TSTP Solution File: SEU083+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU083+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 : n017.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 16:17:26 EDT 2023
% Result : Theorem 0.21s 0.68s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU083+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 : n017.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 14:56:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 start to proof:theBenchmark
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 % File :CSE---1.6
% 0.21/0.66 % Problem :theBenchmark
% 0.21/0.66 % Transform :cnf
% 0.21/0.66 % Format :tptp:raw
% 0.21/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.66
% 0.21/0.66 % Result :Theorem 0.010000s
% 0.21/0.66 % Output :CNFRefutation 0.010000s
% 0.21/0.66 %-------------------------------------------
% 0.21/0.67 %------------------------------------------------------------------------------
% 0.21/0.67 % File : SEU083+1 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.67 % Domain : Set theory
% 0.21/0.67 % Problem : Finite sets, theorem 14
% 0.21/0.67 % Version : [Urb06] axioms : Especial.
% 0.21/0.67 % English :
% 0.21/0.67
% 0.21/0.67 % Refs : [Dar90] Darmochwal (1990), Finite Sets
% 0.21/0.67 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.21/0.67 % Source : [Urb06]
% 0.21/0.67 % Names : finset_1__t14_finset_1 [Urb06]
% 0.21/0.67
% 0.21/0.67 % Status : Theorem
% 0.21/0.67 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v4.0.1, 0.04 v3.7.0, 0.00 v3.2.0
% 0.21/0.67 % Syntax : Number of formulae : 62 ( 10 unt; 0 def)
% 0.21/0.67 % Number of atoms : 188 ( 5 equ)
% 0.21/0.67 % Maximal formula atoms : 10 ( 3 avg)
% 0.21/0.67 % Number of connectives : 147 ( 21 ~; 1 |; 97 &)
% 0.21/0.67 % ( 1 <=>; 27 =>; 0 <=; 0 <~>)
% 0.21/0.67 % Maximal formula depth : 12 ( 5 avg)
% 0.21/0.67 % Maximal term depth : 2 ( 1 avg)
% 0.21/0.67 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty)
% 0.21/0.67 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.21/0.67 % Number of variables : 83 ( 57 !; 26 ?)
% 0.21/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.67
% 0.21/0.67 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.67 % library, www.mizar.org
% 0.21/0.67 %------------------------------------------------------------------------------
% 0.21/0.67 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.67 ! [A,B] : subset(A,A) ).
% 0.21/0.67
% 0.21/0.67 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.67 ! [A,B] :
% 0.21/0.67 ( in(A,B)
% 0.21/0.67 => ~ in(B,A) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc4_relat_1,axiom,
% 0.21/0.67 ( empty(empty_set)
% 0.21/0.67 & relation(empty_set) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc12_relat_1,axiom,
% 0.21/0.67 ( empty(empty_set)
% 0.21/0.67 & relation(empty_set)
% 0.21/0.67 & relation_empty_yielding(empty_set) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc2_ordinal1,axiom,
% 0.21/0.67 ( relation(empty_set)
% 0.21/0.67 & relation_empty_yielding(empty_set)
% 0.21/0.67 & function(empty_set)
% 0.21/0.67 & one_to_one(empty_set)
% 0.21/0.67 & empty(empty_set)
% 0.21/0.67 & epsilon_transitive(empty_set)
% 0.21/0.67 & epsilon_connected(empty_set)
% 0.21/0.67 & ordinal(empty_set) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc1_xboole_0,axiom,
% 0.21/0.67 empty(empty_set) ).
% 0.21/0.67
% 0.21/0.67 fof(t1_boole,axiom,
% 0.21/0.67 ! [A] : set_union2(A,empty_set) = A ).
% 0.21/0.67
% 0.21/0.67 fof(t1_subset,axiom,
% 0.21/0.67 ! [A,B] :
% 0.21/0.67 ( in(A,B)
% 0.21/0.67 => element(A,B) ) ).
% 0.21/0.67
% 0.21/0.67 fof(t4_subset,axiom,
% 0.21/0.67 ! [A,B,C] :
% 0.21/0.67 ( ( in(A,B)
% 0.21/0.67 & element(B,powerset(C)) )
% 0.21/0.67 => element(A,C) ) ).
% 0.21/0.67
% 0.21/0.67 fof(t5_subset,axiom,
% 0.21/0.67 ! [A,B,C] :
% 0.21/0.67 ~ ( in(A,B)
% 0.21/0.67 & element(B,powerset(C))
% 0.21/0.67 & empty(C) ) ).
% 0.21/0.67
% 0.21/0.67 fof(existence_m1_subset_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ? [B] : element(B,A) ).
% 0.21/0.67
% 0.21/0.67 fof(cc1_finset_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( empty(A)
% 0.21/0.67 => finite(A) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc2_finset_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( finite(A)
% 0.21/0.67 => ! [B] :
% 0.21/0.67 ( element(B,powerset(A))
% 0.21/0.67 => finite(B) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc1_funct_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( empty(A)
% 0.21/0.67 => function(A) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc2_funct_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( ( relation(A)
% 0.21/0.67 & empty(A)
% 0.21/0.67 & function(A) )
% 0.21/0.67 => ( relation(A)
% 0.21/0.67 & function(A)
% 0.21/0.67 & one_to_one(A) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc2_relat_1,axiom,
% 0.21/0.67 ! [A,B] :
% 0.21/0.67 ( ( relation(A)
% 0.21/0.67 & relation(B) )
% 0.21/0.67 => relation(set_union2(A,B)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc1_relat_1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( empty(A)
% 0.21/0.67 => relation(A) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc8_arytm_3,axiom,
% 0.21/0.67 ~ empty(positive_rationals) ).
% 0.21/0.67
% 0.21/0.67 fof(cc1_arytm_3,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( ordinal(A)
% 0.21/0.67 => ! [B] :
% 0.21/0.67 ( element(B,A)
% 0.21/0.67 => ( epsilon_transitive(B)
% 0.21/0.67 & epsilon_connected(B)
% 0.21/0.67 & ordinal(B) ) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc2_arytm_3,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( ( empty(A)
% 0.21/0.67 & ordinal(A) )
% 0.21/0.67 => ( epsilon_transitive(A)
% 0.21/0.67 & epsilon_connected(A)
% 0.21/0.67 & ordinal(A)
% 0.21/0.67 & natural(A) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc4_arytm_3,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( element(A,positive_rationals)
% 0.21/0.67 => ( ordinal(A)
% 0.21/0.67 => ( epsilon_transitive(A)
% 0.21/0.67 & epsilon_connected(A)
% 0.21/0.67 & ordinal(A)
% 0.21/0.67 & natural(A) ) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc1_ordinal1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( ordinal(A)
% 0.21/0.67 => ( epsilon_transitive(A)
% 0.21/0.67 & epsilon_connected(A) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc2_ordinal1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( ( epsilon_transitive(A)
% 0.21/0.67 & epsilon_connected(A) )
% 0.21/0.67 => ordinal(A) ) ).
% 0.21/0.67
% 0.21/0.67 fof(cc3_ordinal1,axiom,
% 0.21/0.67 ! [A] :
% 0.21/0.67 ( empty(A)
% 0.21/0.67 => ( epsilon_transitive(A)
% 0.21/0.67 & epsilon_connected(A)
% 0.21/0.67 & ordinal(A) ) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc1_subset_1,axiom,
% 0.21/0.67 ! [A] : ~ empty(powerset(A)) ).
% 0.21/0.67
% 0.21/0.67 fof(fc2_xboole_0,axiom,
% 0.21/0.67 ! [A,B] :
% 0.21/0.67 ( ~ empty(A)
% 0.21/0.67 => ~ empty(set_union2(A,B)) ) ).
% 0.21/0.67
% 0.21/0.67 fof(fc3_xboole_0,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 => ~ empty(set_union2(B,A)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(t2_subset,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( element(A,B)
% 0.21/0.68 => ( empty(B)
% 0.21/0.68 | in(A,B) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(t3_subset,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( element(A,powerset(B))
% 0.21/0.68 <=> subset(A,B) ) ).
% 0.21/0.68
% 0.21/0.68 fof(t6_boole,axiom,
% 0.21/0.68 ! [A] :
% 0.21/0.68 ( empty(A)
% 0.21/0.68 => A = empty_set ) ).
% 0.21/0.68
% 0.21/0.68 fof(t7_boole,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ~ ( in(A,B)
% 0.21/0.68 & empty(B) ) ).
% 0.21/0.68
% 0.21/0.68 fof(t8_boole,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ~ ( empty(A)
% 0.21/0.68 & A != B
% 0.21/0.68 & empty(B) ) ).
% 0.21/0.68
% 0.21/0.68 fof(commutativity_k2_xboole_0,axiom,
% 0.21/0.68 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.21/0.68
% 0.21/0.68 fof(idempotence_k2_xboole_0,axiom,
% 0.21/0.68 ! [A,B] : set_union2(A,A) = A ).
% 0.21/0.68
% 0.21/0.68 fof(fc9_finset_1,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( ( finite(A)
% 0.21/0.68 & finite(B) )
% 0.21/0.68 => finite(set_union2(A,B)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_finset_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 & finite(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_finset_1,axiom,
% 0.21/0.68 ! [A] :
% 0.21/0.68 ? [B] :
% 0.21/0.68 ( element(B,powerset(A))
% 0.21/0.68 & empty(B)
% 0.21/0.68 & relation(B)
% 0.21/0.68 & function(B)
% 0.21/0.68 & one_to_one(B)
% 0.21/0.68 & epsilon_transitive(B)
% 0.21/0.68 & epsilon_connected(B)
% 0.21/0.68 & ordinal(B)
% 0.21/0.68 & natural(B)
% 0.21/0.68 & finite(B) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc3_finset_1,axiom,
% 0.21/0.68 ! [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 => ? [B] :
% 0.21/0.68 ( element(B,powerset(A))
% 0.21/0.68 & ~ empty(B)
% 0.21/0.68 & finite(B) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_funct_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_funct_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & empty(A)
% 0.21/0.68 & function(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc3_funct_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A)
% 0.21/0.68 & one_to_one(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc4_funct_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & relation_empty_yielding(A)
% 0.21/0.68 & function(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc5_funct_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & relation_non_empty(A)
% 0.21/0.68 & function(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_ordinal2,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A)
% 0.21/0.68 & being_limit_ordinal(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_ordinal2,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A)
% 0.21/0.68 & transfinite_sequence(A)
% 0.21/0.68 & ordinal_yielding(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_relat_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( empty(A)
% 0.21/0.68 & relation(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_relat_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 & relation(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc3_relat_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & relation_empty_yielding(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_arytm_3,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 & epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A)
% 0.21/0.68 & natural(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_arytm_3,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( element(A,positive_rationals)
% 0.21/0.68 & ~ empty(A)
% 0.21/0.68 & epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc3_arytm_3,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( element(A,positive_rationals)
% 0.21/0.68 & empty(A)
% 0.21/0.68 & epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A)
% 0.21/0.68 & natural(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_ordinal1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_ordinal1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A)
% 0.21/0.68 & one_to_one(A)
% 0.21/0.68 & empty(A)
% 0.21/0.68 & epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc3_ordinal1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 & epsilon_transitive(A)
% 0.21/0.68 & epsilon_connected(A)
% 0.21/0.68 & ordinal(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc4_ordinal1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A)
% 0.21/0.68 & transfinite_sequence(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_subset_1,axiom,
% 0.21/0.68 ! [A] :
% 0.21/0.68 ( ~ empty(A)
% 0.21/0.68 => ? [B] :
% 0.21/0.68 ( element(B,powerset(A))
% 0.21/0.68 & ~ empty(B) ) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_subset_1,axiom,
% 0.21/0.68 ! [A] :
% 0.21/0.68 ? [B] :
% 0.21/0.68 ( element(B,powerset(A))
% 0.21/0.68 & empty(B) ) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_xboole_0,axiom,
% 0.21/0.68 ? [A] : empty(A) ).
% 0.21/0.68
% 0.21/0.68 fof(rc2_xboole_0,axiom,
% 0.21/0.68 ? [A] : ~ empty(A) ).
% 0.21/0.68
% 0.21/0.68 fof(rc1_funcop_1,axiom,
% 0.21/0.68 ? [A] :
% 0.21/0.68 ( relation(A)
% 0.21/0.68 & function(A)
% 0.21/0.68 & function_yielding(A) ) ).
% 0.21/0.68
% 0.21/0.68 fof(t14_finset_1,conjecture,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( ( finite(A)
% 0.21/0.68 & finite(B) )
% 0.21/0.68 => finite(set_union2(A,B)) ) ).
% 0.21/0.68
% 0.21/0.68 fof(l3_finset_1,axiom,
% 0.21/0.68 ! [A,B] :
% 0.21/0.68 ( ( finite(A)
% 0.21/0.68 & finite(B) )
% 0.21/0.68 => finite(set_union2(A,B)) ) ).
% 0.21/0.68
% 0.21/0.68 %------------------------------------------------------------------------------
% 0.21/0.68 %-------------------------------------------
% 0.21/0.68 % Proof found
% 0.21/0.68 % SZS status Theorem for theBenchmark
% 0.21/0.68 % SZS output start Proof
% 0.21/0.68 %ClaNum:176(EqnAxiom:32)
% 0.21/0.68 %VarNum:140(SingletonVarNum:73)
% 0.21/0.68 %MaxLitNum:4
% 0.21/0.68 %MaxfuncDepth:1
% 0.21/0.68 %SharedTerms:106
% 0.21/0.68 %goalClause: 99 100 136
% 0.21/0.68 %singleGoalClaCount:3
% 0.21/0.68 [36]P1(a1)
% 0.21/0.68 [37]P1(a2)
% 0.21/0.68 [38]P1(a3)
% 0.21/0.68 [39]P1(a6)
% 0.21/0.68 [40]P1(a11)
% 0.21/0.68 [41]P1(a13)
% 0.21/0.68 [44]P4(a1)
% 0.21/0.68 [45]P4(a19)
% 0.21/0.68 [46]P4(a2)
% 0.21/0.68 [47]P4(a27)
% 0.21/0.68 [48]P4(a28)
% 0.21/0.68 [49]P4(a29)
% 0.21/0.68 [50]P4(a4)
% 0.21/0.68 [51]P4(a3)
% 0.21/0.68 [52]P4(a7)
% 0.21/0.68 [53]P4(a8)
% 0.21/0.68 [54]P4(a11)
% 0.21/0.68 [55]P4(a14)
% 0.21/0.68 [56]P4(a20)
% 0.21/0.68 [58]P15(a1)
% 0.21/0.68 [59]P15(a28)
% 0.21/0.68 [60]P15(a8)
% 0.21/0.68 [61]P5(a1)
% 0.21/0.68 [62]P5(a19)
% 0.21/0.68 [63]P5(a2)
% 0.21/0.68 [64]P5(a27)
% 0.21/0.68 [65]P5(a28)
% 0.21/0.68 [66]P5(a29)
% 0.21/0.68 [67]P5(a4)
% 0.21/0.68 [68]P5(a11)
% 0.21/0.68 [69]P5(a14)
% 0.21/0.68 [70]P5(a20)
% 0.21/0.68 [71]P9(a1)
% 0.21/0.68 [72]P9(a27)
% 0.21/0.68 [73]P9(a11)
% 0.21/0.68 [74]P6(a1)
% 0.21/0.68 [75]P6(a5)
% 0.21/0.68 [76]P6(a9)
% 0.21/0.68 [77]P6(a10)
% 0.21/0.68 [78]P6(a6)
% 0.21/0.68 [79]P6(a12)
% 0.21/0.68 [80]P6(a11)
% 0.21/0.68 [81]P6(a15)
% 0.21/0.68 [82]P7(a1)
% 0.21/0.68 [83]P7(a5)
% 0.21/0.68 [84]P7(a9)
% 0.21/0.68 [85]P7(a10)
% 0.21/0.68 [86]P7(a6)
% 0.21/0.68 [87]P7(a12)
% 0.21/0.68 [88]P7(a11)
% 0.21/0.68 [89]P7(a15)
% 0.21/0.68 [90]P13(a1)
% 0.21/0.68 [91]P13(a5)
% 0.21/0.68 [92]P13(a9)
% 0.21/0.68 [93]P13(a10)
% 0.21/0.68 [94]P13(a6)
% 0.21/0.68 [95]P13(a12)
% 0.21/0.68 [96]P13(a11)
% 0.21/0.68 [97]P13(a15)
% 0.21/0.68 [98]P8(a22)
% 0.21/0.68 [99]P8(a23)
% 0.21/0.68 [100]P8(a24)
% 0.21/0.68 [101]P10(a9)
% 0.21/0.68 [102]P10(a6)
% 0.21/0.68 [103]P16(a29)
% 0.21/0.68 [104]P2(a5)
% 0.21/0.68 [105]P17(a4)
% 0.21/0.68 [106]P17(a14)
% 0.21/0.68 [107]P14(a4)
% 0.21/0.68 [108]P11(a20)
% 0.21/0.68 [119]P3(a10,a30)
% 0.21/0.68 [120]P3(a6,a30)
% 0.21/0.68 [128]~P1(a30)
% 0.21/0.68 [129]~P1(a22)
% 0.21/0.68 [130]~P1(a7)
% 0.21/0.68 [131]~P1(a9)
% 0.21/0.68 [132]~P1(a10)
% 0.21/0.68 [133]~P1(a15)
% 0.21/0.68 [134]~P1(a21)
% 0.21/0.68 [136]~P8(f31(a23,a24))
% 0.21/0.68 [122]P18(x1221,x1221)
% 0.21/0.68 [109]P1(f25(x1091))
% 0.21/0.68 [110]P1(f17(x1101))
% 0.21/0.68 [111]P4(f25(x1111))
% 0.21/0.68 [112]P5(f25(x1121))
% 0.21/0.68 [113]P9(f25(x1131))
% 0.21/0.68 [114]P6(f25(x1141))
% 0.21/0.69 [115]P7(f25(x1151))
% 0.21/0.69 [116]P13(f25(x1161))
% 0.21/0.69 [117]P8(f25(x1171))
% 0.21/0.69 [118]P10(f25(x1181))
% 0.21/0.69 [121]E(f31(x1211,a1),x1211)
% 0.21/0.69 [123]E(f31(x1231,x1231),x1231)
% 0.21/0.69 [124]P3(f16(x1241),x1241)
% 0.21/0.69 [125]P3(f25(x1251),f32(x1251))
% 0.21/0.69 [126]P3(f17(x1261),f32(x1261))
% 0.21/0.69 [135]~P1(f32(x1351))
% 0.21/0.69 [127]E(f31(x1271,x1272),f31(x1272,x1271))
% 0.21/0.69 [137]~P1(x1371)+E(x1371,a1)
% 0.21/0.69 [138]~P1(x1381)+P4(x1381)
% 0.21/0.69 [139]~P1(x1391)+P5(x1391)
% 0.21/0.69 [140]~P1(x1401)+P6(x1401)
% 0.21/0.69 [141]~P13(x1411)+P6(x1411)
% 0.21/0.69 [142]~P1(x1421)+P7(x1421)
% 0.21/0.69 [143]~P13(x1431)+P7(x1431)
% 0.21/0.69 [144]~P1(x1441)+P13(x1441)
% 0.21/0.69 [145]~P1(x1451)+P8(x1451)
% 0.21/0.69 [146]P1(x1461)+P8(f26(x1461))
% 0.21/0.69 [152]P1(x1521)+~P1(f26(x1521))
% 0.21/0.69 [153]P1(x1531)+~P1(f18(x1531))
% 0.21/0.69 [156]P1(x1561)+P3(f26(x1561),f32(x1561))
% 0.21/0.69 [157]P1(x1571)+P3(f18(x1571),f32(x1571))
% 0.21/0.69 [155]~P1(x1551)+~P12(x1552,x1551)
% 0.21/0.69 [164]~P12(x1641,x1642)+P3(x1641,x1642)
% 0.21/0.69 [171]~P12(x1712,x1711)+~P12(x1711,x1712)
% 0.21/0.69 [166]~P18(x1661,x1662)+P3(x1661,f32(x1662))
% 0.21/0.69 [172]P18(x1721,x1722)+~P3(x1721,f32(x1722))
% 0.21/0.69 [173]P1(x1731)+~P1(f31(x1732,x1731))
% 0.21/0.69 [174]P1(x1741)+~P1(f31(x1741,x1742))
% 0.21/0.69 [150]~P6(x1501)+~P7(x1501)+P13(x1501)
% 0.21/0.69 [151]~P1(x1511)+~P13(x1511)+P10(x1511)
% 0.21/0.69 [160]~P13(x1601)+P10(x1601)+~P3(x1601,a30)
% 0.21/0.69 [147]~P1(x1472)+~P1(x1471)+E(x1471,x1472)
% 0.21/0.69 [161]~P3(x1611,x1612)+P6(x1611)+~P13(x1612)
% 0.21/0.69 [162]~P3(x1621,x1622)+P7(x1621)+~P13(x1622)
% 0.21/0.69 [163]~P3(x1631,x1632)+P13(x1631)+~P13(x1632)
% 0.21/0.69 [165]~P3(x1652,x1651)+P1(x1651)+P12(x1652,x1651)
% 0.21/0.69 [167]P8(x1671)+~P8(x1672)+~P3(x1671,f32(x1672))
% 0.21/0.69 [168]~P4(x1682)+~P4(x1681)+P4(f31(x1681,x1682))
% 0.21/0.69 [170]~P8(x1702)+~P8(x1701)+P8(f31(x1701,x1702))
% 0.21/0.69 [175]~P1(x1751)+~P12(x1752,x1753)+~P3(x1753,f32(x1751))
% 0.21/0.69 [176]P3(x1761,x1762)+~P12(x1761,x1763)+~P3(x1763,f32(x1762))
% 0.21/0.69 [154]~P1(x1541)+~P4(x1541)+~P5(x1541)+P9(x1541)
% 0.21/0.69 %EqnAxiom
% 0.21/0.69 [1]E(x11,x11)
% 0.21/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.69 [4]~E(x41,x42)+E(f25(x41),f25(x42))
% 0.21/0.69 [5]~E(x51,x52)+E(f17(x51),f17(x52))
% 0.21/0.69 [6]~E(x61,x62)+E(f32(x61),f32(x62))
% 0.21/0.69 [7]~E(x71,x72)+E(f18(x71),f18(x72))
% 0.21/0.69 [8]~E(x81,x82)+E(f31(x81,x83),f31(x82,x83))
% 0.21/0.69 [9]~E(x91,x92)+E(f31(x93,x91),f31(x93,x92))
% 0.21/0.69 [10]~E(x101,x102)+E(f26(x101),f26(x102))
% 0.21/0.69 [11]~E(x111,x112)+E(f16(x111),f16(x112))
% 0.21/0.69 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.21/0.69 [13]P3(x132,x133)+~E(x131,x132)+~P3(x131,x133)
% 0.21/0.69 [14]P3(x143,x142)+~E(x141,x142)+~P3(x143,x141)
% 0.21/0.69 [15]P12(x152,x153)+~E(x151,x152)+~P12(x151,x153)
% 0.21/0.69 [16]P12(x163,x162)+~E(x161,x162)+~P12(x163,x161)
% 0.21/0.69 [17]~P13(x171)+P13(x172)+~E(x171,x172)
% 0.21/0.69 [18]~P7(x181)+P7(x182)+~E(x181,x182)
% 0.21/0.69 [19]~P8(x191)+P8(x192)+~E(x191,x192)
% 0.21/0.69 [20]~P6(x201)+P6(x202)+~E(x201,x202)
% 0.21/0.69 [21]P18(x212,x213)+~E(x211,x212)+~P18(x211,x213)
% 0.21/0.69 [22]P18(x223,x222)+~E(x221,x222)+~P18(x223,x221)
% 0.21/0.69 [23]~P5(x231)+P5(x232)+~E(x231,x232)
% 0.21/0.69 [24]~P4(x241)+P4(x242)+~E(x241,x242)
% 0.21/0.69 [25]~P16(x251)+P16(x252)+~E(x251,x252)
% 0.21/0.69 [26]~P2(x261)+P2(x262)+~E(x261,x262)
% 0.21/0.69 [27]~P17(x271)+P17(x272)+~E(x271,x272)
% 0.21/0.69 [28]~P9(x281)+P9(x282)+~E(x281,x282)
% 0.21/0.69 [29]~P14(x291)+P14(x292)+~E(x291,x292)
% 0.21/0.69 [30]~P11(x301)+P11(x302)+~E(x301,x302)
% 0.21/0.69 [31]~P10(x311)+P10(x312)+~E(x311,x312)
% 0.21/0.69 [32]~P15(x321)+P15(x322)+~E(x321,x322)
% 0.21/0.69
% 0.21/0.69 %-------------------------------------------
% 0.21/0.69 cnf(183,plain,
% 0.21/0.69 (P3(f16(x1831),x1831)),
% 0.21/0.69 inference(rename_variables,[],[124])).
% 0.21/0.69 cnf(193,plain,
% 0.21/0.69 (E(f31(x1931,a1),x1931)),
% 0.21/0.69 inference(rename_variables,[],[121])).
% 0.21/0.69 cnf(197,plain,
% 0.21/0.69 (P3(f16(x1971),x1971)),
% 0.21/0.69 inference(rename_variables,[],[124])).
% 0.21/0.69 cnf(198,plain,
% 0.21/0.69 (E(f31(x1981,x1981),x1981)),
% 0.21/0.69 inference(rename_variables,[],[123])).
% 0.21/0.69 cnf(200,plain,
% 0.21/0.69 (E(f31(x2001,x2001),x2001)),
% 0.21/0.69 inference(rename_variables,[],[123])).
% 0.21/0.69 cnf(210,plain,
% 0.21/0.69 (P3(f16(x2101),x2101)),
% 0.21/0.69 inference(rename_variables,[],[124])).
% 0.21/0.69 cnf(214,plain,
% 0.21/0.69 ($false),
% 0.21/0.69 inference(scs_inference,[],[99,122,100,36,44,58,61,71,74,82,90,93,119,128,136,123,198,200,124,183,197,210,121,193,2,155,145,172,32,28,24,23,22,21,20,19,18,17,14,12,3,165,160,151,175,167,170]),
% 0.21/0.69 ['proof']).
% 0.21/0.69 % SZS output end Proof
% 0.21/0.69 % Total time :0.010000s
%------------------------------------------------------------------------------