TSTP Solution File: LAT268-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 06:49:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('LAT268-10.p',unknown),
[] ).
cnf(2,axiom,
equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A),
file('LAT268-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq(c_lessequals(u,c_Tarski_Opotype_Opset(v,w,tc_Product__Type_Ounit),tc_set(w)),true__dfg,ifeq(c_in(v,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(w,tc_Product__Type_Ounit)),true__dfg,ifeq(c_in(v,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(w,tc_Product__Type_Ounit)),true__dfg,ifeq(c_in(x,u,w),true__dfg,c_in(c_Pair(x,c_Tarski_Olub(u,v,w),w,w),c_Tarski_Opotype_Oorder(v,w,tc_Product__Type_Ounit),tc_prod(w,w)),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(4,axiom,
equal(ifeq(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)),true__dfg,c_in(c_Pair(v,u,w,w),c_Tarski_Opotype_Oorder(x,w,tc_Product__Type_Ounit),tc_prod(w,w)),true__dfg),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(5,axiom,
equal(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(6,axiom,
equal(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(7,axiom,
equal(c_Tarski_Olub(u,c_Tarski_Odual(v,w),w),c_Tarski_Oglb(u,v,w)),
file('LAT268-10.p',unknown),
[] ).
cnf(8,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('LAT268-10.p',unknown),
[] ).
cnf(9,axiom,
equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r),
file('LAT268-10.p',unknown),
[] ).
cnf(10,axiom,
equal(c_lessequals(v_S,v_A,tc_set(t_a)),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(11,axiom,
equal(c_in(v_x,v_S,t_a),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(12,axiom,
~ equal(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)),true__dfg),
file('LAT268-10.p',unknown),
[] ).
cnf(23,plain,
equal(ifeq(c_in(c_Pair(u,v,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true__dfg,c_in(c_Pair(v,u,t_a,t_a),v_r,tc_prod(t_a,t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(32,plain,
equal(ifeq(c_lessequals(u,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true__dfg,ifeq(true__dfg,true__dfg,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true__dfg,ifeq(c_in(v,u,t_a),true__dfg,c_in(c_Pair(v,c_Tarski_Olub(u,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(38,plain,
equal(ifeq(c_lessequals(u,v_A,tc_set(t_a)),true__dfg,ifeq(c_in(v,u,t_a),true__dfg,c_in(c_Pair(v,c_Tarski_Oglb(u,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true__dfg),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,32,8,1,6,7]),
[iquote('0:Rew:2.0,32.0,8.0,32.0,1.0,32.0,1.0,32.0,6.0,32.0,7.0,32.0')] ).
cnf(45,plain,
equal(ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true__dfg,ifeq(true__dfg,true__dfg,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[11,38]),
[iquote('0:SpR:11.0,38.0')] ).
cnf(48,plain,
equal(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,45,10]),
[iquote('0:Rew:1.0,45.0,10.0,45.0,1.0,45.0')] ).
cnf(64,plain,
equal(ifeq(true__dfg,true__dfg,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)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[48,23]),
[iquote('0:SpR:48.0,23.0')] ).
cnf(69,plain,
equal(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)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,64]),
[iquote('0:Rew:1.0,64.0')] ).
cnf(70,plain,
$false,
inference(mrr,[status(thm)],[69,12]),
[iquote('0:MRR:69.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 19:35:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 38 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.19/0.42 SPASS allocated 63476 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 20 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : ifeq_axiom 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
% 0.19/0.42
%------------------------------------------------------------------------------