TSTP Solution File: SEU387+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU387+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n027.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 : 300s
% DateTime : Thu Aug 31 16:19:37 EDT 2023
% Result : Theorem 0.67s 0.79s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU387+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n027.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 : 300
% 0.13/0.34 % DateTime : Wed Aug 23 16:18:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.76 %-------------------------------------------
% 0.20/0.76 % File :CSE---1.6
% 0.20/0.76 % Problem :theBenchmark
% 0.20/0.76 % Transform :cnf
% 0.20/0.76 % Format :tptp:raw
% 0.20/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.76
% 0.20/0.76 % Result :Theorem 0.110000s
% 0.20/0.76 % Output :CNFRefutation 0.110000s
% 0.20/0.76 %-------------------------------------------
% 0.67/0.76 %------------------------------------------------------------------------------
% 0.67/0.76 % File : SEU387+1 : TPTP v8.1.2. Released v3.3.0.
% 0.67/0.76 % Domain : Set theory
% 0.67/0.76 % Problem : MPTP bushy problem t2_yellow19
% 0.67/0.76 % Version : [Urb07] axioms : Especial.
% 0.67/0.76 % English :
% 0.67/0.76
% 0.67/0.76 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.67/0.76 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.67/0.76 % Source : [Urb07]
% 0.67/0.76 % Names : bushy-t2_yellow19 [Urb07]
% 0.67/0.76
% 0.67/0.76 % Status : Theorem
% 0.67/0.76 % Rating : 0.25 v7.5.0, 0.28 v7.4.0, 0.17 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.17 v6.2.0, 0.24 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.30 v5.4.0, 0.36 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.1, 0.39 v4.0.0, 0.42 v3.7.0, 0.45 v3.5.0, 0.47 v3.3.0
% 0.67/0.76 % Syntax : Number of formulae : 85 ( 15 unt; 0 def)
% 0.67/0.76 % Number of atoms : 406 ( 7 equ)
% 0.67/0.76 % Maximal formula atoms : 20 ( 4 avg)
% 0.67/0.76 % Number of connectives : 397 ( 76 ~; 1 |; 255 &)
% 0.67/0.76 % ( 3 <=>; 62 =>; 0 <=; 0 <~>)
% 0.67/0.76 % Maximal formula depth : 21 ( 6 avg)
% 0.67/0.76 % Maximal term depth : 4 ( 1 avg)
% 0.67/0.76 % Number of predicates : 37 ( 35 usr; 1 prp; 0-3 aty)
% 0.67/0.76 % Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% 0.67/0.76 % Number of variables : 117 ( 90 !; 27 ?)
% 0.67/0.76 % SPC : FOF_THM_RFO_SEQ
% 0.67/0.76
% 0.67/0.76 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.67/0.76 % library, www.mizar.org
% 0.67/0.76 %------------------------------------------------------------------------------
% 0.67/0.76 fof(abstractness_v1_orders_2,axiom,
% 0.67/0.76 ! [A] :
% 0.67/0.76 ( rel_str(A)
% 0.67/0.76 => ( strict_rel_str(A)
% 0.67/0.76 => A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ) ).
% 0.67/0.76
% 0.67/0.76 fof(antisymmetry_r2_hidden,axiom,
% 0.67/0.76 ! [A,B] :
% 0.67/0.76 ( in(A,B)
% 0.67/0.76 => ~ in(B,A) ) ).
% 0.67/0.76
% 0.67/0.76 fof(cc10_waybel_0,axiom,
% 0.67/0.76 ! [A] :
% 0.67/0.76 ( rel_str(A)
% 0.67/0.76 => ( ( ~ empty_carrier(A)
% 0.67/0.76 & reflexive_relstr(A)
% 0.67/0.76 & complete_relstr(A) )
% 0.67/0.76 => ( ~ empty_carrier(A)
% 0.67/0.76 & reflexive_relstr(A)
% 0.67/0.76 & up_complete_relstr(A)
% 0.67/0.76 & join_complete_relstr(A) ) ) ) ).
% 0.67/0.76
% 0.67/0.76 fof(cc11_waybel_0,axiom,
% 0.67/0.76 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & join_complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & lower_bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc12_waybel_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & transitive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & lower_bounded_relstr(A)
% 0.67/0.77 & up_complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & transitive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & with_infima_relstr(A)
% 0.67/0.77 & complete_relstr(A)
% 0.67/0.77 & lower_bounded_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A)
% 0.67/0.77 & bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc13_waybel_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & join_complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & with_infima_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc14_waybel_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A)
% 0.67/0.77 & join_complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc1_finset_1,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( empty(A)
% 0.67/0.77 => finite(A) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc1_lattice3,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( with_suprema_relstr(A)
% 0.67/0.77 => ~ empty_carrier(A) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc1_relat_1,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( empty(A)
% 0.67/0.77 => relation(A) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc1_relset_1,axiom,
% 0.67/0.77 ! [A,B,C] :
% 0.67/0.77 ( element(C,powerset(cartesian_product2(A,B)))
% 0.67/0.77 => relation(C) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc1_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & with_infima_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc2_finset_1,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( finite(A)
% 0.67/0.77 => ! [B] :
% 0.67/0.77 ( element(B,powerset(A))
% 0.67/0.77 => finite(B) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc2_lattice3,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( with_infima_relstr(A)
% 0.67/0.77 => ~ empty_carrier(A) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc2_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & trivial_carrier(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & transitive_relstr(A)
% 0.67/0.77 & antisymmetric_relstr(A)
% 0.67/0.77 & complete_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc3_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc4_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( bounded_relstr(A)
% 0.67/0.77 => ( lower_bounded_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc5_waybel_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & trivial_carrier(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & connected_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc5_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( lower_bounded_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A) )
% 0.67/0.77 => bounded_relstr(A) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(cc9_waybel_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => ( ( reflexive_relstr(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & up_complete_relstr(A) )
% 0.67/0.77 => ( ~ empty_carrier(A)
% 0.67/0.77 & reflexive_relstr(A)
% 0.67/0.77 & with_suprema_relstr(A)
% 0.67/0.77 & upper_bounded_relstr(A) ) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_g1_orders_2,axiom,
% 0.67/0.77 ! [A,B] :
% 0.67/0.77 ( relation_of2(B,A,A)
% 0.67/0.77 => ( strict_rel_str(rel_str_of(A,B))
% 0.67/0.77 & rel_str(rel_str_of(A,B)) ) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_k1_xboole_0,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_k1_zfmisc_1,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_k2_zfmisc_1,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_k3_yellow_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => element(bottom_of_relstr(A),the_carrier(A)) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_k3_yellow_1,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( strict_rel_str(boole_POSet(A))
% 0.67/0.77 & rel_str(boole_POSet(A)) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_l1_orders_2,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => one_sorted_str(A) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_l1_struct_0,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_m1_relset_1,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_m1_subset_1,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(dt_m2_relset_1,axiom,
% 0.67/0.77 ! [A,B,C] :
% 0.67/0.77 ( relation_of2_as_subset(C,A,B)
% 0.67/0.77 => element(C,powerset(cartesian_product2(A,B))) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_u1_orders_2,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( rel_str(A)
% 0.67/0.77 => relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ) ).
% 0.67/0.77
% 0.67/0.77 fof(dt_u1_struct_0,axiom,
% 0.67/0.77 $true ).
% 0.67/0.77
% 0.67/0.77 fof(existence_l1_orders_2,axiom,
% 0.67/0.77 ? [A] : rel_str(A) ).
% 0.67/0.77
% 0.67/0.77 fof(existence_l1_struct_0,axiom,
% 0.67/0.77 ? [A] : one_sorted_str(A) ).
% 0.67/0.77
% 0.67/0.77 fof(existence_m1_relset_1,axiom,
% 0.67/0.77 ! [A,B] :
% 0.67/0.77 ? [C] : relation_of2(C,A,B) ).
% 0.67/0.77
% 0.67/0.77 fof(existence_m1_subset_1,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ? [B] : element(B,A) ).
% 0.67/0.77
% 0.67/0.77 fof(existence_m2_relset_1,axiom,
% 0.67/0.77 ! [A,B] :
% 0.67/0.77 ? [C] : relation_of2_as_subset(C,A,B) ).
% 0.67/0.77
% 0.67/0.77 fof(fc12_relat_1,axiom,
% 0.67/0.77 ( empty(empty_set)
% 0.67/0.77 & relation(empty_set)
% 0.67/0.77 & relation_empty_yielding(empty_set) ) ).
% 0.67/0.77
% 0.67/0.77 fof(fc14_finset_1,axiom,
% 0.67/0.77 ! [A,B] :
% 0.67/0.77 ( ( finite(A)
% 0.67/0.77 & finite(B) )
% 0.67/0.77 => finite(cartesian_product2(A,B)) ) ).
% 0.67/0.77
% 0.67/0.77 fof(fc1_struct_0,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( ( ~ empty_carrier(A)
% 0.67/0.77 & one_sorted_str(A) )
% 0.67/0.77 => ~ empty(the_carrier(A)) ) ).
% 0.67/0.77
% 0.67/0.77 fof(fc1_subset_1,axiom,
% 0.67/0.77 ! [A] : ~ empty(powerset(A)) ).
% 0.67/0.77
% 0.67/0.77 fof(fc1_waybel_7,axiom,
% 0.67/0.77 ! [A] :
% 0.67/0.77 ( ~ empty_carrier(boole_POSet(A))
% 0.67/0.77 & strict_rel_str(boole_POSet(A))
% 0.67/0.77 & reflexive_relstr(boole_POSet(A))
% 0.67/0.77 & transitive_relstr(boole_POSet(A))
% 0.67/0.78 & antisymmetric_relstr(boole_POSet(A))
% 0.67/0.78 & lower_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & upper_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & bounded_relstr(boole_POSet(A))
% 0.67/0.78 & up_complete_relstr(boole_POSet(A))
% 0.67/0.78 & join_complete_relstr(boole_POSet(A))
% 0.67/0.78 & ~ v1_yellow_3(boole_POSet(A))
% 0.67/0.78 & distributive_relstr(boole_POSet(A))
% 0.67/0.78 & heyting_relstr(boole_POSet(A))
% 0.67/0.78 & complemented_relstr(boole_POSet(A))
% 0.67/0.78 & boolean_relstr(boole_POSet(A))
% 0.67/0.78 & with_suprema_relstr(boole_POSet(A))
% 0.67/0.78 & with_infima_relstr(boole_POSet(A))
% 0.67/0.78 & complete_relstr(boole_POSet(A)) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc2_waybel_7,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 => ( ~ empty_carrier(boole_POSet(A))
% 0.67/0.78 & ~ trivial_carrier(boole_POSet(A))
% 0.67/0.78 & strict_rel_str(boole_POSet(A))
% 0.67/0.78 & reflexive_relstr(boole_POSet(A))
% 0.67/0.78 & transitive_relstr(boole_POSet(A))
% 0.67/0.78 & antisymmetric_relstr(boole_POSet(A))
% 0.67/0.78 & lower_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & upper_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & bounded_relstr(boole_POSet(A))
% 0.67/0.78 & up_complete_relstr(boole_POSet(A))
% 0.67/0.78 & join_complete_relstr(boole_POSet(A))
% 0.67/0.78 & ~ v1_yellow_3(boole_POSet(A))
% 0.67/0.78 & distributive_relstr(boole_POSet(A))
% 0.67/0.78 & heyting_relstr(boole_POSet(A))
% 0.67/0.78 & complemented_relstr(boole_POSet(A))
% 0.67/0.78 & boolean_relstr(boole_POSet(A))
% 0.67/0.78 & with_suprema_relstr(boole_POSet(A))
% 0.67/0.78 & with_infima_relstr(boole_POSet(A))
% 0.67/0.78 & complete_relstr(boole_POSet(A)) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc4_relat_1,axiom,
% 0.67/0.78 ( empty(empty_set)
% 0.67/0.78 & relation(empty_set) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc4_subset_1,axiom,
% 0.67/0.78 ! [A,B] :
% 0.67/0.78 ( ( ~ empty(A)
% 0.67/0.78 & ~ empty(B) )
% 0.67/0.78 => ~ empty(cartesian_product2(A,B)) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc7_yellow_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty_carrier(boole_POSet(A))
% 0.67/0.78 & strict_rel_str(boole_POSet(A))
% 0.67/0.78 & reflexive_relstr(boole_POSet(A))
% 0.67/0.78 & transitive_relstr(boole_POSet(A))
% 0.67/0.78 & antisymmetric_relstr(boole_POSet(A)) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc8_yellow_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty_carrier(boole_POSet(A))
% 0.67/0.78 & strict_rel_str(boole_POSet(A))
% 0.67/0.78 & reflexive_relstr(boole_POSet(A))
% 0.67/0.78 & transitive_relstr(boole_POSet(A))
% 0.67/0.78 & antisymmetric_relstr(boole_POSet(A))
% 0.67/0.78 & lower_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & upper_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & bounded_relstr(boole_POSet(A))
% 0.67/0.78 & with_suprema_relstr(boole_POSet(A))
% 0.67/0.78 & with_infima_relstr(boole_POSet(A))
% 0.67/0.78 & complete_relstr(boole_POSet(A)) ) ).
% 0.67/0.78
% 0.67/0.78 fof(fc8_yellow_6,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty_carrier(boole_POSet(A))
% 0.67/0.78 & strict_rel_str(boole_POSet(A))
% 0.67/0.78 & reflexive_relstr(boole_POSet(A))
% 0.67/0.78 & transitive_relstr(boole_POSet(A))
% 0.67/0.78 & antisymmetric_relstr(boole_POSet(A))
% 0.67/0.78 & lower_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & upper_bounded_relstr(boole_POSet(A))
% 0.67/0.78 & bounded_relstr(boole_POSet(A))
% 0.67/0.78 & directed_relstr(boole_POSet(A))
% 0.67/0.78 & up_complete_relstr(boole_POSet(A))
% 0.67/0.78 & join_complete_relstr(boole_POSet(A))
% 0.67/0.78 & ~ v1_yellow_3(boole_POSet(A))
% 0.67/0.78 & with_suprema_relstr(boole_POSet(A))
% 0.67/0.78 & with_infima_relstr(boole_POSet(A))
% 0.67/0.78 & complete_relstr(boole_POSet(A)) ) ).
% 0.67/0.78
% 0.67/0.78 fof(free_g1_orders_2,axiom,
% 0.67/0.78 ! [A,B] :
% 0.67/0.78 ( relation_of2(B,A,A)
% 0.67/0.78 => ! [C,D] :
% 0.67/0.78 ( rel_str_of(A,B) = rel_str_of(C,D)
% 0.67/0.78 => ( A = C
% 0.67/0.78 & B = D ) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc10_waybel_0,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ( ~ empty_carrier(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & rel_str(A) )
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(the_carrier(A)))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & filtered_subset(B,A)
% 0.67/0.78 & upper_relstr_subset(B,A) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc12_waybel_0,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & connected_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc13_waybel_0,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & with_suprema_relstr(A)
% 0.67/0.78 & with_infima_relstr(A)
% 0.67/0.78 & complete_relstr(A)
% 0.67/0.78 & lower_bounded_relstr(A)
% 0.67/0.78 & upper_bounded_relstr(A)
% 0.67/0.78 & bounded_relstr(A)
% 0.67/0.78 & up_complete_relstr(A)
% 0.67/0.78 & join_complete_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_finset_1,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 & finite(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_lattice3,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & complete_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_relat_1,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( empty(A)
% 0.67/0.78 & relation(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_subset_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(A))
% 0.67/0.78 & ~ empty(B) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_waybel_7,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & ~ trivial_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & lower_bounded_relstr(A)
% 0.67/0.78 & upper_bounded_relstr(A)
% 0.67/0.78 & bounded_relstr(A)
% 0.67/0.78 & ~ v1_yellow_3(A)
% 0.67/0.78 & distributive_relstr(A)
% 0.67/0.78 & heyting_relstr(A)
% 0.67/0.78 & complemented_relstr(A)
% 0.67/0.78 & boolean_relstr(A)
% 0.67/0.78 & with_suprema_relstr(A)
% 0.67/0.78 & with_infima_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc1_yellow_0,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & with_suprema_relstr(A)
% 0.67/0.78 & with_infima_relstr(A)
% 0.67/0.78 & complete_relstr(A)
% 0.67/0.78 & trivial_carrier(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc2_lattice3,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & with_suprema_relstr(A)
% 0.67/0.78 & with_infima_relstr(A)
% 0.67/0.78 & complete_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc2_relat_1,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 & relation(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc2_subset_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ? [B] :
% 0.67/0.78 ( element(B,powerset(A))
% 0.67/0.78 & empty(B) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc2_waybel_7,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ? [B] :
% 0.67/0.78 ( element(B,powerset(powerset(A)))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & finite(B) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc2_yellow_0,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & with_suprema_relstr(A)
% 0.67/0.78 & with_infima_relstr(A)
% 0.67/0.78 & complete_relstr(A)
% 0.67/0.78 & lower_bounded_relstr(A)
% 0.67/0.78 & upper_bounded_relstr(A)
% 0.67/0.78 & bounded_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc3_finset_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(A))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & finite(B) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc3_relat_1,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( relation(A)
% 0.67/0.78 & relation_empty_yielding(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc3_struct_0,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( one_sorted_str(A)
% 0.67/0.78 & ~ empty_carrier(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc3_waybel_7,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( one_sorted_str(A)
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(powerset(the_carrier(A))))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & finite(B) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc4_finset_1,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ~ empty(A)
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(A))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & finite(B) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc4_waybel_7,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ( ~ empty_carrier(A)
% 0.67/0.78 & ~ trivial_carrier(A)
% 0.67/0.78 & reflexive_relstr(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & antisymmetric_relstr(A)
% 0.67/0.78 & upper_bounded_relstr(A)
% 0.67/0.78 & rel_str(A) )
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(the_carrier(A)))
% 0.67/0.78 & ~ empty(B)
% 0.67/0.78 & proper_element(B,powerset(the_carrier(A)))
% 0.67/0.78 & filtered_subset(B,A)
% 0.67/0.78 & upper_relstr_subset(B,A) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc4_yellow_6,axiom,
% 0.67/0.78 ? [A] :
% 0.67/0.78 ( rel_str(A)
% 0.67/0.78 & ~ empty_carrier(A)
% 0.67/0.78 & strict_rel_str(A)
% 0.67/0.78 & transitive_relstr(A)
% 0.67/0.78 & directed_relstr(A) ) ).
% 0.67/0.78
% 0.67/0.78 fof(rc5_struct_0,axiom,
% 0.67/0.78 ! [A] :
% 0.67/0.78 ( ( ~ empty_carrier(A)
% 0.67/0.78 & one_sorted_str(A) )
% 0.67/0.78 => ? [B] :
% 0.67/0.78 ( element(B,powerset(the_carrier(A)))
% 0.67/0.78 & ~ empty(B) ) ) ).
% 0.67/0.78
% 0.67/0.78 fof(redefinition_m2_relset_1,axiom,
% 0.67/0.78 ! [A,B,C] :
% 0.67/0.78 ( relation_of2_as_subset(C,A,B)
% 0.67/0.78 <=> relation_of2(C,A,B) ) ).
% 0.67/0.78
% 0.67/0.78 fof(reflexivity_r1_tarski,axiom,
% 0.67/0.78 ! [A,B] : subset(A,A) ).
% 0.67/0.78
% 0.67/0.78 fof(t18_yellow_1,axiom,
% 0.67/0.78 ! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set ).
% 0.67/0.78
% 0.67/0.78 fof(t1_subset,axiom,
% 0.67/0.78 ! [A,B] :
% 0.67/0.79 ( in(A,B)
% 0.67/0.79 => element(A,B) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t2_subset,axiom,
% 0.67/0.79 ! [A,B] :
% 0.67/0.79 ( element(A,B)
% 0.67/0.79 => ( empty(B)
% 0.67/0.79 | in(A,B) ) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t2_yellow19,conjecture,
% 0.67/0.79 ! [A] :
% 0.67/0.79 ( ~ empty(A)
% 0.67/0.79 => ! [B] :
% 0.67/0.79 ( ( ~ empty(B)
% 0.67/0.79 & filtered_subset(B,boole_POSet(A))
% 0.67/0.79 & upper_relstr_subset(B,boole_POSet(A))
% 0.67/0.79 & proper_element(B,powerset(the_carrier(boole_POSet(A))))
% 0.67/0.79 & element(B,powerset(the_carrier(boole_POSet(A)))) )
% 0.67/0.79 => ! [C] :
% 0.67/0.79 ~ ( in(C,B)
% 0.67/0.79 & empty(C) ) ) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t3_subset,axiom,
% 0.67/0.79 ! [A,B] :
% 0.67/0.79 ( element(A,powerset(B))
% 0.67/0.79 <=> subset(A,B) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t4_subset,axiom,
% 0.67/0.79 ! [A,B,C] :
% 0.67/0.79 ( ( in(A,B)
% 0.67/0.79 & element(B,powerset(C)) )
% 0.67/0.79 => element(A,C) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t5_subset,axiom,
% 0.67/0.79 ! [A,B,C] :
% 0.67/0.79 ~ ( in(A,B)
% 0.67/0.79 & element(B,powerset(C))
% 0.67/0.79 & empty(C) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t6_boole,axiom,
% 0.67/0.79 ! [A] :
% 0.67/0.79 ( empty(A)
% 0.67/0.79 => A = empty_set ) ).
% 0.67/0.79
% 0.67/0.79 fof(t7_boole,axiom,
% 0.67/0.79 ! [A,B] :
% 0.67/0.79 ~ ( in(A,B)
% 0.67/0.79 & empty(B) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t8_boole,axiom,
% 0.67/0.79 ! [A,B] :
% 0.67/0.79 ~ ( empty(A)
% 0.67/0.79 & A != B
% 0.67/0.79 & empty(B) ) ).
% 0.67/0.79
% 0.67/0.79 fof(t8_waybel_7,axiom,
% 0.67/0.79 ! [A] :
% 0.67/0.79 ( ( ~ empty_carrier(A)
% 0.67/0.79 & reflexive_relstr(A)
% 0.67/0.79 & transitive_relstr(A)
% 0.67/0.79 & antisymmetric_relstr(A)
% 0.67/0.79 & lower_bounded_relstr(A)
% 0.67/0.79 & rel_str(A) )
% 0.67/0.79 => ! [B] :
% 0.67/0.79 ( ( ~ empty(B)
% 0.67/0.79 & filtered_subset(B,A)
% 0.67/0.79 & upper_relstr_subset(B,A)
% 0.67/0.79 & element(B,powerset(the_carrier(A))) )
% 0.67/0.79 => ( proper_element(B,powerset(the_carrier(A)))
% 0.67/0.79 <=> ~ in(bottom_of_relstr(A),B) ) ) ) ).
% 0.67/0.79
% 0.67/0.79 %------------------------------------------------------------------------------
% 0.67/0.79 %-------------------------------------------
% 0.67/0.79 % Proof found
% 0.67/0.79 % SZS status Theorem for theBenchmark
% 0.67/0.79 % SZS output start Proof
% 0.67/0.79 %ClaNum:331(EqnAxiom:71)
% 0.67/0.79 %VarNum:409(SingletonVarNum:139)
% 0.67/0.79 %MaxLitNum:12
% 0.67/0.79 %MaxfuncDepth:3
% 0.67/0.79 %SharedTerms:120
% 0.67/0.79 %goalClause: 138 204 206 207 211 212 226 227
% 0.67/0.79 %singleGoalClaCount:8
% 0.67/0.79 [72]P1(a1)
% 0.67/0.79 [73]P1(a16)
% 0.67/0.79 [74]P1(a33)
% 0.67/0.79 [75]P1(a2)
% 0.67/0.79 [76]P1(a7)
% 0.67/0.79 [77]P1(a10)
% 0.67/0.79 [78]P1(a11)
% 0.67/0.79 [79]P1(a12)
% 0.67/0.79 [80]P1(a17)
% 0.67/0.79 [81]P22(a33)
% 0.67/0.79 [82]P22(a2)
% 0.67/0.79 [83]P22(a7)
% 0.67/0.79 [84]P22(a10)
% 0.67/0.79 [85]P22(a11)
% 0.67/0.79 [86]P22(a17)
% 0.67/0.79 [87]P2(a16)
% 0.67/0.79 [88]P2(a33)
% 0.67/0.79 [89]P2(a2)
% 0.67/0.79 [90]P2(a7)
% 0.67/0.79 [91]P2(a10)
% 0.67/0.79 [92]P2(a11)
% 0.67/0.79 [93]P2(a12)
% 0.67/0.79 [94]P3(a33)
% 0.67/0.79 [95]P3(a2)
% 0.67/0.79 [96]P3(a10)
% 0.67/0.79 [97]P3(a11)
% 0.67/0.79 [98]P3(a12)
% 0.67/0.79 [99]P27(a33)
% 0.67/0.79 [100]P8(a33)
% 0.67/0.79 [101]P19(a33)
% 0.67/0.79 [102]P19(a7)
% 0.67/0.79 [103]P19(a12)
% 0.67/0.79 [104]P28(a16)
% 0.67/0.79 [105]P28(a33)
% 0.67/0.79 [106]P28(a2)
% 0.67/0.79 [107]P28(a7)
% 0.67/0.79 [108]P28(a10)
% 0.67/0.79 [109]P28(a11)
% 0.67/0.79 [110]P28(a12)
% 0.67/0.79 [111]P28(a17)
% 0.67/0.79 [112]P4(a16)
% 0.67/0.79 [113]P4(a33)
% 0.67/0.79 [114]P4(a2)
% 0.67/0.79 [115]P4(a7)
% 0.67/0.79 [116]P4(a10)
% 0.67/0.79 [117]P4(a11)
% 0.67/0.79 [118]P4(a12)
% 0.67/0.79 [119]P31(a33)
% 0.67/0.79 [120]P31(a7)
% 0.67/0.79 [121]P31(a10)
% 0.67/0.79 [122]P31(a11)
% 0.67/0.79 [123]P31(a12)
% 0.67/0.79 [124]P32(a33)
% 0.67/0.79 [125]P32(a7)
% 0.67/0.79 [126]P32(a10)
% 0.67/0.79 [127]P32(a11)
% 0.67/0.79 [128]P32(a12)
% 0.67/0.79 [129]P33(a33)
% 0.67/0.79 [130]P33(a7)
% 0.67/0.79 [131]P33(a12)
% 0.67/0.79 [132]P5(a33)
% 0.67/0.79 [133]P5(a7)
% 0.67/0.79 [134]P5(a12)
% 0.67/0.79 [136]P9(a3)
% 0.67/0.79 [137]P9(a8)
% 0.67/0.79 [138]P9(a24)
% 0.67/0.79 [139]P14(a34)
% 0.67/0.79 [141]P23(a3)
% 0.67/0.79 [142]P23(a8)
% 0.67/0.79 [143]P23(a13)
% 0.67/0.79 [144]P23(a18)
% 0.67/0.79 [145]P30(a10)
% 0.67/0.79 [146]P10(a16)
% 0.67/0.79 [147]P20(a25)
% 0.67/0.79 [148]P20(a20)
% 0.67/0.79 [149]P24(a3)
% 0.67/0.79 [150]P24(a18)
% 0.67/0.79 [151]P11(a7)
% 0.67/0.79 [152]P17(a7)
% 0.67/0.79 [153]P7(a7)
% 0.67/0.79 [154]P6(a7)
% 0.67/0.79 [155]P12(a17)
% 0.67/0.79 [204]P18(a24,a26)
% 0.67/0.79 [215]~P16(a16)
% 0.67/0.79 [216]~P16(a33)
% 0.67/0.79 [217]~P16(a2)
% 0.67/0.79 [218]~P16(a7)
% 0.67/0.79 [219]~P16(a10)
% 0.67/0.79 [220]~P16(a11)
% 0.67/0.79 [221]~P16(a12)
% 0.67/0.79 [222]~P16(a20)
% 0.67/0.79 [223]~P16(a17)
% 0.67/0.79 [224]~P9(a34)
% 0.67/0.79 [225]~P9(a13)
% 0.67/0.79 [226]~P9(a27)
% 0.67/0.79 [227]~P9(a26)
% 0.67/0.79 [228]~P30(a7)
% 0.67/0.79 [229]~P35(a7)
% 0.67/0.79 [206]P15(a26,f4(a27))
% 0.67/0.79 [207]P34(a26,f4(a27))
% 0.67/0.79 [211]P13(a26,f35(f36(f4(a27))))
% 0.67/0.79 [212]P21(a26,f35(f36(f4(a27))))
% 0.67/0.79 [205]P29(x2051,x2051)
% 0.67/0.79 [157]P1(f4(x1571))
% 0.67/0.79 [162]P22(f4(x1621))
% 0.67/0.79 [166]P2(f4(x1661))
% 0.67/0.79 [169]P3(f4(x1691))
% 0.67/0.79 [171]P27(f4(x1711))
% 0.67/0.79 [173]P8(f4(x1731))
% 0.67/0.79 [176]P19(f4(x1761))
% 0.67/0.79 [180]P28(f4(x1801))
% 0.67/0.79 [184]P4(f4(x1841))
% 0.67/0.79 [187]P31(f4(x1871))
% 0.67/0.79 [190]P32(f4(x1901))
% 0.67/0.79 [193]P33(f4(x1931))
% 0.67/0.79 [196]P5(f4(x1961))
% 0.67/0.79 [197]P9(f14(x1971))
% 0.67/0.79 [198]P14(f15(x1981))
% 0.67/0.79 [199]P11(f4(x1991))
% 0.67/0.79 [200]P17(f4(x2001))
% 0.67/0.79 [201]P7(f4(x2011))
% 0.67/0.79 [202]P6(f4(x2021))
% 0.67/0.79 [203]P12(f4(x2031))
% 0.67/0.79 [208]P13(f29(x2081),x2081)
% 0.67/0.79 [209]P13(f14(x2091),f35(x2091))
% 0.67/0.79 [233]~P16(f4(x2331))
% 0.67/0.79 [234]~P9(f35(x2341))
% 0.67/0.79 [235]~P9(f15(x2351))
% 0.67/0.79 [237]~P35(f4(x2371))
% 0.67/0.79 [156]E(f5(f4(x1561)),a3)
% 0.67/0.79 [210]P13(f15(x2101),f35(f35(x2101)))
% 0.67/0.79 [213]P25(f30(x2131,x2132),x2131,x2132)
% 0.67/0.79 [214]P26(f31(x2141,x2142),x2141,x2142)
% 0.67/0.79 [238]~P9(x2381)+E(x2381,a3)
% 0.67/0.79 [239]~P9(x2391)+P14(x2391)
% 0.67/0.79 [240]~P9(x2401)+P23(x2401)
% 0.67/0.79 [241]~P1(x2411)+P20(x2411)
% 0.67/0.79 [254]P9(x2541)+P14(f19(x2541))
% 0.67/0.79 [255]P9(x2551)+P14(f21(x2551))
% 0.67/0.79 [261]~P20(x2611)+P14(f22(x2611))
% 0.67/0.79 [265]P9(x2651)+~P9(f9(x2651))
% 0.67/0.79 [266]P9(x2661)+~P9(f19(x2661))
% 0.67/0.79 [267]P9(x2671)+~P9(f21(x2671))
% 0.67/0.79 [268]P9(x2681)+~P30(f4(x2681))
% 0.67/0.79 [275]~P20(x2751)+~P9(f22(x2751))
% 0.67/0.79 [287]P9(x2871)+P13(f9(x2871),f35(x2871))
% 0.67/0.79 [288]P9(x2881)+P13(f19(x2881),f35(x2881))
% 0.67/0.79 [289]P9(x2891)+P13(f21(x2891),f35(x2891))
% 0.67/0.79 [291]~P1(x2911)+P13(f5(x2911),f36(x2911))
% 0.67/0.79 [319]~P1(x3191)+P26(f37(x3191),f36(x3191),f36(x3191))
% 0.67/0.79 [318]~P20(x3181)+P13(f22(x3181),f35(f35(f36(x3181))))
% 0.67/0.79 [279]~P9(x2791)+~P18(x2792,x2791)
% 0.67/0.79 [293]~P18(x2931,x2932)+P13(x2931,x2932)
% 0.67/0.79 [302]~P18(x3022,x3021)+~P18(x3021,x3022)
% 0.67/0.79 [298]~P29(x2981,x2982)+P13(x2981,f35(x2982))
% 0.67/0.79 [305]P29(x3051,x3052)+~P13(x3051,f35(x3052))
% 0.67/0.79 [322]~P25(x3222,x3221,x3221)+P1(f38(x3221,x3222))
% 0.67/0.79 [323]~P25(x3232,x3231,x3231)+P22(f38(x3231,x3232))
% 0.67/0.79 [327]~P26(x3271,x3272,x3273)+P25(x3271,x3272,x3273)
% 0.67/0.79 [328]~P25(x3281,x3282,x3283)+P26(x3281,x3282,x3283)
% 0.67/0.79 [324]P23(x3241)+~P13(x3241,f35(f6(x3242,x3243)))
% 0.67/0.79 [329]~P26(x3291,x3292,x3293)+P13(x3291,f35(f6(x3292,x3293)))
% 0.67/0.79 [262]~P1(x2621)+~P5(x2621)+P19(x2621)
% 0.67/0.79 [263]~P1(x2631)+~P5(x2631)+P33(x2631)
% 0.67/0.79 [270]~P16(x2701)+~P31(x2701)+~P1(x2701)
% 0.67/0.79 [271]~P16(x2711)+~P32(x2711)+~P1(x2711)
% 0.67/0.79 [277]~P20(x2771)+P16(x2771)+~P9(f36(x2771))
% 0.67/0.79 [278]~P20(x2781)+P16(x2781)+~P9(f28(x2781))
% 0.67/0.79 [296]~P1(x2961)+~P22(x2961)+E(f38(f36(x2961),f37(x2961)),x2961)
% 0.67/0.79 [306]~P20(x3061)+P16(x3061)+P13(f28(x3061),f35(f36(x3061)))
% 0.67/0.79 [260]~P9(x2602)+~P9(x2601)+E(x2601,x2602)
% 0.67/0.79 [295]~P13(x2952,x2951)+P9(x2951)+P18(x2952,x2951)
% 0.67/0.79 [299]P14(x2991)+~P14(x2992)+~P13(x2991,f35(x2992))
% 0.67/0.79 [300]~P14(x3002)+~P14(x3001)+P14(f6(x3001,x3002))
% 0.67/0.79 [307]P9(x3071)+P9(x3072)+~P9(f6(x3072,x3071))
% 0.67/0.79 [313]~P9(x3131)+~P18(x3132,x3133)+~P13(x3133,f35(x3131))
% 0.67/0.79 [317]P13(x3171,x3172)+~P18(x3171,x3173)+~P13(x3173,f35(x3172))
% 0.67/0.79 [325]~P25(x3251,x3253,x3253)+E(x3251,x3252)+~E(f38(x3253,x3251),f38(x3254,x3252))
% 0.67/0.79 [326]~P25(x3263,x3261,x3261)+E(x3261,x3262)+~E(f38(x3261,x3263),f38(x3262,x3264))
% 0.67/0.79 [272]P31(x2721)+~P1(x2721)+~P3(x2721)+P16(x2721)
% 0.67/0.79 [273]P32(x2731)+~P1(x2731)+~P3(x2731)+P16(x2731)
% 0.67/0.79 [274]P5(x2741)+~P1(x2741)+~P3(x2741)+P16(x2741)
% 0.67/0.79 [276]~P1(x2761)+~P19(x2761)+~P33(x2761)+P5(x2761)
% 0.67/0.79 [280]P3(x2801)+~P1(x2801)+~P2(x2801)+~P30(x2801)+P16(x2801)
% 0.67/0.79 [281]P27(x2811)+~P1(x2811)+~P2(x2811)+~P3(x2811)+P16(x2811)
% 0.67/0.79 [282]P8(x2821)+~P1(x2821)+~P2(x2821)+~P3(x2821)+P16(x2821)
% 0.67/0.79 [283]P19(x2831)+~P1(x2831)+~P2(x2831)+~P8(x2831)+P16(x2831)
% 0.67/0.79 [284]P28(x2841)+~P1(x2841)+~P2(x2841)+~P30(x2841)+P16(x2841)
% 0.67/0.79 [285]P4(x2851)+~P1(x2851)+~P2(x2851)+~P30(x2851)+P16(x2851)
% 0.67/0.79 [286]P10(x2861)+~P1(x2861)+~P2(x2861)+~P30(x2861)+P16(x2861)
% 0.67/0.79 [290]~P1(x2901)+~P2(x2901)+~P27(x2901)+~P31(x2901)+P33(x2901)
% 0.67/0.79 [297]~P1(x2971)+~P2(x2971)+~P28(x2971)+P16(x2971)+~P9(f32(x2971))
% 0.67/0.79 [303]~P1(x3031)+~P2(x3031)+~P28(x3031)+P16(x3031)+P15(f32(x3031),x3031)
% 0.67/0.79 [304]~P1(x3041)+~P2(x3041)+~P28(x3041)+P16(x3041)+P34(f32(x3041),x3041)
% 0.67/0.79 [314]~P1(x3141)+~P2(x3141)+~P28(x3141)+P16(x3141)+P13(f32(x3141),f35(f36(x3141)))
% 0.67/0.79 [294]P32(x2941)+~P1(x2941)+~P2(x2941)+~P8(x2941)+~P4(x2941)+P16(x2941)
% 0.67/0.79 [301]P31(x3011)+~P1(x3011)+~P2(x3011)+~P8(x3011)+~P4(x3011)+~P33(x3011)+P16(x3011)
% 0.67/0.79 [312]P30(x3121)+~P1(x3121)+~P2(x3121)+~P28(x3121)+~P4(x3121)+~P33(x3121)+P16(x3121)+~P9(f23(x3121))
% 0.67/0.79 [315]P30(x3151)+~P1(x3151)+~P2(x3151)+~P28(x3151)+~P4(x3151)+~P33(x3151)+P16(x3151)+P15(f23(x3151),x3151)
% 0.67/0.79 [316]P30(x3161)+~P1(x3161)+~P2(x3161)+~P28(x3161)+~P4(x3161)+~P33(x3161)+P16(x3161)+P34(f23(x3161),x3161)
% 0.67/0.79 [320]P30(x3201)+~P1(x3201)+~P2(x3201)+~P28(x3201)+~P4(x3201)+~P33(x3201)+P16(x3201)+P13(f23(x3201),f35(f36(x3201)))
% 0.67/0.79 [321]P30(x3211)+~P1(x3211)+~P2(x3211)+~P28(x3211)+~P4(x3211)+~P33(x3211)+P16(x3211)+P21(f23(x3211),f35(f36(x3211)))
% 0.67/0.79 [308]P3(x3081)+~P1(x3081)+~P2(x3081)+~P27(x3081)+~P19(x3081)+~P28(x3081)+~P4(x3081)+~P31(x3081)+P16(x3081)
% 0.67/0.79 [309]P32(x3091)+~P1(x3091)+~P2(x3091)+~P27(x3091)+~P19(x3091)+~P28(x3091)+~P4(x3091)+~P31(x3091)+P16(x3091)
% 0.67/0.79 [311]P5(x3111)+~P1(x3111)+~P2(x3111)+~P27(x3111)+~P19(x3111)+~P28(x3111)+~P4(x3111)+~P31(x3111)+P16(x3111)
% 0.67/0.79 [330]~P1(x3301)+~P2(x3301)+~P19(x3301)+~P28(x3301)+~P4(x3301)+~P15(x3302,x3301)+~P34(x3302,x3301)+P16(x3301)+P9(x3302)+P18(f5(x3301),x3302)+P21(x3302,f35(f36(x3301)))+~P13(x3302,f35(f36(x3301)))
% 0.67/0.79 [331]~P1(x3311)+~P2(x3311)+~P19(x3311)+~P28(x3311)+~P4(x3311)+~P15(x3312,x3311)+~P34(x3312,x3311)+P16(x3311)+P9(x3312)+~P18(f5(x3311),x3312)+~P13(x3312,f35(f36(x3311)))+~P21(x3312,f35(f36(x3311)))
% 0.67/0.79 %EqnAxiom
% 0.67/0.79 [1]E(x11,x11)
% 0.67/0.79 [2]E(x22,x21)+~E(x21,x22)
% 0.67/0.79 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.67/0.79 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.67/0.79 [5]~E(x51,x52)+E(f5(x51),f5(x52))
% 0.67/0.79 [6]~E(x61,x62)+E(f35(x61),f35(x62))
% 0.67/0.79 [7]~E(x71,x72)+E(f36(x71),f36(x72))
% 0.67/0.79 [8]~E(x81,x82)+E(f21(x81),f21(x82))
% 0.67/0.79 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93))
% 0.67/0.79 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102))
% 0.67/0.79 [11]~E(x111,x112)+E(f22(x111),f22(x112))
% 0.67/0.79 [12]~E(x121,x122)+E(f19(x121),f19(x122))
% 0.67/0.79 [13]~E(x131,x132)+E(f30(x131,x133),f30(x132,x133))
% 0.67/0.79 [14]~E(x141,x142)+E(f30(x143,x141),f30(x143,x142))
% 0.67/0.79 [15]~E(x151,x152)+E(f37(x151),f37(x152))
% 0.67/0.79 [16]~E(x161,x162)+E(f32(x161),f32(x162))
% 0.67/0.79 [17]~E(x171,x172)+E(f9(x171),f9(x172))
% 0.67/0.79 [18]~E(x181,x182)+E(f28(x181),f28(x182))
% 0.67/0.79 [19]~E(x191,x192)+E(f23(x191),f23(x192))
% 0.67/0.79 [20]~E(x201,x202)+E(f38(x201,x203),f38(x202,x203))
% 0.67/0.79 [21]~E(x211,x212)+E(f38(x213,x211),f38(x213,x212))
% 0.67/0.79 [22]~E(x221,x222)+E(f15(x221),f15(x222))
% 0.67/0.79 [23]~E(x231,x232)+E(f29(x231),f29(x232))
% 0.67/0.79 [24]~E(x241,x242)+E(f14(x241),f14(x242))
% 0.67/0.79 [25]~E(x251,x252)+E(f31(x251,x253),f31(x252,x253))
% 0.67/0.79 [26]~E(x261,x262)+E(f31(x263,x261),f31(x263,x262))
% 0.67/0.79 [27]~P1(x271)+P1(x272)+~E(x271,x272)
% 0.67/0.79 [28]P21(x282,x283)+~E(x281,x282)+~P21(x281,x283)
% 0.67/0.79 [29]P21(x293,x292)+~E(x291,x292)+~P21(x293,x291)
% 0.67/0.79 [30]P13(x302,x303)+~E(x301,x302)+~P13(x301,x303)
% 0.67/0.79 [31]P13(x313,x312)+~E(x311,x312)+~P13(x313,x311)
% 0.67/0.79 [32]P18(x322,x323)+~E(x321,x322)+~P18(x321,x323)
% 0.67/0.79 [33]P18(x333,x332)+~E(x331,x332)+~P18(x333,x331)
% 0.67/0.79 [34]P34(x342,x343)+~E(x341,x342)+~P34(x341,x343)
% 0.67/0.79 [35]P34(x353,x352)+~E(x351,x352)+~P34(x353,x351)
% 0.67/0.79 [36]P15(x362,x363)+~E(x361,x362)+~P15(x361,x363)
% 0.67/0.79 [37]P15(x373,x372)+~E(x371,x372)+~P15(x373,x371)
% 0.67/0.79 [38]~P4(x381)+P4(x382)+~E(x381,x382)
% 0.67/0.79 [39]~P28(x391)+P28(x392)+~E(x391,x392)
% 0.67/0.79 [40]~P19(x401)+P19(x402)+~E(x401,x402)
% 0.67/0.79 [41]~P22(x411)+P22(x412)+~E(x411,x412)
% 0.67/0.79 [42]~P33(x421)+P33(x422)+~E(x421,x422)
% 0.67/0.79 [43]~P14(x431)+P14(x432)+~E(x431,x432)
% 0.67/0.79 [44]~P2(x441)+P2(x442)+~E(x441,x442)
% 0.67/0.79 [45]P29(x452,x453)+~E(x451,x452)+~P29(x451,x453)
% 0.67/0.79 [46]P29(x463,x462)+~E(x461,x462)+~P29(x463,x461)
% 0.67/0.79 [47]~P16(x471)+P16(x472)+~E(x471,x472)
% 0.67/0.79 [48]~P9(x481)+P9(x482)+~E(x481,x482)
% 0.67/0.79 [49]~P30(x491)+P30(x492)+~E(x491,x492)
% 0.67/0.79 [50]P25(x502,x503,x504)+~E(x501,x502)+~P25(x501,x503,x504)
% 0.67/0.79 [51]P25(x513,x512,x514)+~E(x511,x512)+~P25(x513,x511,x514)
% 0.67/0.79 [52]P25(x523,x524,x522)+~E(x521,x522)+~P25(x523,x524,x521)
% 0.67/0.79 [53]~P10(x531)+P10(x532)+~E(x531,x532)
% 0.67/0.79 [54]~P5(x541)+P5(x542)+~E(x541,x542)
% 0.67/0.79 [55]~P35(x551)+P35(x552)+~E(x551,x552)
% 0.67/0.79 [56]~P31(x561)+P31(x562)+~E(x561,x562)
% 0.67/0.79 [57]~P3(x571)+P3(x572)+~E(x571,x572)
% 0.67/0.79 [58]~P32(x581)+P32(x582)+~E(x581,x582)
% 0.67/0.79 [59]~P23(x591)+P23(x592)+~E(x591,x592)
% 0.67/0.79 [60]~P8(x601)+P8(x602)+~E(x601,x602)
% 0.67/0.79 [61]~P12(x611)+P12(x612)+~E(x611,x612)
% 0.67/0.79 [62]~P27(x621)+P27(x622)+~E(x621,x622)
% 0.67/0.79 [63]P26(x632,x633,x634)+~E(x631,x632)+~P26(x631,x633,x634)
% 0.67/0.79 [64]P26(x643,x642,x644)+~E(x641,x642)+~P26(x643,x641,x644)
% 0.67/0.79 [65]P26(x653,x654,x652)+~E(x651,x652)+~P26(x653,x654,x651)
% 0.67/0.79 [66]~P11(x661)+P11(x662)+~E(x661,x662)
% 0.67/0.79 [67]~P20(x671)+P20(x672)+~E(x671,x672)
% 0.67/0.79 [68]~P24(x681)+P24(x682)+~E(x681,x682)
% 0.67/0.79 [69]~P7(x691)+P7(x692)+~E(x691,x692)
% 0.67/0.79 [70]~P17(x701)+P17(x702)+~E(x701,x702)
% 0.67/0.79 [71]~P6(x711)+P6(x712)+~E(x711,x712)
% 0.67/0.79
% 0.67/0.79 %-------------------------------------------
% 0.67/0.79 cnf(338,plain,
% 0.67/0.79 (P13(f29(x3381),x3381)),
% 0.67/0.79 inference(rename_variables,[],[208])).
% 0.67/0.79 cnf(347,plain,
% 0.67/0.79 (P25(f30(x3471,x3472),x3471,x3472)),
% 0.67/0.79 inference(rename_variables,[],[213])).
% 0.67/0.79 cnf(352,plain,
% 0.67/0.79 (~E(a26,a24)),
% 0.67/0.79 inference(scs_inference,[],[138,205,204,136,141,149,211,213,347,214,208,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33])).
% 0.67/0.79 cnf(354,plain,
% 0.67/0.79 (P13(f29(x3541),x3541)),
% 0.67/0.79 inference(rename_variables,[],[208])).
% 0.67/0.79 cnf(355,plain,
% 0.67/0.79 (P18(f29(a27),a27)),
% 0.67/0.79 inference(scs_inference,[],[138,205,204,226,136,141,149,211,213,347,214,208,338,354,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295])).
% 0.67/0.79 cnf(356,plain,
% 0.67/0.79 (P13(f29(x3561),x3561)),
% 0.67/0.79 inference(rename_variables,[],[208])).
% 0.67/0.79 cnf(368,plain,
% 0.67/0.79 (P31(a2)),
% 0.67/0.79 inference(scs_inference,[],[138,205,204,226,75,95,136,139,141,149,217,211,213,347,214,208,338,354,356,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272])).
% 0.67/0.79 cnf(372,plain,
% 0.67/0.79 (P8(a2)),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,75,77,89,91,95,136,139,141,145,149,217,219,211,213,347,214,208,338,354,356,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282])).
% 0.67/0.80 cnf(374,plain,
% 0.67/0.80 (P27(a2)),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,75,77,89,91,95,136,139,141,145,149,217,219,211,213,347,214,208,338,354,356,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281])).
% 0.67/0.80 cnf(380,plain,
% 0.67/0.80 (P25(f31(f5(f4(x3801)),f5(f4(x3801))),a3,a3)),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,227,75,77,89,91,95,136,139,141,145,149,217,219,206,207,211,212,213,347,214,208,338,354,356,157,166,176,180,184,233,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281,331,328,327])).
% 0.67/0.80 cnf(390,plain,
% 0.67/0.80 (E(a24,a3)),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,227,72,75,77,89,91,95,136,139,141,145,149,217,219,206,207,211,212,213,347,214,208,338,354,356,157,166,176,180,184,233,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281,331,328,327,293,241,240,239,238])).
% 0.67/0.80 cnf(396,plain,
% 0.67/0.80 (~P30(f4(a27))),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,227,72,75,77,89,91,95,136,139,141,145,147,149,217,219,206,207,211,212,213,347,214,208,338,354,356,157,166,176,180,184,233,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281,331,328,327,293,241,240,239,238,298,275,268])).
% 0.67/0.80 cnf(410,plain,
% 0.67/0.80 (E(f31(x4101,f5(f4(x4102))),f31(x4101,a3))),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,227,72,75,77,89,91,95,136,139,141,145,147,149,217,219,206,207,211,212,213,347,214,208,338,354,356,157,166,176,180,184,233,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281,331,328,327,293,241,240,239,238,298,275,268,267,266,265,261,255,254,26])).
% 0.67/0.80 cnf(448,plain,
% 0.67/0.80 (~P18(a3,a26)),
% 0.67/0.80 inference(scs_inference,[],[138,205,204,226,227,72,75,77,89,91,95,136,139,141,145,147,149,154,217,219,228,206,207,211,212,213,347,214,208,338,354,356,157,166,176,180,184,233,156,2,302,279,324,305,68,65,64,59,52,51,48,46,45,33,31,295,317,313,299,274,273,272,286,282,281,331,328,327,293,241,240,239,238,298,275,268,267,266,265,261,255,254,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,318,291,289,288,287,319,71,49,43,32])).
% 0.67/0.80 cnf(451,plain,
% 0.67/0.80 (E(f31(x4511,f5(f4(x4512))),f31(x4511,a3))),
% 0.67/0.80 inference(rename_variables,[],[410])).
% 0.67/0.80 cnf(514,plain,
% 0.67/0.80 ($false),
% 0.67/0.80 inference(scs_inference,[],[138,73,74,76,78,81,87,90,92,96,97,102,104,107,115,130,148,215,218,220,222,224,209,198,227,77,219,228,213,214,89,145,204,75,217,410,451,396,448,380,355,352,368,372,374,390,63,50,307,300,278,277,326,306,296,304,303,297,314,316,315,312,321,320,290,283,295,317,313,331,282,281,302,293,49,48,274,2,32]),
% 0.67/0.80 ['proof']).
% 0.67/0.80 % SZS output end Proof
% 0.67/0.80 % Total time :0.110000s
%------------------------------------------------------------------------------