w,c_Tarski_Opotype_Opset(u,v,tc_Product__Type_Ounit),tc_set(v))
| c_in(c_Tarski_Oglb(w,u,v),c_Tarski_Opotype_Opset(u,v,tc_Product__Type_Ounit),v) ),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.3,6.0,14.2')] ).
cnf(18,plain,
( ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(u,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Oglb(u,v_cl,t_a),v_A,t_a) ),
inference(spr,[status(thm),theory(equality)],[1,16]),
[iquote('0:SpR:1.0,16.3')] ).
cnf(20,plain,
( ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(u,v_A,tc_set(t_a))
| c_in(c_Tarski_Oglb(u,v_cl,t_a),v_A,t_a) ),
inference(rew,[status(thm),theory(equality)],[1,18]),
[iquote('0:Rew:1.0,18.2')] ).
cnf(21,plain,
( ~ c_lessequals(u,v_A,tc_set(t_a))
| c_in(c_Tarski_Oglb(u,v_cl,t_a),v_A,t_a) ),
inference(mrr,[status(thm)],[20,4,3]),
[iquote('0:MRR:20.0,20.1,4.0,3.0')] ).
cnf(23,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[21,8]),
[iquote('0:Res:21.1,8.0')] ).
cnf(24,plain,
$false,
inference(mrr,[status(thm)],[23,7]),
[iquote('0:MRR:23.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Wed Jun 29 05:42:28 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.35
% 0.14/0.35 SPASS V 3.9
% 0.14/0.35 SPASS beiseite: Proof found.
% 0.14/0.35 % SZS status Theorem
% 0.14/0.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.14/0.35 SPASS allocated 63129 KBytes.
% 0.14/0.35 SPASS spent 0:00:00.05 on the problem.
% 0.14/0.35 0:00:00.03 for the input.
% 0.14/0.35 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.35 0:00:00.00 for inferences.
% 0.14/0.35 0:00:00.00 for the backtracking.
% 0.14/0.35 0:00:00.00 for the reduction.
% 0.14/0.35
% 0.14/0.35
% 0.14/0.35 Here is a proof with depth 3, length 15 :
% 0.14/0.35 % SZS output start Refutation
% See solution above
% 0.14/0.35 Formulae used in the proof : cls_Tarski_OA_A_61_61_Apset_Acl_0 cls_Tarski_OCL_Olub__in__lattice_0 cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0 cls_Tarski_Odual_Acl_A_58_APartialOrder_0 cls_Tarski_Oglb__dual__lub_0 cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0 cls_conjecture_0 cls_conjecture_1
% 0.14/0.35
%------------------------------------------------------------------------------