TSTP Solution File: SEU097+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n028.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 16:17:29 EDT 2023
% Result : Theorem 0.68s 0.78s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n028.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 13:27:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 start to proof:theBenchmark
% 0.68/0.76 %-------------------------------------------
% 0.68/0.76 % File :CSE---1.6
% 0.68/0.76 % Problem :theBenchmark
% 0.68/0.76 % Transform :cnf
% 0.68/0.76 % Format :tptp:raw
% 0.68/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.68/0.76
% 0.68/0.76 % Result :Theorem 0.090000s
% 0.68/0.76 % Output :CNFRefutation 0.090000s
% 0.68/0.76 %-------------------------------------------
% 0.68/0.77 %------------------------------------------------------------------------------
% 0.68/0.77 % File : SEU097+1 : TPTP v8.1.2. Released v3.2.0.
% 0.68/0.77 % Domain : Set theory
% 0.68/0.77 % Problem : Finite sets, theorem 28
% 0.68/0.77 % Version : [Urb06] axioms : Especial.
% 0.68/0.77 % English :
% 0.68/0.77
% 0.68/0.77 % Refs : [Dar90] Darmochwal (1990), Finite Sets
% 0.68/0.77 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.68/0.77 % Source : [Urb06]
% 0.68/0.77 % Names : finset_1__t28_finset_1 [Urb06]
% 0.68/0.77
% 0.68/0.77 % Status : Theorem
% 0.68/0.77 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.30 v4.0.0, 0.29 v3.7.0, 0.25 v3.5.0, 0.21 v3.3.0, 0.14 v3.2.0
% 0.68/0.77 % Syntax : Number of formulae : 70 ( 15 unt; 0 def)
% 0.68/0.77 % Number of atoms : 200 ( 10 equ)
% 0.68/0.77 % Maximal formula atoms : 10 ( 2 avg)
% 0.68/0.77 % Number of connectives : 151 ( 21 ~; 1 |; 98 &)
% 0.68/0.77 % ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% 0.68/0.77 % Maximal formula depth : 12 ( 4 avg)
% 0.68/0.77 % Maximal term depth : 3 ( 1 avg)
% 0.68/0.77 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty)
% 0.68/0.77 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.68/0.77 % Number of variables : 96 ( 70 !; 26 ?)
% 0.68/0.77 % SPC : FOF_THM_RFO_SEQ
% 0.68/0.77
% 0.68/0.77 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.68/0.77 % library, www.mizar.org
% 0.68/0.77 %------------------------------------------------------------------------------
% 0.68/0.77 fof(antisymmetry_r2_hidden,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( in(A,B)
% 0.68/0.77 => ~ in(B,A) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc1_arytm_3,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( ordinal(A)
% 0.68/0.77 => ! [B] :
% 0.68/0.77 ( element(B,A)
% 0.68/0.77 => ( epsilon_transitive(B)
% 0.68/0.77 & epsilon_connected(B)
% 0.68/0.77 & ordinal(B) ) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc1_finset_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( empty(A)
% 0.68/0.77 => finite(A) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc1_funct_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( empty(A)
% 0.68/0.77 => function(A) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc1_ordinal1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( ordinal(A)
% 0.68/0.77 => ( epsilon_transitive(A)
% 0.68/0.77 & epsilon_connected(A) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc1_relat_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( empty(A)
% 0.68/0.77 => relation(A) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc2_arytm_3,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( ( empty(A)
% 0.68/0.77 & ordinal(A) )
% 0.68/0.77 => ( epsilon_transitive(A)
% 0.68/0.77 & epsilon_connected(A)
% 0.68/0.77 & ordinal(A)
% 0.68/0.77 & natural(A) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc2_finset_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( finite(A)
% 0.68/0.77 => ! [B] :
% 0.68/0.77 ( element(B,powerset(A))
% 0.68/0.77 => finite(B) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc2_funct_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( ( relation(A)
% 0.68/0.77 & empty(A)
% 0.68/0.77 & function(A) )
% 0.68/0.77 => ( relation(A)
% 0.68/0.77 & function(A)
% 0.68/0.77 & one_to_one(A) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc2_ordinal1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( ( epsilon_transitive(A)
% 0.68/0.77 & epsilon_connected(A) )
% 0.68/0.77 => ordinal(A) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc3_ordinal1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( empty(A)
% 0.68/0.77 => ( epsilon_transitive(A)
% 0.68/0.77 & epsilon_connected(A)
% 0.68/0.77 & ordinal(A) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(cc4_arytm_3,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ( element(A,positive_rationals)
% 0.68/0.77 => ( ordinal(A)
% 0.68/0.77 => ( epsilon_transitive(A)
% 0.68/0.77 & epsilon_connected(A)
% 0.68/0.77 & ordinal(A)
% 0.68/0.77 & natural(A) ) ) ) ).
% 0.68/0.77
% 0.68/0.77 fof(commutativity_k2_xboole_0,axiom,
% 0.68/0.77 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.68/0.77
% 0.68/0.77 fof(commutativity_k5_xboole_0,axiom,
% 0.68/0.77 ! [A,B] : symmetric_difference(A,B) = symmetric_difference(B,A) ).
% 0.68/0.77
% 0.68/0.77 fof(d6_xboole_0,axiom,
% 0.68/0.77 ! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)) ).
% 0.68/0.77
% 0.68/0.77 fof(existence_m1_subset_1,axiom,
% 0.68/0.77 ! [A] :
% 0.68/0.77 ? [B] : element(B,A) ).
% 0.68/0.77
% 0.68/0.77 fof(fc12_finset_1,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( finite(A)
% 0.68/0.77 => finite(set_difference(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc12_relat_1,axiom,
% 0.68/0.77 ( empty(empty_set)
% 0.68/0.77 & relation(empty_set)
% 0.68/0.77 & relation_empty_yielding(empty_set) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc1_subset_1,axiom,
% 0.68/0.77 ! [A] : ~ empty(powerset(A)) ).
% 0.68/0.77
% 0.68/0.77 fof(fc1_xboole_0,axiom,
% 0.68/0.77 empty(empty_set) ).
% 0.68/0.77
% 0.68/0.77 fof(fc2_ordinal1,axiom,
% 0.68/0.77 ( relation(empty_set)
% 0.68/0.77 & relation_empty_yielding(empty_set)
% 0.68/0.77 & function(empty_set)
% 0.68/0.77 & one_to_one(empty_set)
% 0.68/0.77 & empty(empty_set)
% 0.68/0.77 & epsilon_transitive(empty_set)
% 0.68/0.77 & epsilon_connected(empty_set)
% 0.68/0.77 & ordinal(empty_set) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc2_relat_1,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ( relation(A)
% 0.68/0.77 & relation(B) )
% 0.68/0.77 => relation(set_union2(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc2_xboole_0,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ~ empty(A)
% 0.68/0.77 => ~ empty(set_union2(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc3_relat_1,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ( relation(A)
% 0.68/0.77 & relation(B) )
% 0.68/0.77 => relation(set_difference(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc3_xboole_0,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ~ empty(A)
% 0.68/0.77 => ~ empty(set_union2(B,A)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc4_relat_1,axiom,
% 0.68/0.77 ( empty(empty_set)
% 0.68/0.77 & relation(empty_set) ) ).
% 0.68/0.77
% 0.68/0.77 fof(fc8_arytm_3,axiom,
% 0.68/0.77 ~ empty(positive_rationals) ).
% 0.68/0.77
% 0.68/0.77 fof(fc9_finset_1,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ( finite(A)
% 0.68/0.77 & finite(B) )
% 0.68/0.77 => finite(set_union2(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(idempotence_k2_xboole_0,axiom,
% 0.68/0.77 ! [A,B] : set_union2(A,A) = A ).
% 0.68/0.77
% 0.68/0.77 fof(l3_finset_1,axiom,
% 0.68/0.77 ! [A,B] :
% 0.68/0.77 ( ( finite(A)
% 0.68/0.77 & finite(B) )
% 0.68/0.77 => finite(set_union2(A,B)) ) ).
% 0.68/0.77
% 0.68/0.77 fof(rc1_arytm_3,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 & epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A)
% 0.68/0.78 & natural(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_finset_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 & finite(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_funcop_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A)
% 0.68/0.78 & function_yielding(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_funct_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_ordinal1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_ordinal2,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A)
% 0.68/0.78 & being_limit_ordinal(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_relat_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( empty(A)
% 0.68/0.78 & relation(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_subset_1,axiom,
% 0.68/0.78 ! [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 => ? [B] :
% 0.68/0.78 ( element(B,powerset(A))
% 0.68/0.78 & ~ empty(B) ) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc1_xboole_0,axiom,
% 0.68/0.78 ? [A] : empty(A) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_arytm_3,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( element(A,positive_rationals)
% 0.68/0.78 & ~ empty(A)
% 0.68/0.78 & epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_finset_1,axiom,
% 0.68/0.78 ! [A] :
% 0.68/0.78 ? [B] :
% 0.68/0.78 ( element(B,powerset(A))
% 0.68/0.78 & empty(B)
% 0.68/0.78 & relation(B)
% 0.68/0.78 & function(B)
% 0.68/0.78 & one_to_one(B)
% 0.68/0.78 & epsilon_transitive(B)
% 0.68/0.78 & epsilon_connected(B)
% 0.68/0.78 & ordinal(B)
% 0.68/0.78 & natural(B)
% 0.68/0.78 & finite(B) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_funct_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & empty(A)
% 0.68/0.78 & function(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_ordinal1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A)
% 0.68/0.78 & one_to_one(A)
% 0.68/0.78 & empty(A)
% 0.68/0.78 & epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_ordinal2,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A)
% 0.68/0.78 & transfinite_sequence(A)
% 0.68/0.78 & ordinal_yielding(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_relat_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 & relation(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_subset_1,axiom,
% 0.68/0.78 ! [A] :
% 0.68/0.78 ? [B] :
% 0.68/0.78 ( element(B,powerset(A))
% 0.68/0.78 & empty(B) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc2_xboole_0,axiom,
% 0.68/0.78 ? [A] : ~ empty(A) ).
% 0.68/0.78
% 0.68/0.78 fof(rc3_arytm_3,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( element(A,positive_rationals)
% 0.68/0.78 & empty(A)
% 0.68/0.78 & epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A)
% 0.68/0.78 & natural(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc3_finset_1,axiom,
% 0.68/0.78 ! [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 => ? [B] :
% 0.68/0.78 ( element(B,powerset(A))
% 0.68/0.78 & ~ empty(B)
% 0.68/0.78 & finite(B) ) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc3_funct_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A)
% 0.68/0.78 & one_to_one(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc3_ordinal1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( ~ empty(A)
% 0.68/0.78 & epsilon_transitive(A)
% 0.68/0.78 & epsilon_connected(A)
% 0.68/0.78 & ordinal(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc3_relat_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & relation_empty_yielding(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc4_funct_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & relation_empty_yielding(A)
% 0.68/0.78 & function(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc4_ordinal1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & function(A)
% 0.68/0.78 & transfinite_sequence(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(rc5_funct_1,axiom,
% 0.68/0.78 ? [A] :
% 0.68/0.78 ( relation(A)
% 0.68/0.78 & relation_non_empty(A)
% 0.68/0.78 & function(A) ) ).
% 0.68/0.78
% 0.68/0.78 fof(reflexivity_r1_tarski,axiom,
% 0.68/0.78 ! [A,B] : subset(A,A) ).
% 0.68/0.78
% 0.68/0.78 fof(t16_finset_1,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ( finite(A)
% 0.68/0.78 => finite(set_difference(A,B)) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t1_boole,axiom,
% 0.68/0.78 ! [A] : set_union2(A,empty_set) = A ).
% 0.68/0.78
% 0.68/0.78 fof(t1_subset,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ( in(A,B)
% 0.68/0.78 => element(A,B) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t28_finset_1,conjecture,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ( ( finite(A)
% 0.68/0.78 & finite(B) )
% 0.68/0.78 => finite(symmetric_difference(A,B)) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t2_subset,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ( element(A,B)
% 0.68/0.78 => ( empty(B)
% 0.68/0.78 | in(A,B) ) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t3_boole,axiom,
% 0.68/0.78 ! [A] : set_difference(A,empty_set) = A ).
% 0.68/0.78
% 0.68/0.78 fof(t3_subset,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ( element(A,powerset(B))
% 0.68/0.78 <=> subset(A,B) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t4_boole,axiom,
% 0.68/0.78 ! [A] : set_difference(empty_set,A) = empty_set ).
% 0.68/0.78
% 0.68/0.78 fof(t4_subset,axiom,
% 0.68/0.78 ! [A,B,C] :
% 0.68/0.78 ( ( in(A,B)
% 0.68/0.78 & element(B,powerset(C)) )
% 0.68/0.78 => element(A,C) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t5_boole,axiom,
% 0.68/0.78 ! [A] : symmetric_difference(A,empty_set) = A ).
% 0.68/0.78
% 0.68/0.78 fof(t5_subset,axiom,
% 0.68/0.78 ! [A,B,C] :
% 0.68/0.78 ~ ( in(A,B)
% 0.68/0.78 & element(B,powerset(C))
% 0.68/0.78 & empty(C) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t6_boole,axiom,
% 0.68/0.78 ! [A] :
% 0.68/0.78 ( empty(A)
% 0.68/0.78 => A = empty_set ) ).
% 0.68/0.78
% 0.68/0.78 fof(t7_boole,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ~ ( in(A,B)
% 0.68/0.78 & empty(B) ) ).
% 0.68/0.78
% 0.68/0.78 fof(t8_boole,axiom,
% 0.68/0.78 ! [A,B] :
% 0.68/0.78 ~ ( empty(A)
% 0.68/0.78 & A != B
% 0.68/0.78 & empty(B) ) ).
% 0.68/0.78
% 0.68/0.78 %------------------------------------------------------------------------------
% 0.68/0.78 %-------------------------------------------
% 0.68/0.78 % Proof found
% 0.68/0.78 % SZS status Theorem for theBenchmark
% 0.68/0.78 % SZS output start Proof
% 0.68/0.78 %ClaNum:185(EqnAxiom:34)
% 0.68/0.78 %VarNum:153(SingletonVarNum:80)
% 0.68/0.78 %MaxLitNum:4
% 0.68/0.78 %MaxfuncDepth:2
% 0.68/0.78 %SharedTerms:108
% 0.68/0.78 %goalClause: 69 70 142
% 0.68/0.78 %singleGoalClaCount:3
% 0.68/0.78 [35]P1(a1)
% 0.68/0.78 [36]P1(a2)
% 0.68/0.78 [37]P1(a23)
% 0.68/0.78 [38]P1(a27)
% 0.68/0.78 [39]P1(a3)
% 0.68/0.78 [40]P1(a5)
% 0.68/0.78 [41]P1(a8)
% 0.68/0.78 [42]P1(a13)
% 0.68/0.78 [43]P2(a1)
% 0.68/0.78 [44]P2(a2)
% 0.68/0.78 [45]P2(a23)
% 0.68/0.78 [46]P2(a27)
% 0.68/0.78 [47]P2(a3)
% 0.68/0.78 [48]P2(a5)
% 0.68/0.78 [49]P2(a8)
% 0.68/0.78 [50]P2(a13)
% 0.68/0.78 [51]P3(a1)
% 0.68/0.78 [52]P3(a2)
% 0.68/0.78 [53]P3(a23)
% 0.68/0.78 [54]P3(a27)
% 0.68/0.78 [55]P3(a3)
% 0.68/0.78 [56]P3(a5)
% 0.68/0.78 [57]P3(a8)
% 0.68/0.78 [58]P3(a13)
% 0.68/0.78 [62]P4(a1)
% 0.68/0.78 [63]P4(a28)
% 0.68/0.78 [64]P4(a4)
% 0.68/0.78 [65]P4(a6)
% 0.68/0.78 [66]P4(a5)
% 0.68/0.78 [67]P4(a8)
% 0.68/0.78 [68]P7(a24)
% 0.68/0.78 [69]P7(a17)
% 0.68/0.78 [70]P7(a22)
% 0.68/0.78 [71]P8(a1)
% 0.68/0.78 [72]P8(a25)
% 0.68/0.78 [73]P8(a26)
% 0.68/0.78 [74]P8(a6)
% 0.68/0.78 [75]P8(a5)
% 0.68/0.78 [76]P8(a9)
% 0.68/0.78 [77]P8(a14)
% 0.68/0.78 [78]P8(a18)
% 0.68/0.78 [79]P8(a20)
% 0.68/0.78 [80]P8(a21)
% 0.68/0.78 [83]P13(a1)
% 0.68/0.78 [84]P13(a25)
% 0.68/0.78 [85]P13(a26)
% 0.68/0.78 [86]P13(a28)
% 0.68/0.78 [87]P13(a6)
% 0.68/0.78 [88]P13(a5)
% 0.68/0.78 [89]P13(a9)
% 0.68/0.78 [90]P13(a10)
% 0.68/0.78 [91]P13(a14)
% 0.68/0.78 [92]P13(a19)
% 0.68/0.78 [93]P13(a18)
% 0.68/0.78 [94]P13(a20)
% 0.68/0.78 [95]P13(a21)
% 0.68/0.78 [96]P9(a2)
% 0.68/0.78 [97]P9(a8)
% 0.68/0.78 [98]P12(a1)
% 0.68/0.78 [99]P12(a5)
% 0.68/0.78 [100]P12(a14)
% 0.68/0.78 [102]P15(a1)
% 0.68/0.78 [103]P15(a19)
% 0.68/0.78 [104]P15(a18)
% 0.68/0.78 [105]P10(a25)
% 0.68/0.78 [106]P5(a27)
% 0.68/0.78 [107]P16(a9)
% 0.68/0.78 [108]P16(a20)
% 0.68/0.78 [109]P14(a9)
% 0.68/0.78 [110]P17(a21)
% 0.68/0.78 [121]P6(a3,a29)
% 0.68/0.78 [122]P6(a8,a29)
% 0.68/0.78 [134]~P4(a29)
% 0.68/0.78 [135]~P4(a2)
% 0.68/0.78 [136]~P4(a24)
% 0.68/0.78 [137]~P4(a3)
% 0.68/0.78 [138]~P4(a10)
% 0.68/0.78 [139]~P4(a12)
% 0.68/0.78 [140]~P4(a13)
% 0.68/0.78 [142]~P7(f33(f31(a17,a22),f31(a22,a17)))
% 0.68/0.79 [126]P18(x1261,x1261)
% 0.68/0.79 [111]P1(f7(x1111))
% 0.68/0.79 [112]P2(f7(x1121))
% 0.68/0.79 [113]P3(f7(x1131))
% 0.68/0.79 [114]P4(f7(x1141))
% 0.68/0.79 [115]P4(f11(x1151))
% 0.68/0.79 [116]P7(f7(x1161))
% 0.68/0.79 [117]P8(f7(x1171))
% 0.68/0.79 [118]P13(f7(x1181))
% 0.68/0.79 [119]P9(f7(x1191))
% 0.68/0.79 [120]P12(f7(x1201))
% 0.68/0.79 [123]E(f31(a1,x1231),a1)
% 0.68/0.79 [124]E(f33(x1241,a1),x1241)
% 0.68/0.79 [125]E(f31(x1251,a1),x1251)
% 0.68/0.79 [127]E(f33(x1271,x1271),x1271)
% 0.68/0.79 [128]P6(f15(x1281),x1281)
% 0.68/0.79 [129]P6(f7(x1291),f32(x1291))
% 0.68/0.79 [130]P6(f11(x1301),f32(x1301))
% 0.68/0.79 [141]~P4(f32(x1411))
% 0.68/0.79 [132]E(f33(f31(x1321,a1),f31(a1,x1321)),x1321)
% 0.68/0.79 [131]E(f33(x1311,x1312),f33(x1312,x1311))
% 0.68/0.79 [143]~P4(x1431)+E(x1431,a1)
% 0.68/0.79 [144]~P4(x1441)+P1(x1441)
% 0.68/0.79 [145]~P1(x1451)+P2(x1451)
% 0.68/0.79 [146]~P4(x1461)+P2(x1461)
% 0.68/0.79 [147]~P1(x1471)+P3(x1471)
% 0.68/0.79 [148]~P4(x1481)+P3(x1481)
% 0.68/0.79 [149]~P4(x1491)+P7(x1491)
% 0.68/0.79 [150]~P4(x1501)+P8(x1501)
% 0.68/0.79 [151]~P4(x1511)+P13(x1511)
% 0.68/0.79 [152]P4(x1521)+P7(f16(x1521))
% 0.68/0.79 [158]P4(x1581)+~P4(f30(x1581))
% 0.68/0.79 [159]P4(x1591)+~P4(f16(x1591))
% 0.68/0.79 [162]P4(x1621)+P6(f30(x1621),f32(x1621))
% 0.68/0.79 [163]P4(x1631)+P6(f16(x1631),f32(x1631))
% 0.68/0.79 [161]~P4(x1611)+~P11(x1612,x1611)
% 0.68/0.79 [170]~P11(x1701,x1702)+P6(x1701,x1702)
% 0.68/0.79 [180]~P11(x1802,x1801)+~P11(x1801,x1802)
% 0.68/0.79 [172]~P7(x1721)+P7(f31(x1721,x1722))
% 0.68/0.79 [174]~P18(x1741,x1742)+P6(x1741,f32(x1742))
% 0.68/0.79 [181]P18(x1811,x1812)+~P6(x1811,f32(x1812))
% 0.68/0.79 [182]P4(x1821)+~P4(f33(x1822,x1821))
% 0.68/0.79 [183]P4(x1831)+~P4(f33(x1831,x1832))
% 0.68/0.79 [154]~P2(x1541)+~P3(x1541)+P1(x1541)
% 0.68/0.79 [157]~P1(x1571)+~P4(x1571)+P9(x1571)
% 0.68/0.79 [166]~P1(x1661)+P9(x1661)+~P6(x1661,a29)
% 0.68/0.79 [153]~P4(x1532)+~P4(x1531)+E(x1531,x1532)
% 0.68/0.79 [167]~P6(x1671,x1672)+P1(x1671)+~P1(x1672)
% 0.68/0.79 [168]~P6(x1681,x1682)+P2(x1681)+~P1(x1682)
% 0.68/0.79 [169]~P6(x1691,x1692)+P3(x1691)+~P1(x1692)
% 0.68/0.79 [173]~P6(x1732,x1731)+P4(x1731)+P11(x1732,x1731)
% 0.68/0.79 [175]P7(x1751)+~P7(x1752)+~P6(x1751,f32(x1752))
% 0.68/0.79 [177]~P7(x1772)+~P7(x1771)+P7(f33(x1771,x1772))
% 0.68/0.79 [178]~P13(x1782)+~P13(x1781)+P13(f33(x1781,x1782))
% 0.68/0.79 [179]~P13(x1792)+~P13(x1791)+P13(f31(x1791,x1792))
% 0.68/0.79 [184]~P4(x1841)+~P11(x1842,x1843)+~P6(x1843,f32(x1841))
% 0.68/0.79 [185]P6(x1851,x1852)+~P11(x1851,x1853)+~P6(x1853,f32(x1852))
% 0.68/0.79 [160]~P4(x1601)+~P8(x1601)+~P13(x1601)+P12(x1601)
% 0.68/0.79 %EqnAxiom
% 0.68/0.79 [1]E(x11,x11)
% 0.68/0.79 [2]E(x22,x21)+~E(x21,x22)
% 0.68/0.79 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.68/0.79 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 0.68/0.79 [5]~E(x51,x52)+E(f32(x51),f32(x52))
% 0.68/0.79 [6]~E(x61,x62)+E(f31(x61,x63),f31(x62,x63))
% 0.68/0.79 [7]~E(x71,x72)+E(f31(x73,x71),f31(x73,x72))
% 0.68/0.79 [8]~E(x81,x82)+E(f33(x81,x83),f33(x82,x83))
% 0.68/0.79 [9]~E(x91,x92)+E(f33(x93,x91),f33(x93,x92))
% 0.68/0.79 [10]~E(x101,x102)+E(f11(x101),f11(x102))
% 0.68/0.79 [11]~E(x111,x112)+E(f30(x111),f30(x112))
% 0.68/0.79 [12]~E(x121,x122)+E(f15(x121),f15(x122))
% 0.68/0.79 [13]~E(x131,x132)+E(f16(x131),f16(x132))
% 0.68/0.79 [14]~P1(x141)+P1(x142)+~E(x141,x142)
% 0.68/0.79 [15]P6(x152,x153)+~E(x151,x152)+~P6(x151,x153)
% 0.68/0.79 [16]P6(x163,x162)+~E(x161,x162)+~P6(x163,x161)
% 0.68/0.79 [17]P11(x172,x173)+~E(x171,x172)+~P11(x171,x173)
% 0.68/0.79 [18]P11(x183,x182)+~E(x181,x182)+~P11(x183,x181)
% 0.68/0.79 [19]~P7(x191)+P7(x192)+~E(x191,x192)
% 0.68/0.79 [20]~P13(x201)+P13(x202)+~E(x201,x202)
% 0.68/0.79 [21]~P3(x211)+P3(x212)+~E(x211,x212)
% 0.68/0.79 [22]~P4(x221)+P4(x222)+~E(x221,x222)
% 0.68/0.79 [23]P18(x232,x233)+~E(x231,x232)+~P18(x231,x233)
% 0.68/0.79 [24]P18(x243,x242)+~E(x241,x242)+~P18(x243,x241)
% 0.68/0.79 [25]~P2(x251)+P2(x252)+~E(x251,x252)
% 0.68/0.79 [26]~P8(x261)+P8(x262)+~E(x261,x262)
% 0.68/0.79 [27]~P9(x271)+P9(x272)+~E(x271,x272)
% 0.68/0.79 [28]~P10(x281)+P10(x282)+~E(x281,x282)
% 0.68/0.79 [29]~P5(x291)+P5(x292)+~E(x291,x292)
% 0.68/0.79 [30]~P12(x301)+P12(x302)+~E(x301,x302)
% 0.68/0.79 [31]~P14(x311)+P14(x312)+~E(x311,x312)
% 0.68/0.79 [32]~P17(x321)+P17(x322)+~E(x321,x322)
% 0.68/0.79 [33]~P15(x331)+P15(x332)+~E(x331,x332)
% 0.68/0.79 [34]~P16(x341)+P16(x342)+~E(x341,x342)
% 0.68/0.79
% 0.68/0.79 %-------------------------------------------
% 0.68/0.79 cnf(186,plain,
% 0.68/0.79 (E(x1861,f33(x1861,x1861))),
% 0.68/0.79 inference(scs_inference,[],[127,2])).
% 0.68/0.79 cnf(187,plain,
% 0.68/0.79 (~P11(x1871,a1)),
% 0.68/0.79 inference(scs_inference,[],[62,127,2,161])).
% 0.68/0.79 cnf(192,plain,
% 0.68/0.79 (P6(f15(x1921),x1921)),
% 0.68/0.79 inference(rename_variables,[],[128])).
% 0.68/0.79 cnf(200,plain,
% 0.68/0.79 (E(f33(x2001,a1),x2001)),
% 0.68/0.79 inference(rename_variables,[],[124])).
% 0.68/0.79 cnf(202,plain,
% 0.68/0.79 (~P7(f33(f31(a22,a17),f31(a17,a22)))),
% 0.68/0.79 inference(scs_inference,[],[126,62,76,89,107,109,134,142,127,128,124,131,2,161,149,181,34,31,26,24,23,22,20,19])).
% 0.68/0.79 cnf(205,plain,
% 0.68/0.79 (P6(f15(x2051),x2051)),
% 0.68/0.79 inference(rename_variables,[],[128])).
% 0.68/0.79 cnf(206,plain,
% 0.68/0.79 (E(f33(x2061,x2061),x2061)),
% 0.68/0.79 inference(rename_variables,[],[127])).
% 0.68/0.79 cnf(209,plain,
% 0.68/0.79 (P11(a3,a29)),
% 0.68/0.79 inference(scs_inference,[],[126,62,76,89,107,109,121,134,142,127,206,128,192,124,200,131,2,161,149,181,34,31,26,24,23,22,20,19,16,3,173])).
% 0.68/0.79 cnf(215,plain,
% 0.68/0.79 (~P11(x2151,f15(f32(a1)))),
% 0.68/0.79 inference(scs_inference,[],[126,35,39,62,76,89,107,109,121,134,142,127,206,128,192,205,124,200,131,2,161,149,181,34,31,26,24,23,22,20,19,16,3,173,166,157,184])).
% 0.68/0.79 cnf(216,plain,
% 0.68/0.79 (P6(f15(x2161),x2161)),
% 0.68/0.79 inference(rename_variables,[],[128])).
% 0.68/0.79 cnf(226,plain,
% 0.68/0.79 (P8(a28)),
% 0.68/0.79 inference(scs_inference,[],[69,126,35,39,62,63,64,65,74,76,87,89,107,109,121,134,142,127,206,128,192,205,216,124,200,131,2,161,149,181,34,31,26,24,23,22,20,19,16,3,173,166,157,184,175,160,180,151,150])).
% 0.68/0.79 cnf(242,plain,
% 0.68/0.79 (P7(f31(a17,x2421))),
% 0.68/0.79 inference(scs_inference,[],[69,126,35,39,62,63,64,65,74,76,87,89,107,109,121,134,142,127,206,128,192,205,216,124,200,131,2,161,149,181,34,31,26,24,23,22,20,19,16,3,173,166,157,184,175,160,180,151,150,148,146,144,143,183,182,174,172])).
% 0.68/0.79 cnf(264,plain,
% 0.68/0.79 (~E(a1,x2641)+P15(x2641)),
% 0.68/0.79 inference(scs_inference,[],[69,126,35,39,62,63,64,65,74,76,87,89,102,107,109,121,134,142,127,206,128,192,205,216,124,200,131,2,161,149,181,34,31,26,24,23,22,20,19,16,3,173,166,157,184,175,160,180,151,150,148,146,144,143,183,182,174,172,159,158,152,13,12,11,10,9,8,7,6,5,4,163,162,33])).
% 0.68/0.79 cnf(284,plain,
% 0.68/0.79 (E(x2841,f33(x2841,x2841))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(286,plain,
% 0.68/0.79 (E(x2861,f33(x2861,x2861))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(288,plain,
% 0.68/0.79 (E(x2881,f33(x2881,x2881))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(289,plain,
% 0.68/0.79 (P5(f33(a27,a27))),
% 0.68/0.79 inference(scs_inference,[],[98,106,110,186,284,286,288,264,32,30,29])).
% 0.68/0.79 cnf(290,plain,
% 0.68/0.79 (E(x2901,f33(x2901,x2901))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(292,plain,
% 0.68/0.79 (E(x2921,f33(x2921,x2921))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(294,plain,
% 0.68/0.79 (E(x2941,f33(x2941,x2941))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(296,plain,
% 0.68/0.79 (E(x2961,f33(x2961,x2961))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(298,plain,
% 0.68/0.79 (E(x2981,f33(x2981,x2981))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(300,plain,
% 0.68/0.79 (E(x3001,f33(x3001,x3001))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(311,plain,
% 0.68/0.79 (~P6(a29,f32(a5))),
% 0.68/0.79 inference(scs_inference,[],[36,51,66,84,96,98,105,106,110,43,128,186,284,286,288,290,292,294,296,298,215,209,264,32,30,29,28,27,25,21,14,147,145,173,179,178,184])).
% 0.68/0.79 cnf(333,plain,
% 0.68/0.79 (~P11(x3331,f31(a1,x3332))),
% 0.68/0.79 inference(scs_inference,[],[69,70,36,51,66,79,84,86,94,96,98,105,106,108,110,135,125,123,129,130,132,43,128,142,63,186,284,286,288,290,292,294,296,298,300,215,187,209,226,264,32,30,29,28,27,25,21,14,147,145,173,179,178,184,160,149,174,34,26,24,20,15,185,175,177,23,22,19,18])).
% 0.68/0.79 cnf(335,plain,
% 0.68/0.79 (~E(f7(a5),f33(f31(a29,a1),f31(a1,a29)))),
% 0.68/0.79 inference(scs_inference,[],[69,70,36,51,66,79,84,86,94,96,98,105,106,108,110,135,125,123,129,130,132,43,128,124,142,63,186,284,286,288,290,292,294,296,298,300,215,187,209,226,264,32,30,29,28,27,25,21,14,147,145,173,179,178,184,160,149,174,34,26,24,20,15,185,175,177,23,22,19,18,16,3])).
% 0.68/0.79 cnf(354,plain,
% 0.68/0.79 (P6(f15(x3541),x3541)),
% 0.68/0.79 inference(rename_variables,[],[128])).
% 0.68/0.79 cnf(357,plain,
% 0.68/0.79 (P6(f15(x3571),x3571)),
% 0.68/0.79 inference(rename_variables,[],[128])).
% 0.68/0.79 cnf(375,plain,
% 0.68/0.79 (E(f31(x3751,a1),x3751)),
% 0.68/0.79 inference(rename_variables,[],[125])).
% 0.68/0.79 cnf(383,plain,
% 0.68/0.79 (E(x3831,f33(x3831,x3831))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(384,plain,
% 0.68/0.79 (P18(x3841,x3841)),
% 0.68/0.79 inference(rename_variables,[],[126])).
% 0.68/0.79 cnf(386,plain,
% 0.68/0.79 (E(f31(x3861,a1),x3861)),
% 0.68/0.79 inference(rename_variables,[],[125])).
% 0.68/0.79 cnf(388,plain,
% 0.68/0.79 (E(f31(x3881,a1),x3881)),
% 0.68/0.79 inference(rename_variables,[],[125])).
% 0.68/0.79 cnf(392,plain,
% 0.68/0.79 (E(x3921,f33(x3921,x3921))),
% 0.68/0.79 inference(rename_variables,[],[186])).
% 0.68/0.79 cnf(397,plain,
% 0.68/0.79 ($false),
% 0.68/0.79 inference(scs_inference,[],[70,38,136,114,122,186,383,392,129,125,375,386,388,128,354,357,126,384,142,134,333,202,242,335,311,289,209,153,169,168,167,29,173,180,174,181,2,149,15,185,177,24,22,19,18,16,3,23,172]),
% 0.68/0.79 ['proof']).
% 0.68/0.79 % SZS output end Proof
% 0.68/0.79 % Total time :0.090000s
%------------------------------------------------------------------------------