TSTP Solution File: SEU085+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU085+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n012.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 16:17:27 EDT 2023
% Result : Theorem 0.21s 0.71s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU085+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 20:20:42 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 start to proof:theBenchmark
% 0.21/0.69 %-------------------------------------------
% 0.21/0.69 % File :CSE---1.6
% 0.21/0.69 % Problem :theBenchmark
% 0.21/0.69 % Transform :cnf
% 0.21/0.69 % Format :tptp:raw
% 0.21/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.69
% 0.21/0.69 % Result :Theorem 0.000000s
% 0.21/0.69 % Output :CNFRefutation 0.000000s
% 0.21/0.69 %-------------------------------------------
% 0.21/0.69 %------------------------------------------------------------------------------
% 0.21/0.69 % File : SEU085+1 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.69 % Domain : Set theory
% 0.21/0.69 % Problem : Finite sets, theorem 16
% 0.21/0.69 % Version : [Urb06] axioms : Especial.
% 0.21/0.69 % English :
% 0.21/0.69
% 0.21/0.69 % Refs : [Dar90] Darmochwal (1990), Finite Sets
% 0.21/0.69 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.21/0.69 % Source : [Urb06]
% 0.21/0.69 % Names : finset_1__t16_finset_1 [Urb06]
% 0.21/0.69
% 0.21/0.69 % Status : Theorem
% 0.21/0.69 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v3.2.0
% 0.21/0.69 % Syntax : Number of formulae : 60 ( 10 unt; 0 def)
% 0.21/0.69 % Number of atoms : 182 ( 4 equ)
% 0.21/0.69 % Maximal formula atoms : 10 ( 3 avg)
% 0.21/0.69 % Number of connectives : 139 ( 17 ~; 1 |; 95 &)
% 0.21/0.69 % ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% 0.21/0.69 % Maximal formula depth : 12 ( 4 avg)
% 0.21/0.69 % Maximal term depth : 2 ( 1 avg)
% 0.21/0.69 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty)
% 0.21/0.69 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.21/0.69 % Number of variables : 78 ( 52 !; 26 ?)
% 0.21/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.69
% 0.21/0.69 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.69 % library, www.mizar.org
% 0.21/0.69 %------------------------------------------------------------------------------
% 0.21/0.69 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.69 ! [A,B] :
% 0.21/0.69 ( in(A,B)
% 0.21/0.69 => ~ in(B,A) ) ).
% 0.21/0.69
% 0.21/0.69 fof(cc1_arytm_3,axiom,
% 0.21/0.69 ! [A] :
% 0.21/0.69 ( ordinal(A)
% 0.21/0.69 => ! [B] :
% 0.21/0.69 ( element(B,A)
% 0.21/0.69 => ( epsilon_transitive(B)
% 0.21/0.69 & epsilon_connected(B)
% 0.21/0.69 & ordinal(B) ) ) ) ).
% 0.21/0.69
% 0.21/0.69 fof(cc1_finset_1,axiom,
% 0.21/0.69 ! [A] :
% 0.21/0.69 ( empty(A)
% 0.21/0.69 => finite(A) ) ).
% 0.21/0.69
% 0.21/0.69 fof(cc1_funct_1,axiom,
% 0.21/0.69 ! [A] :
% 0.21/0.70 ( empty(A)
% 0.21/0.70 => function(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc1_ordinal1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ordinal(A)
% 0.21/0.70 => ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc1_relat_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( empty(A)
% 0.21/0.70 => relation(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc2_arytm_3,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ( empty(A)
% 0.21/0.70 & ordinal(A) )
% 0.21/0.70 => ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A)
% 0.21/0.70 & natural(A) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc2_finset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( finite(A)
% 0.21/0.70 => ! [B] :
% 0.21/0.70 ( element(B,powerset(A))
% 0.21/0.70 => finite(B) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc2_funct_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ( relation(A)
% 0.21/0.70 & empty(A)
% 0.21/0.70 & function(A) )
% 0.21/0.70 => ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & one_to_one(A) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc2_ordinal1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A) )
% 0.21/0.70 => ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc3_ordinal1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( empty(A)
% 0.21/0.70 => ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(cc4_arytm_3,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( element(A,positive_rationals)
% 0.21/0.70 => ( ordinal(A)
% 0.21/0.70 => ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A)
% 0.21/0.70 & natural(A) ) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(existence_m1_subset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ? [B] : element(B,A) ).
% 0.21/0.70
% 0.21/0.70 fof(fc12_finset_1,axiom,
% 0.21/0.70 ! [A,B] :
% 0.21/0.70 ( finite(A)
% 0.21/0.70 => finite(set_difference(A,B)) ) ).
% 0.21/0.70
% 0.21/0.70 fof(fc12_relat_1,axiom,
% 0.21/0.70 ( empty(empty_set)
% 0.21/0.70 & relation(empty_set)
% 0.21/0.70 & relation_empty_yielding(empty_set) ) ).
% 0.21/0.70
% 0.21/0.70 fof(fc1_subset_1,axiom,
% 0.21/0.70 ! [A] : ~ empty(powerset(A)) ).
% 0.21/0.70
% 0.21/0.70 fof(fc1_xboole_0,axiom,
% 0.21/0.70 empty(empty_set) ).
% 0.21/0.70
% 0.21/0.70 fof(fc2_ordinal1,axiom,
% 0.21/0.70 ( relation(empty_set)
% 0.21/0.70 & relation_empty_yielding(empty_set)
% 0.21/0.70 & function(empty_set)
% 0.21/0.70 & one_to_one(empty_set)
% 0.21/0.70 & empty(empty_set)
% 0.21/0.70 & epsilon_transitive(empty_set)
% 0.21/0.70 & epsilon_connected(empty_set)
% 0.21/0.70 & ordinal(empty_set) ) ).
% 0.21/0.70
% 0.21/0.70 fof(fc3_relat_1,axiom,
% 0.21/0.70 ! [A,B] :
% 0.21/0.70 ( ( relation(A)
% 0.21/0.70 & relation(B) )
% 0.21/0.70 => relation(set_difference(A,B)) ) ).
% 0.21/0.70
% 0.21/0.70 fof(fc4_relat_1,axiom,
% 0.21/0.70 ( empty(empty_set)
% 0.21/0.70 & relation(empty_set) ) ).
% 0.21/0.70
% 0.21/0.70 fof(fc8_arytm_3,axiom,
% 0.21/0.70 ~ empty(positive_rationals) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_arytm_3,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 & epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A)
% 0.21/0.70 & natural(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_finset_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 & finite(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_funcop_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & function_yielding(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_funct_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_ordinal1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_ordinal2,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A)
% 0.21/0.70 & being_limit_ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_relat_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( empty(A)
% 0.21/0.70 & relation(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_subset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 => ? [B] :
% 0.21/0.70 ( element(B,powerset(A))
% 0.21/0.70 & ~ empty(B) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc1_xboole_0,axiom,
% 0.21/0.70 ? [A] : empty(A) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_arytm_3,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( element(A,positive_rationals)
% 0.21/0.70 & ~ empty(A)
% 0.21/0.70 & epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_finset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ? [B] :
% 0.21/0.70 ( element(B,powerset(A))
% 0.21/0.70 & empty(B)
% 0.21/0.70 & relation(B)
% 0.21/0.70 & function(B)
% 0.21/0.70 & one_to_one(B)
% 0.21/0.70 & epsilon_transitive(B)
% 0.21/0.70 & epsilon_connected(B)
% 0.21/0.70 & ordinal(B)
% 0.21/0.70 & natural(B)
% 0.21/0.70 & finite(B) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_funct_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & empty(A)
% 0.21/0.70 & function(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_ordinal1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & one_to_one(A)
% 0.21/0.70 & empty(A)
% 0.21/0.70 & epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_ordinal2,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & transfinite_sequence(A)
% 0.21/0.70 & ordinal_yielding(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_relat_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 & relation(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_subset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ? [B] :
% 0.21/0.70 ( element(B,powerset(A))
% 0.21/0.70 & empty(B) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc2_xboole_0,axiom,
% 0.21/0.70 ? [A] : ~ empty(A) ).
% 0.21/0.70
% 0.21/0.70 fof(rc3_arytm_3,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( element(A,positive_rationals)
% 0.21/0.70 & empty(A)
% 0.21/0.70 & epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A)
% 0.21/0.70 & natural(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc3_finset_1,axiom,
% 0.21/0.70 ! [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 => ? [B] :
% 0.21/0.70 ( element(B,powerset(A))
% 0.21/0.70 & ~ empty(B)
% 0.21/0.70 & finite(B) ) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc3_funct_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & one_to_one(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc3_ordinal1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( ~ empty(A)
% 0.21/0.70 & epsilon_transitive(A)
% 0.21/0.70 & epsilon_connected(A)
% 0.21/0.70 & ordinal(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc3_relat_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & relation_empty_yielding(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc4_funct_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & relation_empty_yielding(A)
% 0.21/0.70 & function(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc4_ordinal1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.70 & function(A)
% 0.21/0.70 & transfinite_sequence(A) ) ).
% 0.21/0.70
% 0.21/0.70 fof(rc5_funct_1,axiom,
% 0.21/0.70 ? [A] :
% 0.21/0.70 ( relation(A)
% 0.21/0.71 & relation_non_empty(A)
% 0.21/0.71 & function(A) ) ).
% 0.21/0.71
% 0.21/0.71 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.71 ! [A,B] : subset(A,A) ).
% 0.21/0.71
% 0.21/0.71 fof(t13_finset_1,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ( ( subset(A,B)
% 0.21/0.71 & finite(B) )
% 0.21/0.71 => finite(A) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t16_finset_1,conjecture,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ( finite(A)
% 0.21/0.71 => finite(set_difference(A,B)) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t1_subset,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ( in(A,B)
% 0.21/0.71 => element(A,B) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t2_subset,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ( element(A,B)
% 0.21/0.71 => ( empty(B)
% 0.21/0.71 | in(A,B) ) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t36_xboole_1,axiom,
% 0.21/0.71 ! [A,B] : subset(set_difference(A,B),A) ).
% 0.21/0.71
% 0.21/0.71 fof(t3_boole,axiom,
% 0.21/0.71 ! [A] : set_difference(A,empty_set) = A ).
% 0.21/0.71
% 0.21/0.71 fof(t3_subset,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ( element(A,powerset(B))
% 0.21/0.71 <=> subset(A,B) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t4_boole,axiom,
% 0.21/0.71 ! [A] : set_difference(empty_set,A) = empty_set ).
% 0.21/0.71
% 0.21/0.71 fof(t4_subset,axiom,
% 0.21/0.71 ! [A,B,C] :
% 0.21/0.71 ( ( in(A,B)
% 0.21/0.71 & element(B,powerset(C)) )
% 0.21/0.71 => element(A,C) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t5_subset,axiom,
% 0.21/0.71 ! [A,B,C] :
% 0.21/0.71 ~ ( in(A,B)
% 0.21/0.71 & element(B,powerset(C))
% 0.21/0.71 & empty(C) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t6_boole,axiom,
% 0.21/0.71 ! [A] :
% 0.21/0.71 ( empty(A)
% 0.21/0.71 => A = empty_set ) ).
% 0.21/0.71
% 0.21/0.71 fof(t7_boole,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ~ ( in(A,B)
% 0.21/0.71 & empty(B) ) ).
% 0.21/0.71
% 0.21/0.71 fof(t8_boole,axiom,
% 0.21/0.71 ! [A,B] :
% 0.21/0.71 ~ ( empty(A)
% 0.21/0.71 & A != B
% 0.21/0.71 & empty(B) ) ).
% 0.21/0.71
% 0.21/0.71 %------------------------------------------------------------------------------
% 0.21/0.71 %-------------------------------------------
% 0.21/0.71 % Proof found
% 0.21/0.71 % SZS status Theorem for theBenchmark
% 0.21/0.71 % SZS output start Proof
% 0.21/0.71 %ClaNum:173(EqnAxiom:32)
% 0.21/0.71 %VarNum:134(SingletonVarNum:71)
% 0.21/0.71 %MaxLitNum:4
% 0.21/0.71 %MaxfuncDepth:1
% 0.21/0.71 %SharedTerms:105
% 0.21/0.71 %goalClause: 67 135
% 0.21/0.71 %singleGoalClaCount:2
% 0.21/0.71 [33]P1(a1)
% 0.21/0.71 [34]P1(a2)
% 0.21/0.71 [35]P1(a23)
% 0.21/0.71 [36]P1(a27)
% 0.21/0.71 [37]P1(a3)
% 0.21/0.71 [38]P1(a5)
% 0.21/0.71 [39]P1(a8)
% 0.21/0.71 [40]P1(a13)
% 0.21/0.71 [41]P2(a1)
% 0.21/0.71 [42]P2(a2)
% 0.21/0.71 [43]P2(a23)
% 0.21/0.71 [44]P2(a27)
% 0.21/0.71 [45]P2(a3)
% 0.21/0.71 [46]P2(a5)
% 0.21/0.71 [47]P2(a8)
% 0.21/0.71 [48]P2(a13)
% 0.21/0.71 [49]P3(a1)
% 0.21/0.71 [50]P3(a2)
% 0.21/0.71 [51]P3(a23)
% 0.21/0.71 [52]P3(a27)
% 0.21/0.71 [53]P3(a3)
% 0.21/0.71 [54]P3(a5)
% 0.21/0.71 [55]P3(a8)
% 0.21/0.71 [56]P3(a13)
% 0.21/0.71 [60]P4(a1)
% 0.21/0.71 [61]P4(a28)
% 0.21/0.71 [62]P4(a4)
% 0.21/0.71 [63]P4(a6)
% 0.21/0.71 [64]P4(a5)
% 0.21/0.71 [65]P4(a8)
% 0.21/0.71 [66]P7(a24)
% 0.21/0.71 [67]P7(a17)
% 0.21/0.71 [68]P8(a1)
% 0.21/0.71 [69]P8(a25)
% 0.21/0.71 [70]P8(a26)
% 0.21/0.71 [71]P8(a6)
% 0.21/0.71 [72]P8(a5)
% 0.21/0.71 [73]P8(a9)
% 0.21/0.71 [74]P8(a14)
% 0.21/0.71 [75]P8(a18)
% 0.21/0.71 [76]P8(a20)
% 0.21/0.71 [77]P8(a21)
% 0.21/0.71 [80]P13(a1)
% 0.21/0.71 [81]P13(a25)
% 0.21/0.71 [82]P13(a26)
% 0.21/0.71 [83]P13(a28)
% 0.21/0.71 [84]P13(a6)
% 0.21/0.71 [85]P13(a5)
% 0.21/0.71 [86]P13(a9)
% 0.21/0.71 [87]P13(a10)
% 0.21/0.71 [88]P13(a14)
% 0.21/0.71 [89]P13(a19)
% 0.21/0.71 [90]P13(a18)
% 0.21/0.71 [91]P13(a20)
% 0.21/0.71 [92]P13(a21)
% 0.21/0.71 [93]P9(a2)
% 0.21/0.71 [94]P9(a8)
% 0.21/0.71 [95]P12(a1)
% 0.21/0.71 [96]P12(a5)
% 0.21/0.71 [97]P12(a14)
% 0.21/0.71 [99]P15(a1)
% 0.21/0.71 [100]P15(a19)
% 0.21/0.71 [101]P15(a18)
% 0.21/0.71 [102]P10(a25)
% 0.21/0.71 [103]P5(a27)
% 0.21/0.71 [104]P16(a9)
% 0.21/0.71 [105]P16(a20)
% 0.21/0.71 [106]P14(a9)
% 0.21/0.71 [107]P17(a21)
% 0.21/0.71 [118]P6(a3,a29)
% 0.21/0.71 [119]P6(a8,a29)
% 0.21/0.71 [127]~P4(a29)
% 0.21/0.71 [128]~P4(a2)
% 0.21/0.71 [129]~P4(a24)
% 0.21/0.71 [130]~P4(a3)
% 0.21/0.71 [131]~P4(a10)
% 0.21/0.71 [132]~P4(a12)
% 0.21/0.71 [133]~P4(a13)
% 0.21/0.71 [135]~P7(f31(a17,a22))
% 0.21/0.71 [122]P18(x1221,x1221)
% 0.21/0.71 [108]P1(f7(x1081))
% 0.21/0.71 [109]P2(f7(x1091))
% 0.21/0.71 [110]P3(f7(x1101))
% 0.21/0.71 [111]P4(f7(x1111))
% 0.21/0.71 [112]P4(f11(x1121))
% 0.21/0.71 [113]P7(f7(x1131))
% 0.21/0.71 [114]P8(f7(x1141))
% 0.21/0.71 [115]P13(f7(x1151))
% 0.21/0.71 [116]P9(f7(x1161))
% 0.21/0.71 [117]P12(f7(x1171))
% 0.21/0.71 [120]E(f31(a1,x1201),a1)
% 0.21/0.71 [121]E(f31(x1211,a1),x1211)
% 0.21/0.71 [123]P6(f15(x1231),x1231)
% 0.21/0.71 [124]P6(f7(x1241),f32(x1241))
% 0.21/0.71 [125]P6(f11(x1251),f32(x1251))
% 0.21/0.71 [134]~P4(f32(x1341))
% 0.21/0.71 [126]P18(f31(x1261,x1262),x1261)
% 0.21/0.71 [136]~P4(x1361)+E(x1361,a1)
% 0.21/0.71 [137]~P4(x1371)+P1(x1371)
% 0.21/0.71 [138]~P1(x1381)+P2(x1381)
% 0.21/0.71 [139]~P4(x1391)+P2(x1391)
% 0.21/0.71 [140]~P1(x1401)+P3(x1401)
% 0.21/0.71 [141]~P4(x1411)+P3(x1411)
% 0.21/0.71 [142]~P4(x1421)+P7(x1421)
% 0.21/0.71 [143]~P4(x1431)+P8(x1431)
% 0.21/0.71 [144]~P4(x1441)+P13(x1441)
% 0.21/0.71 [145]P4(x1451)+P7(f16(x1451))
% 0.21/0.71 [151]P4(x1511)+~P4(f30(x1511))
% 0.21/0.71 [152]P4(x1521)+~P4(f16(x1521))
% 0.21/0.71 [155]P4(x1551)+P6(f30(x1551),f32(x1551))
% 0.21/0.71 [156]P4(x1561)+P6(f16(x1561),f32(x1561))
% 0.21/0.71 [154]~P4(x1541)+~P11(x1542,x1541)
% 0.21/0.71 [164]~P11(x1641,x1642)+P6(x1641,x1642)
% 0.21/0.71 [170]~P11(x1702,x1701)+~P11(x1701,x1702)
% 0.21/0.71 [165]~P7(x1651)+P7(f31(x1651,x1652))
% 0.21/0.71 [167]~P18(x1671,x1672)+P6(x1671,f32(x1672))
% 0.21/0.71 [171]P18(x1711,x1712)+~P6(x1711,f32(x1712))
% 0.21/0.71 [147]~P2(x1471)+~P3(x1471)+P1(x1471)
% 0.21/0.71 [150]~P1(x1501)+~P4(x1501)+P9(x1501)
% 0.21/0.71 [159]~P1(x1591)+P9(x1591)+~P6(x1591,a29)
% 0.21/0.71 [146]~P4(x1462)+~P4(x1461)+E(x1461,x1462)
% 0.21/0.71 [160]~P6(x1601,x1602)+P1(x1601)+~P1(x1602)
% 0.21/0.71 [161]~P6(x1611,x1612)+P2(x1611)+~P1(x1612)
% 0.21/0.71 [162]~P6(x1621,x1622)+P3(x1621)+~P1(x1622)
% 0.21/0.71 [163]~P18(x1631,x1632)+P7(x1631)+~P7(x1632)
% 0.21/0.71 [166]~P6(x1662,x1661)+P4(x1661)+P11(x1662,x1661)
% 0.21/0.71 [168]P7(x1681)+~P7(x1682)+~P6(x1681,f32(x1682))
% 0.21/0.71 [169]~P13(x1692)+~P13(x1691)+P13(f31(x1691,x1692))
% 0.21/0.71 [172]~P4(x1721)+~P11(x1722,x1723)+~P6(x1723,f32(x1721))
% 0.21/0.71 [173]P6(x1731,x1732)+~P11(x1731,x1733)+~P6(x1733,f32(x1732))
% 0.21/0.71 [153]~P4(x1531)+~P8(x1531)+~P13(x1531)+P12(x1531)
% 0.21/0.71 %EqnAxiom
% 0.21/0.71 [1]E(x11,x11)
% 0.21/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.71 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 0.21/0.71 [5]~E(x51,x52)+E(f32(x51),f32(x52))
% 0.21/0.71 [6]~E(x61,x62)+E(f30(x61),f30(x62))
% 0.21/0.71 [7]~E(x71,x72)+E(f16(x71),f16(x72))
% 0.21/0.71 [8]~E(x81,x82)+E(f11(x81),f11(x82))
% 0.21/0.71 [9]~E(x91,x92)+E(f31(x91,x93),f31(x92,x93))
% 0.21/0.71 [10]~E(x101,x102)+E(f31(x103,x101),f31(x103,x102))
% 0.21/0.71 [11]~E(x111,x112)+E(f15(x111),f15(x112))
% 0.21/0.71 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.21/0.71 [13]P6(x132,x133)+~E(x131,x132)+~P6(x131,x133)
% 0.21/0.71 [14]P6(x143,x142)+~E(x141,x142)+~P6(x143,x141)
% 0.21/0.71 [15]P11(x152,x153)+~E(x151,x152)+~P11(x151,x153)
% 0.21/0.71 [16]P11(x163,x162)+~E(x161,x162)+~P11(x163,x161)
% 0.21/0.71 [17]~P7(x171)+P7(x172)+~E(x171,x172)
% 0.21/0.71 [18]~P3(x181)+P3(x182)+~E(x181,x182)
% 0.21/0.71 [19]P18(x192,x193)+~E(x191,x192)+~P18(x191,x193)
% 0.21/0.71 [20]P18(x203,x202)+~E(x201,x202)+~P18(x203,x201)
% 0.21/0.71 [21]~P4(x211)+P4(x212)+~E(x211,x212)
% 0.21/0.71 [22]~P13(x221)+P13(x222)+~E(x221,x222)
% 0.21/0.71 [23]~P2(x231)+P2(x232)+~E(x231,x232)
% 0.21/0.71 [24]~P9(x241)+P9(x242)+~E(x241,x242)
% 0.21/0.71 [25]~P8(x251)+P8(x252)+~E(x251,x252)
% 0.21/0.71 [26]~P12(x261)+P12(x262)+~E(x261,x262)
% 0.21/0.71 [27]~P16(x271)+P16(x272)+~E(x271,x272)
% 0.21/0.71 [28]~P14(x281)+P14(x282)+~E(x281,x282)
% 0.21/0.71 [29]~P15(x291)+P15(x292)+~E(x291,x292)
% 0.21/0.71 [30]~P5(x301)+P5(x302)+~E(x301,x302)
% 0.21/0.71 [31]~P10(x311)+P10(x312)+~E(x311,x312)
% 0.21/0.71 [32]~P17(x321)+P17(x322)+~E(x321,x322)
% 0.21/0.71
% 0.21/0.71 %-------------------------------------------
% 0.21/0.71 cnf(174,plain,
% 0.21/0.71 ($false),
% 0.21/0.71 inference(scs_inference,[],[67,135,165]),
% 0.21/0.71 ['proof']).
% 0.21/0.71 % SZS output end Proof
% 0.21/0.71 % Total time :0.000000s
%------------------------------------------------------------------------------