TSTP Solution File: LAT268-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 37 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-4 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('LAT268-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| ~ c_in(x,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(w,tc_Product__Type_Ounit))
| ~ c_in(x,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(w,tc_Product__Type_Ounit))
| ~ c_lessequals(v,c_Tarski_Opotype_Opset(x,w,tc_Product__Type_Ounit),tc_set(w))
| c_in(c_Pair(u,c_Tarski_Olub(v,x,w),w,w),c_Tarski_Opotype_Oorder(x,w,tc_Product__Type_Ounit),tc_prod(w,w)) ),
file('LAT268-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(c_Pair(u,v,w,w),c_Tarski_Opotype_Oorder(c_Tarski_Odual(x,w),w,tc_Product__Type_Ounit),tc_prod(w,w))
| c_in(c_Pair(v,u,w,w),c_Tarski_Opotype_Oorder(x,w,tc_Product__Type_Ounit),tc_prod(w,w)) ),
file('LAT268-2.p',unknown),
[] ).
cnf(4,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('LAT268-2.p',unknown),
[] ).
cnf(5,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('LAT268-2.p',unknown),
[] ).
cnf(6,axiom,
equal(c_Tarski_Olub(u,c_Tarski_Odual(v,w),w),c_Tarski_Oglb(u,v,w)),
file('LAT268-2.p',unknown),
[] ).
cnf(7,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('LAT268-2.p',unknown),
[] ).
cnf(8,axiom,
equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r),
file('LAT268-2.p',unknown),
[] ).
cnf(9,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('LAT268-2.p',unknown),
[] ).
cnf(10,axiom,
c_in(v_x,v_S,t_a),
file('LAT268-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('LAT268-2.p',unknown),
[] ).
cnf(12,plain,
( ~ c_in(u,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(u,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(u,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,u,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(u,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.0,2.0')] ).
cnf(19,plain,
( ~ c_in(c_Tarski_Odual(u,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(u,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(u,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(u,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(u,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.3,3.0')] ).
cnf(22,plain,
( ~ c_in(c_Tarski_Odual(u,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(u,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(u,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,u,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(u,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(rew,[status(thm),theory(equality)],[6,19,7]),
[iquote('0:Rew:6.0,19.3,7.0,19.2')] ).
cnf(24,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(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(spr,[status(thm),theory(equality)],[8,22]),
[iquote('0:SpR:8.0,22.3')] ).
cnf(26,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(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rew,[status(thm),theory(equality)],[1,24]),
[iquote('0:Rew:1.0,24.2')] ).
cnf(27,plain,
$false,
inference(mrr,[status(thm)],[26,5,4,9,11]),
[iquote('0:MRR:26.0,26.1,26.2,26.3,5.0,4.0,9.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 29 00:03:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.20/0.43 SPASS allocated 63154 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.00 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 3, length 17 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : cls_Tarski_OA_A_61_61_Apset_Acl_0 cls_Tarski_OCL_Olub__upper_0 cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_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_Tarski_Or_A_61_61_Aorder_Acl_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.20/0.43
%------------------------------------------------------------------------------