TSTP Solution File: SWW469+5 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n026.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 : Fri Sep 1 00:14:23 EDT 2023
% Result : Theorem 0.65s 0.84s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n026.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 : Sun Aug 27 19:22:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.65/0.82 %-------------------------------------------
% 0.65/0.82 % File :CSE---1.6
% 0.65/0.82 % Problem :theBenchmark
% 0.65/0.82 % Transform :cnf
% 0.65/0.82 % Format :tptp:raw
% 0.65/0.82 % Command :java -jar mcs_scs.jar %d %s
% 0.65/0.82
% 0.65/0.82 % Result :Theorem 0.180000s
% 0.65/0.82 % Output :CNFRefutation 0.180000s
% 0.65/0.82 %-------------------------------------------
% 0.65/0.83 %------------------------------------------------------------------------------
% 0.65/0.83 % File : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.65/0.83 % Domain : Software Verification
% 0.65/0.83 % Problem : Hoare's Logic with Procedures line 112, 100 axioms selected
% 0.65/0.83 % Version : Especial.
% 0.65/0.83 % English :
% 0.65/0.83
% 0.65/0.83 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.65/0.83 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.65/0.83 % Source : [Bla11]
% 0.65/0.83 % Names : hoare_100_fofpt_l112 [Bla11]
% 0.65/0.83
% 0.65/0.83 % Status : Theorem
% 0.65/0.83 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0
% 0.65/0.83 % Syntax : Number of formulae : 63 ( 31 unt; 0 def)
% 0.65/0.83 % Number of atoms : 114 ( 45 equ)
% 0.65/0.83 % Maximal formula atoms : 5 ( 1 avg)
% 0.65/0.83 % Number of connectives : 64 ( 13 ~; 2 |; 3 &)
% 0.65/0.83 % ( 10 <=>; 36 =>; 0 <=; 0 <~>)
% 0.65/0.83 % Maximal formula depth : 12 ( 5 avg)
% 0.65/0.83 % Maximal term depth : 12 ( 2 avg)
% 0.65/0.83 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.65/0.83 % Number of functors : 22 ( 22 usr; 6 con; 0-4 aty)
% 0.65/0.83 % Number of variables : 157 ( 155 !; 2 ?)
% 0.65/0.83 % SPC : FOF_THM_RFO_SEQ
% 0.65/0.83
% 0.65/0.83 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.65/0.83 % 2011-08-09 13:53:52
% 0.65/0.83 % : Encoded with polymorphic tags.
% 0.65/0.83 %------------------------------------------------------------------------------
% 0.65/0.83 %----Explicit typings (17)
% 0.65/0.83 fof(tsy_c_HOL_Oequal__class_Oequal_res,axiom,
% 0.65/0.83 ! [X_a] :
% 0.65/0.83 ( cl_HOL_Oequal(X_a)
% 0.65/0.83 => ti(fun(X_a,fun(X_a,bool)),equal_equal(X_a)) = equal_equal(X_a) ) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_HOL_Oinduct__equal_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(X_a,fun(X_a,bool)),induct_equal(X_a)) = induct_equal(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_HOL_Oinduct__false_res,axiom,
% 0.65/0.83 ti(bool,induct_false) = induct_false ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_HOL_Oinduct__true_res,axiom,
% 0.65/0.83 ti(bool,induct_true) = induct_true ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_HOL_Oundefined_res,axiom,
% 0.65/0.83 ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),hoare_244953527triple(X_a)) = hoare_244953527triple(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)) = hoare_2037801986triple(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res,hypothesis,
% 0.65/0.83 ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),hoare_1580379338ep_set(X_a)) = hoare_1580379338ep_set(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Set_OCollect_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_Typedef_Otype__definition_res,axiom,
% 0.65/0.83 ! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool))),type_definition(X_a,X_b)) = type_definition(X_a,X_b) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_fequal_res,axiom,
% 0.65/0.83 ! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_hAPP_arg1,axiom,
% 0.65/0.83 ! [X_b,X_a,B_1,B_2] : hAPP(X_b,X_a,ti(fun(X_b,X_a),B_1),B_2) = hAPP(X_b,X_a,B_1,B_2) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_hAPP_arg2,axiom,
% 0.65/0.83 ! [X_b,X_a,B_1,B_2] : hAPP(X_b,X_a,B_1,ti(X_b,B_2)) = hAPP(X_b,X_a,B_1,B_2) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_hAPP_res,axiom,
% 0.65/0.83 ! [X_a,X_b,B_1,B_2] : ti(X_a,hAPP(X_b,X_a,B_1,B_2)) = hAPP(X_b,X_a,B_1,B_2) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_hBOOL_arg1,hypothesis,
% 0.65/0.83 ! [B_1] :
% 0.65/0.83 ( hBOOL(ti(bool,B_1))
% 0.65/0.83 <=> hBOOL(B_1) ) ).
% 0.65/0.83
% 0.65/0.83 fof(tsy_c_member_res,axiom,
% 0.65/0.83 ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b) ).
% 0.65/0.83
% 0.65/0.83 %----Relevant facts (32)
% 0.65/0.83 fof(fact_0_state__not__singleton__def,axiom,
% 0.65/0.83 ( hBOOL(hoare_1883395792gleton)
% 0.65/0.83 <=> ? [S,T] : ti(state,S) != ti(state,T) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_1_equal__triple__def,axiom,
% 0.65/0.83 ! [X_a,X_1,Y_1] :
% 0.65/0.83 ( hBOOL(hAPP(hoare_509422987triple(X_a),bool,hAPP(hoare_509422987triple(X_a),fun(hoare_509422987triple(X_a),bool),equal_equal(hoare_509422987triple(X_a)),X_1),Y_1))
% 0.65/0.83 <=> X_1 = Y_1 ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_2_Rep__triple__inject,axiom,
% 0.65/0.83 ! [X_a,X_1,Y_1] :
% 0.65/0.83 ( hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1) = hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),Y_1)
% 0.65/0.83 <=> X_1 = Y_1 ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_3_equal,axiom,
% 0.65/0.83 ! [X_a] :
% 0.65/0.83 ( cl_HOL_Oequal(X_a)
% 0.65/0.83 => equal_equal(X_a) = fequal(X_a) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_4_equal__refl,axiom,
% 0.65/0.83 ! [X_a] :
% 0.65/0.83 ( cl_HOL_Oequal(X_a)
% 0.65/0.83 => ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X),X)) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_5_equal__eq,axiom,
% 0.65/0.83 ! [X_a] :
% 0.65/0.83 ( cl_HOL_Oequal(X_a)
% 0.65/0.83 => ! [X_1,Y_1] :
% 0.65/0.83 ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1))
% 0.65/0.83 <=> ti(X_a,X_1) = ti(X_a,Y_1) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_6_eq__equal,axiom,
% 0.65/0.83 ! [X_a] :
% 0.65/0.83 ( cl_HOL_Oequal(X_a)
% 0.65/0.83 => fequal(X_a) = equal_equal(X_a) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_7_Rep__triple__inverse,axiom,
% 0.65/0.83 ! [X_a,X_1] : hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)) = X_1 ).
% 0.65/0.83
% 0.65/0.83 fof(fact_8_Rep__triple,axiom,
% 0.65/0.83 ! [X_a,X_1] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_9_Rep__triple__induct,axiom,
% 0.65/0.83 ! [X_a,P,Y_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => ( ! [X_2] : hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2)))
% 0.65/0.83 => hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,Y_1)) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_10_Rep__triple__cases,axiom,
% 0.65/0.83 ! [X_a,Y_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => ~ ! [X_2] : Y_1 != hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_11_Abs__triple__inverse,axiom,
% 0.65/0.83 ! [X_a,Y_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)) = Y_1 ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_12_type__definition__triple,axiom,
% 0.65/0.83 ! [X_a] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool)),type_definition(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)),hoare_244953527triple(X_a)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_13_Abs__triple__inject,axiom,
% 0.65/0.83 ! [X_a,Y_1,X_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),X_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => ( hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),X_1) = hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)
% 0.65/0.83 <=> X_1 = Y_1 ) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_14_Abs__triple__induct,axiom,
% 0.65/0.83 ! [X_a,X_1,P] :
% 0.65/0.83 ( ! [Y_2] :
% 0.65/0.83 ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))
% 0.65/0.83 => hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2))) )
% 0.65/0.83 => hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,X_1)) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_15_Abs__triple__cases,axiom,
% 0.65/0.83 ! [X_a,X_1] :
% 0.65/0.83 ~ ! [Y_2] :
% 0.65/0.83 ( X_1 = hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2)
% 0.65/0.83 => ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_16_type__definition_OAbs__inject,axiom,
% 0.65/0.83 ! [X_b,X_a,Y_1,X_1,Rep,Abs,A_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.83 => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
% 0.65/0.83 => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))
% 0.65/0.83 => ( hAPP(X_b,X_a,Abs,X_1) = hAPP(X_b,X_a,Abs,Y_1)
% 0.65/0.83 <=> ti(X_b,X_1) = ti(X_b,Y_1) ) ) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_17_type__definition_OAbs__inverse,axiom,
% 0.65/0.83 ! [X_b,X_a,Y_1,Rep,Abs,A_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.83 => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))
% 0.65/0.83 => hAPP(X_a,X_b,Rep,hAPP(X_b,X_a,Abs,Y_1)) = ti(X_b,Y_1) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_18_type__definition_ORep__inject,axiom,
% 0.65/0.83 ! [X_b,X_a,X_1,Y_1,Rep,Abs,A_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.83 => ( hAPP(X_a,X_b,Rep,X_1) = hAPP(X_a,X_b,Rep,Y_1)
% 0.65/0.83 <=> ti(X_a,X_1) = ti(X_a,Y_1) ) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_19_type__definition_ORep__inverse,axiom,
% 0.65/0.83 ! [X_b,X_a,X_1,Rep,Abs,A_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.83 => hAPP(X_b,X_a,Abs,hAPP(X_a,X_b,Rep,X_1)) = ti(X_a,X_1) ) ).
% 0.65/0.83
% 0.65/0.83 fof(fact_20_type__definition_ORep,axiom,
% 0.65/0.83 ! [X_b,X_a,X_1,Rep,Abs,A_1] :
% 0.65/0.83 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.84 => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Rep,X_1)),A_1)) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_21_induct__false__def,axiom,
% 0.65/0.84 ~ hBOOL(induct_false) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_22_type__definition_ORep__cases,axiom,
% 0.65/0.84 ! [X_b,X_a,Y_1,Rep,Abs,A_1] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.84 => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))
% 0.65/0.84 => ~ ! [X_2] : ti(X_b,Y_1) != hAPP(X_a,X_b,Rep,X_2) ) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_23_type__definition_OAbs__cases,axiom,
% 0.65/0.84 ! [X_b,X_a,X_1,Rep,Abs,A_1] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.84 => ~ ! [Y_2] :
% 0.65/0.84 ( ti(X_a,X_1) = hAPP(X_b,X_a,Abs,Y_2)
% 0.65/0.84 => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1)) ) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_24_type__definition_OAbs__induct,axiom,
% 0.65/0.84 ! [X_b,X_a,X_1,P,Rep,Abs,A_1] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.84 => ( ! [Y_2] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1))
% 0.65/0.84 => hBOOL(hAPP(X_a,bool,P,hAPP(X_b,X_a,Abs,Y_2))) )
% 0.65/0.84 => hBOOL(hAPP(X_a,bool,P,X_1)) ) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_25_type__definition_ORep__induct,axiom,
% 0.65/0.84 ! [X_b,X_a,P,Y_1,Rep,Abs,A_1] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))
% 0.65/0.84 => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))
% 0.65/0.84 => ( ! [X_2] : hBOOL(hAPP(X_b,bool,P,hAPP(X_a,X_b,Rep,X_2)))
% 0.65/0.84 => hBOOL(hAPP(X_b,bool,P,Y_1)) ) ) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_26_induct__trueI,axiom,
% 0.65/0.84 hBOOL(induct_true) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_27_induct__true__def,axiom,
% 0.65/0.84 hBOOL(induct_true) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_28_induct__equal__def,axiom,
% 0.65/0.84 ! [X_a,X_1,Y_1] :
% 0.65/0.84 ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),induct_equal(X_a),X_1),Y_1))
% 0.65/0.84 <=> ti(X_a,X_1) = ti(X_a,Y_1) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_29_ext,axiom,
% 0.65/0.84 ! [X_a,X_b,F,G] :
% 0.65/0.84 ( ! [X_2] : hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)
% 0.65/0.84 => ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_30_mem__def,axiom,
% 0.65/0.84 ! [X_a,X_1,A_1] :
% 0.65/0.84 ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
% 0.65/0.84 <=> hBOOL(hAPP(X_a,bool,A_1,X_1)) ) ).
% 0.65/0.84
% 0.65/0.84 fof(fact_31_Collect__def,axiom,
% 0.65/0.84 ! [X_a,P] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P) = ti(fun(X_a,bool),P) ).
% 0.65/0.84
% 0.65/0.84 %----Arities (9)
% 0.65/0.84 fof(arity_sum___Enum_Oenum,axiom,
% 0.65/0.84 ! [T_2,T_1_1] :
% 0.65/0.84 ( ( enum(T_1_1)
% 0.65/0.84 & enum(T_2) )
% 0.65/0.84 => enum(sum_sum(T_2,T_1_1)) ) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_HOL_Obool___Enum_Oenum,axiom,
% 0.65/0.84 enum(bool) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_fun___Enum_Oenum,axiom,
% 0.65/0.84 ! [T_2,T_1_1] :
% 0.65/0.84 ( ( enum(T_1_1)
% 0.65/0.84 & enum(T_2) )
% 0.65/0.84 => enum(fun(T_2,T_1_1)) ) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_fun___HOL_Oequal,axiom,
% 0.65/0.84 ! [T_2,T_1_1] :
% 0.65/0.84 ( ( cl_HOL_Oequal(T_1_1)
% 0.65/0.84 & enum(T_2) )
% 0.65/0.84 => cl_HOL_Oequal(fun(T_2,T_1_1)) ) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_Com_Ocom___HOL_Oequal,axiom,
% 0.65/0.84 cl_HOL_Oequal(com) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_HOL_Obool___HOL_Oequal,axiom,
% 0.65/0.84 cl_HOL_Oequal(bool) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_Com_Ostate___HOL_Oequal,axiom,
% 0.65/0.84 cl_HOL_Oequal(state) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_sum___HOL_Oequal,axiom,
% 0.65/0.84 ! [T_2,T_1_1] : cl_HOL_Oequal(sum_sum(T_2,T_1_1)) ).
% 0.65/0.84
% 0.65/0.84 fof(arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal,axiom,
% 0.65/0.84 ! [T_1_1] : cl_HOL_Oequal(hoare_509422987triple(T_1_1)) ).
% 0.65/0.84
% 0.65/0.84 %----Helper facts (3)
% 0.65/0.84 fof(help_ti_idem,axiom,
% 0.65/0.84 ! [T_1,A] : ti(T_1,ti(T_1,A)) = ti(T_1,A) ).
% 0.65/0.84
% 0.65/0.84 fof(help_fequal_1_1_T,axiom,
% 0.65/0.84 ! [X_a,X,Y] :
% 0.65/0.84 ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
% 0.65/0.84 | ti(X_a,X) = ti(X_a,Y) ) ).
% 0.65/0.84
% 0.65/0.84 fof(help_fequal_2_1_T,axiom,
% 0.65/0.84 ! [X_a,X,Y] :
% 0.65/0.84 ( ti(X_a,X) != ti(X_a,Y)
% 0.65/0.84 | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ) ).
% 0.65/0.84
% 0.65/0.84 %----Conjectures (2)
% 0.65/0.84 fof(conj_0,hypothesis,
% 0.65/0.84 hBOOL(hoare_1883395792gleton) ).
% 0.65/0.84
% 0.65/0.84 fof(conj_1,conjecture,
% 0.65/0.84 ! [T] :
% 0.65/0.84 ~ ! [S] : ti(state,S) = ti(state,T) ).
% 0.65/0.84
% 0.65/0.84 %------------------------------------------------------------------------------
% 0.65/0.84 %-------------------------------------------
% 0.65/0.84 % Proof found
% 0.65/0.84 % SZS status Theorem for theBenchmark
% 0.65/0.84 % SZS output start Proof
% 0.65/0.84 %ClaNum:145(EqnAxiom:70)
% 0.65/0.84 %VarNum:858(SingletonVarNum:189)
% 0.65/0.84 %MaxLitNum:5
% 0.65/0.84 %MaxfuncDepth:4
% 0.65/0.84 %SharedTerms:28
% 0.65/0.84 %goalClause: 82
% 0.65/0.84 %singleGoalClaCount:1
% 0.65/0.84 [71]P1(a1)
% 0.65/0.84 [72]P1(a2)
% 0.65/0.84 [73]P1(a4)
% 0.65/0.84 [75]P2(a5)
% 0.65/0.84 [76]P2(a6)
% 0.65/0.84 [77]P3(a1)
% 0.65/0.84 [103]~P2(a27)
% 0.65/0.84 [79]E(f31(a1,a27),a27)
% 0.65/0.84 [80]E(f31(a1,a5),a5)
% 0.65/0.84 [81]E(f31(a1,a6),a6)
% 0.65/0.84 [78]P1(f24(x781))
% 0.65/0.84 [82]E(f31(a4,x821),f31(a4,a7))
% 0.65/0.84 [83]E(f31(x831,f33(x831)),f33(x831))
% 0.65/0.84 [86]E(f31(f11(x861,f11(x861,a1)),f28(x861)),f28(x861))
% 0.65/0.84 [87]E(f31(f11(x871,f11(x871,a1)),f12(x871)),f12(x871))
% 0.65/0.84 [88]E(f31(f11(f11(x881,a1),f11(x881,a1)),f3(x881)),f3(x881))
% 0.65/0.84 [89]E(f31(f11(x891,f11(f11(x891,a1),a1)),f29(x891)),f29(x891))
% 0.65/0.84 [96]E(f31(f11(f11(f30(f32(a2,f11(x961,f11(a4,a1))),f32(a4,x961)),a1),a1),f23(x961)),f23(x961))
% 0.65/0.84 [97]E(f31(f11(f24(x971),f11(f30(f32(a2,f11(x971,f11(a4,a1))),f32(a4,x971)),a1)),f26(x971)),f26(x971))
% 0.65/0.84 [98]E(f31(f11(f11(f30(f32(a2,f11(x981,f11(a4,a1))),f32(a4,x981)),a1),f24(x981)),f25(x981)),f25(x981))
% 0.65/0.84 [102]P2(f22(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),a1),a1,f22(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),f24(x1021)),f11(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),a1),a1),f22(f11(f24(x1021),f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1)),f11(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),f24(x1021)),f11(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),a1),a1)),f34(f24(x1021),f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1)),f26(x1021)),f25(x1021)),f22(f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),a1),f11(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1),a1),f3(f11(f30(f32(a2,f11(x1021,f11(a4,a1))),f32(a4,x1021)),a1)),f23(x1021))))
% 0.65/0.84 [84]P1(f32(x841,x842))
% 0.65/0.84 [85]E(f31(x851,f31(x851,x852)),f31(x851,x852))
% 0.65/0.84 [90]E(f22(f11(x901,a1),f11(x901,a1),f3(x901),x902),f31(f11(x901,a1),x902))
% 0.65/0.84 [92]E(f31(f11(f11(x921,x922),f11(f11(x922,x921),f11(f11(x922,a1),a1))),f34(x921,x922)),f34(x921,x922))
% 0.65/0.84 [95]E(f22(f11(f30(f32(a2,f11(x951,f11(a4,a1))),f32(a4,x951)),a1),f24(x951),f25(x951),f13(x951,x952)),x952)
% 0.65/0.84 [99]E(f22(f11(f30(f32(a2,f11(x991,f11(a4,a1))),f32(a4,x991)),a1),f24(x991),f25(x991),f22(f24(x991),f11(f30(f32(a2,f11(x991,f11(a4,a1))),f32(a4,x991)),a1),f26(x991),x992)),x992)
% 0.65/0.84 [100]P2(f22(f11(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1),f11(f11(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1)),f13(x1001,x1002)),f22(f11(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1),a1),f11(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1),a1),f3(f11(f30(f32(a2,f11(x1001,f11(a4,a1))),f32(a4,x1001)),a1)),f23(x1001))))
% 0.65/0.84 [101]P2(f22(f11(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),f11(f11(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1)),f22(f24(x1011),f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),f26(x1011),x1012)),f22(f11(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),a1),f11(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1),a1),f3(f11(f30(f32(a2,f11(x1011,f11(a4,a1))),f32(a4,x1011)),a1)),f23(x1011))))
% 0.65/0.84 [91]E(f22(x911,x912,x913,f31(x911,x914)),f22(x911,x912,x913,x914))
% 0.65/0.84 [94]E(f31(x941,f22(x942,x941,x943,x944)),f22(x942,x941,x943,x944))
% 0.65/0.84 [93]E(f22(x931,x932,f31(f11(x931,x932),x933),x934),f22(x931,x932,x933,x934))
% 0.65/0.84 [108]~E(f31(a4,a14),f31(a4,a15))+~P2(a6)
% 0.65/0.84 [105]~P1(x1051)+E(f12(x1051),f8(x1051))
% 0.65/0.84 [107]~P2(x1071)+P2(f31(a1,x1071))
% 0.65/0.84 [112]P2(x1121)+~P2(f31(a1,x1121))
% 0.65/0.84 [113]~P1(x1131)+E(f31(f11(x1131,f11(x1131,a1)),f8(x1131)),f8(x1131))
% 0.65/0.84 [114]~P1(x1141)+P2(f22(x1141,a1,f22(x1141,f11(x1141,a1),f8(x1141),x1142),x1142))
% 0.65/0.84 [139]E(f22(f24(x1391),f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),f26(x1391),f17(x1391,x1392)),x1392)+~P2(f22(f11(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),f11(f11(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1)),x1392),f22(f11(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),a1),f11(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1),a1),f3(f11(f30(f32(a2,f11(x1391,f11(a4,a1))),f32(a4,x1391)),a1)),f23(x1391))))
% 0.65/0.84 [140]E(f22(f24(x1401),f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),f26(x1401),f22(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),f24(x1401),f25(x1401),x1402)),x1402)+~P2(f22(f11(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),f11(f11(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1)),x1402),f22(f11(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),a1),f11(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1),a1),f3(f11(f30(f32(a2,f11(x1401,f11(a4,a1))),f32(a4,x1401)),a1)),f23(x1401))))
% 0.65/0.84 [125]E(x1251,x1252)+~E(f22(f24(x1253),f11(f30(f32(a2,f11(x1253,f11(a4,a1))),f32(a4,x1253)),a1),f26(x1253),x1251),f22(f24(x1253),f11(f30(f32(a2,f11(x1253,f11(a4,a1))),f32(a4,x1253)),a1),f26(x1253),x1252))
% 0.65/0.84 [115]~E(f31(x1151,x1152),f31(x1151,x1153))+P2(f22(x1151,a1,f22(x1151,f11(x1151,a1),f28(x1151),x1152),x1153))
% 0.65/0.84 [116]~E(f31(x1161,x1162),f31(x1161,x1163))+P2(f22(x1161,a1,f22(x1161,f11(x1161,a1),f12(x1161),x1162),x1163))
% 0.65/0.84 [120]E(f31(x1201,x1202),f31(x1201,x1203))+~P2(f22(x1201,a1,f22(x1201,f11(x1201,a1),f28(x1201),x1202),x1203))
% 0.65/0.84 [121]E(f31(x1211,x1212),f31(x1211,x1213))+~P2(f22(x1211,a1,f22(x1211,f11(x1211,a1),f12(x1211),x1212),x1213))
% 0.65/0.84 [123]~P2(f22(x1231,a1,x1233,x1232))+P2(f22(f11(x1231,a1),a1,f22(x1231,f11(f11(x1231,a1),a1),f29(x1231),x1232),x1233))
% 0.65/0.84 [126]P2(f22(x1261,a1,x1262,x1263))+~P2(f22(f11(x1261,a1),a1,f22(x1261,f11(f11(x1261,a1),a1),f29(x1261),x1263),x1262))
% 0.65/0.84 [127]P2(f22(f24(x1271),a1,x1272,x1273))+~P2(f22(f24(x1271),a1,x1272,f22(f11(f30(f32(a2,f11(x1271,f11(a4,a1))),f32(a4,x1271)),a1),f24(x1271),f25(x1271),f16(x1271,x1273,x1272))))
% 0.65/0.84 [137]P2(f22(f24(x1371),a1,x1372,x1373))+P2(f22(f11(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1),f11(f11(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1)),f16(x1371,x1373,x1372)),f22(f11(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1),a1),f11(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1),a1),f3(f11(f30(f32(a2,f11(x1371,f11(a4,a1))),f32(a4,x1371)),a1)),f23(x1371))))
% 0.65/0.84 [118]~E(x1182,x1183)+P2(f22(f24(x1181),a1,f22(f24(x1181),f11(f24(x1181),a1),f8(f24(x1181)),x1182),x1183))
% 0.65/0.84 [124]E(x1241,x1242)+~P2(f22(f24(x1243),a1,f22(f24(x1243),f11(f24(x1243),a1),f8(f24(x1243)),x1241),x1242))
% 0.65/0.84 [119]~E(f22(x1191,x1192,x1193,f9(x1191,x1192,x1193,x1194)),f22(x1191,x1192,x1194,f9(x1191,x1192,x1193,x1194)))+E(f31(f11(x1191,x1192),x1193),f31(f11(x1191,x1192),x1194))
% 0.65/0.84 [129]E(f22(x1291,x1292,x1293,f22(x1292,x1291,x1294,x1295)),f31(x1292,x1295))+~P2(f22(f11(x1291,a1),a1,f22(f11(x1291,x1292),f11(f11(x1291,a1),a1),f22(f11(x1292,x1291),f11(f11(x1291,x1292),f11(f11(x1291,a1),a1)),f34(x1292,x1291),x1294),x1293),x1296))
% 0.65/0.84 [132]P2(f22(f11(x1321,a1),a1,f22(x1321,f11(f11(x1321,a1),a1),f29(x1321),f22(x1322,x1321,x1323,x1324)),x1325))+~P2(f22(f11(x1321,a1),a1,f22(f11(x1321,x1322),f11(f11(x1321,a1),a1),f22(f11(x1322,x1321),f11(f11(x1321,x1322),f11(f11(x1321,a1),a1)),f34(x1322,x1321),x1323),x1326),x1325))
% 0.65/0.84 [135]E(f22(x1351,x1352,x1353,f19(x1351,x1352,x1354,x1355,x1353,x1356)),f31(x1352,x1354))+~P2(f22(f11(x1351,a1),a1,f22(f11(x1351,x1352),f11(f11(x1351,a1),a1),f22(f11(x1352,x1351),f11(f11(x1351,x1352),f11(f11(x1351,a1),a1)),f34(x1352,x1351),x1355),x1353),x1356))
% 0.65/0.84 [138]P2(f22(f11(x1381,a1),a1,f22(x1381,f11(f11(x1381,a1),a1),f29(x1381),f19(x1381,x1382,x1383,x1384,x1385,x1386)),x1386))+~P2(f22(f11(x1381,a1),a1,f22(f11(x1381,x1382),f11(f11(x1381,a1),a1),f22(f11(x1382,x1381),f11(f11(x1381,x1382),f11(f11(x1381,a1),a1)),f34(x1382,x1381),x1384),x1385),x1386))
% 0.65/0.84 [109]~P1(x1092)+~P3(x1091)+P1(f11(x1091,x1092))
% 0.65/0.84 [110]~P3(x1101)+~P3(x1102)+P3(f11(x1101,x1102))
% 0.65/0.84 [111]~P3(x1111)+~P3(x1112)+P3(f32(x1111,x1112))
% 0.65/0.84 [117]~P1(x1171)+~E(f31(x1171,x1172),f31(x1171,x1173))+P2(f22(x1171,a1,f22(x1171,f11(x1171,a1),f8(x1171),x1172),x1173))
% 0.65/0.84 [122]~P1(x1221)+E(f31(x1221,x1222),f31(x1221,x1223))+~P2(f22(x1221,a1,f22(x1221,f11(x1221,a1),f8(x1221),x1222),x1223))
% 0.65/0.84 [141]~P2(f22(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1,x1412,f22(f24(x1411),f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),f26(x1411),f18(x1411,x1412,x1413))))+~P2(f22(f11(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),f11(f11(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1)),x1413),f22(f11(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1),f11(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1),f3(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1)),f23(x1411))))+P2(f22(f11(f30(f32(a2,f11(x1411,f11(a4,a1))),f32(a4,x1411)),a1),a1,x1412,x1413))
% 0.65/0.84 [131]E(f22(x1311,x1312,x1313,f22(x1312,x1311,x1314,x1315)),f31(x1312,x1315))+~P2(f22(f11(x1312,a1),a1,f22(x1312,f11(f11(x1312,a1),a1),f29(x1312),x1315),x1316))+~P2(f22(f11(x1312,a1),a1,f22(f11(x1312,x1311),f11(f11(x1312,a1),a1),f22(f11(x1311,x1312),f11(f11(x1312,x1311),f11(f11(x1312,a1),a1)),f34(x1311,x1312),x1313),x1314),x1316))
% 0.65/0.84 [136]E(f22(x1361,x1362,x1363,f20(x1362,x1361,x1364,x1363,x1365,x1366)),f31(x1362,x1364))+~P2(f22(f11(x1362,a1),a1,f22(x1362,f11(f11(x1362,a1),a1),f29(x1362),x1364),x1366))+~P2(f22(f11(x1362,a1),a1,f22(f11(x1362,x1361),f11(f11(x1362,a1),a1),f22(f11(x1361,x1362),f11(f11(x1362,x1361),f11(f11(x1362,a1),a1)),f34(x1361,x1362),x1363),x1365),x1366))
% 0.65/0.84 [128]~E(f31(x1281,x1284),f31(x1281,x1285))+E(f22(x1281,x1282,x1283,x1284),f22(x1281,x1282,x1283,x1285))+~P2(f22(f11(x1282,a1),a1,f22(f11(x1282,x1281),f11(f11(x1282,a1),a1),f22(f11(x1281,x1282),f11(f11(x1282,x1281),f11(f11(x1282,a1),a1)),f34(x1281,x1282),x1283),x1286),x1287))
% 0.65/0.84 [130]~E(f22(x1301,x1304,x1305,x1302),f22(x1301,x1304,x1305,x1303))+E(f31(x1301,x1302),f31(x1301,x1303))+~P2(f22(f11(x1304,a1),a1,f22(f11(x1304,x1301),f11(f11(x1304,a1),a1),f22(f11(x1301,x1304),f11(f11(x1304,x1301),f11(f11(x1304,a1),a1)),f34(x1301,x1304),x1305),x1306),x1307))
% 0.65/0.84 [143]P2(f22(x1431,a1,x1432,x1433))+P2(f22(f11(x1434,a1),a1,f22(x1434,f11(f11(x1434,a1),a1),f29(x1434),f21(x1434,x1431,x1433,x1432,x1435,x1436,x1437)),x1437))+~P2(f22(f11(x1434,a1),a1,f22(f11(x1434,x1431),f11(f11(x1434,a1),a1),f22(f11(x1431,x1434),f11(f11(x1434,x1431),f11(f11(x1434,a1),a1)),f34(x1431,x1434),x1435),x1436),x1437))
% 0.65/0.84 [144]P2(f22(x1441,a1,x1442,x1443))+~P2(f22(x1441,a1,x1442,f22(x1444,x1441,x1445,f21(x1444,x1441,x1443,x1442,x1446,x1445,x1447))))+~P2(f22(f11(x1444,a1),a1,f22(f11(x1444,x1441),f11(f11(x1444,a1),a1),f22(f11(x1441,x1444),f11(f11(x1444,x1441),f11(f11(x1444,a1),a1)),f34(x1441,x1444),x1446),x1445),x1447))
% 0.65/0.84 [142]E(x1421,x1422)+~E(f22(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),f24(x1423),f25(x1423),x1421),f22(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),f24(x1423),f25(x1423),x1422))+~P2(f22(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),f11(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1)),x1421),f22(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),f3(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1)),f23(x1423))))+~P2(f22(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),f11(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1)),x1422),f22(f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),f11(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1),a1),f3(f11(f30(f32(a2,f11(x1423,f11(a4,a1))),f32(a4,x1423)),a1)),f23(x1423))))
% 0.65/0.84 [145]P2(f22(x1451,a1,x1452,x1453))+~P2(f22(x1451,a1,x1452,f22(x1454,x1451,x1455,f10(x1451,x1454,x1452,x1453,x1455,x1456,x1457))))+~P2(f22(f11(x1451,a1),a1,f22(x1451,f11(f11(x1451,a1),a1),f29(x1451),x1453),x1457))+~P2(f22(f11(x1451,a1),a1,f22(f11(x1451,x1454),f11(f11(x1451,a1),a1),f22(f11(x1454,x1451),f11(f11(x1451,x1454),f11(f11(x1451,a1),a1)),f34(x1454,x1451),x1455),x1456),x1457))
% 0.65/0.84 [133]~E(f31(x1331,x1334),f31(x1331,x1335))+E(f22(x1331,x1332,x1333,x1334),f22(x1331,x1332,x1333,x1335))+~P2(f22(f11(x1331,a1),a1,f22(x1331,f11(f11(x1331,a1),a1),f29(x1331),x1334),x1336))+~P2(f22(f11(x1331,a1),a1,f22(x1331,f11(f11(x1331,a1),a1),f29(x1331),x1335),x1336))+~P2(f22(f11(x1331,a1),a1,f22(f11(x1331,x1332),f11(f11(x1331,a1),a1),f22(f11(x1332,x1331),f11(f11(x1331,x1332),f11(f11(x1331,a1),a1)),f34(x1332,x1331),x1337),x1333),x1336))
% 0.65/0.84 [134]~E(f22(x1341,x1344,x1345,x1342),f22(x1341,x1344,x1345,x1343))+E(f31(x1341,x1342),f31(x1341,x1343))+~P2(f22(f11(x1341,a1),a1,f22(x1341,f11(f11(x1341,a1),a1),f29(x1341),x1342),x1346))+~P2(f22(f11(x1341,a1),a1,f22(x1341,f11(f11(x1341,a1),a1),f29(x1341),x1343),x1346))+~P2(f22(f11(x1341,a1),a1,f22(f11(x1341,x1344),f11(f11(x1341,a1),a1),f22(f11(x1344,x1341),f11(f11(x1341,x1344),f11(f11(x1341,a1),a1)),f34(x1344,x1341),x1347),x1345),x1346))
% 0.65/0.84 %EqnAxiom
% 0.65/0.84 [1]E(x11,x11)
% 0.65/0.84 [2]E(x22,x21)+~E(x21,x22)
% 0.65/0.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.65/0.84 [4]~E(x41,x42)+E(f24(x41),f24(x42))
% 0.65/0.84 [5]~E(x51,x52)+E(f31(x51,x53),f31(x52,x53))
% 0.65/0.84 [6]~E(x61,x62)+E(f31(x63,x61),f31(x63,x62))
% 0.65/0.84 [7]~E(x71,x72)+E(f11(x71,x73),f11(x72,x73))
% 0.65/0.84 [8]~E(x81,x82)+E(f11(x83,x81),f11(x83,x82))
% 0.65/0.84 [9]~E(x91,x92)+E(f22(x91,x93,x94,x95),f22(x92,x93,x94,x95))
% 0.65/0.84 [10]~E(x101,x102)+E(f22(x103,x101,x104,x105),f22(x103,x102,x104,x105))
% 0.65/0.84 [11]~E(x111,x112)+E(f22(x113,x114,x111,x115),f22(x113,x114,x112,x115))
% 0.65/0.84 [12]~E(x121,x122)+E(f22(x123,x124,x125,x121),f22(x123,x124,x125,x122))
% 0.65/0.84 [13]~E(x131,x132)+E(f29(x131),f29(x132))
% 0.65/0.84 [14]~E(x141,x142)+E(f30(x141,x143),f30(x142,x143))
% 0.65/0.84 [15]~E(x151,x152)+E(f30(x153,x151),f30(x153,x152))
% 0.65/0.84 [16]~E(x161,x162)+E(f33(x161),f33(x162))
% 0.65/0.84 [17]~E(x171,x172)+E(f32(x171,x173),f32(x172,x173))
% 0.65/0.84 [18]~E(x181,x182)+E(f32(x183,x181),f32(x183,x182))
% 0.65/0.84 [19]~E(x191,x192)+E(f26(x191),f26(x192))
% 0.65/0.84 [20]~E(x201,x202)+E(f34(x201,x203),f34(x202,x203))
% 0.65/0.84 [21]~E(x211,x212)+E(f34(x213,x211),f34(x213,x212))
% 0.65/0.84 [22]~E(x221,x222)+E(f25(x221),f25(x222))
% 0.65/0.84 [23]~E(x231,x232)+E(f16(x231,x233,x234),f16(x232,x233,x234))
% 0.65/0.84 [24]~E(x241,x242)+E(f16(x243,x241,x244),f16(x243,x242,x244))
% 0.65/0.84 [25]~E(x251,x252)+E(f16(x253,x254,x251),f16(x253,x254,x252))
% 0.65/0.84 [26]~E(x261,x262)+E(f9(x261,x263,x264,x265),f9(x262,x263,x264,x265))
% 0.65/0.84 [27]~E(x271,x272)+E(f9(x273,x271,x274,x275),f9(x273,x272,x274,x275))
% 0.65/0.84 [28]~E(x281,x282)+E(f9(x283,x284,x281,x285),f9(x283,x284,x282,x285))
% 0.65/0.84 [29]~E(x291,x292)+E(f9(x293,x294,x295,x291),f9(x293,x294,x295,x292))
% 0.65/0.84 [30]~E(x301,x302)+E(f23(x301),f23(x302))
% 0.65/0.84 [31]~E(x311,x312)+E(f3(x311),f3(x312))
% 0.65/0.84 [32]~E(x321,x322)+E(f28(x321),f28(x322))
% 0.65/0.84 [33]~E(x331,x332)+E(f21(x331,x333,x334,x335,x336,x337,x338),f21(x332,x333,x334,x335,x336,x337,x338))
% 0.65/0.84 [34]~E(x341,x342)+E(f21(x343,x341,x344,x345,x346,x347,x348),f21(x343,x342,x344,x345,x346,x347,x348))
% 0.65/0.84 [35]~E(x351,x352)+E(f21(x353,x354,x351,x355,x356,x357,x358),f21(x353,x354,x352,x355,x356,x357,x358))
% 0.65/0.84 [36]~E(x361,x362)+E(f21(x363,x364,x365,x361,x366,x367,x368),f21(x363,x364,x365,x362,x366,x367,x368))
% 0.65/0.84 [37]~E(x371,x372)+E(f21(x373,x374,x375,x376,x371,x377,x378),f21(x373,x374,x375,x376,x372,x377,x378))
% 0.65/0.84 [38]~E(x381,x382)+E(f21(x383,x384,x385,x386,x387,x381,x388),f21(x383,x384,x385,x386,x387,x382,x388))
% 0.65/0.84 [39]~E(x391,x392)+E(f21(x393,x394,x395,x396,x397,x398,x391),f21(x393,x394,x395,x396,x397,x398,x392))
% 0.65/0.84 [40]~E(x401,x402)+E(f12(x401),f12(x402))
% 0.65/0.84 [41]~E(x411,x412)+E(f8(x411),f8(x412))
% 0.65/0.84 [42]~E(x421,x422)+E(f13(x421,x423),f13(x422,x423))
% 0.65/0.84 [43]~E(x431,x432)+E(f13(x433,x431),f13(x433,x432))
% 0.65/0.84 [44]~E(x441,x442)+E(f19(x441,x443,x444,x445,x446,x447),f19(x442,x443,x444,x445,x446,x447))
% 0.65/0.84 [45]~E(x451,x452)+E(f19(x453,x451,x454,x455,x456,x457),f19(x453,x452,x454,x455,x456,x457))
% 0.65/0.84 [46]~E(x461,x462)+E(f19(x463,x464,x461,x465,x466,x467),f19(x463,x464,x462,x465,x466,x467))
% 0.65/0.84 [47]~E(x471,x472)+E(f19(x473,x474,x475,x471,x476,x477),f19(x473,x474,x475,x472,x476,x477))
% 0.65/0.84 [48]~E(x481,x482)+E(f19(x483,x484,x485,x486,x481,x487),f19(x483,x484,x485,x486,x482,x487))
% 0.65/0.84 [49]~E(x491,x492)+E(f19(x493,x494,x495,x496,x497,x491),f19(x493,x494,x495,x496,x497,x492))
% 0.65/0.84 [50]~E(x501,x502)+E(f18(x501,x503,x504),f18(x502,x503,x504))
% 0.65/0.84 [51]~E(x511,x512)+E(f18(x513,x511,x514),f18(x513,x512,x514))
% 0.65/0.84 [52]~E(x521,x522)+E(f18(x523,x524,x521),f18(x523,x524,x522))
% 0.65/0.84 [53]~E(x531,x532)+E(f17(x531,x533),f17(x532,x533))
% 0.65/0.84 [54]~E(x541,x542)+E(f17(x543,x541),f17(x543,x542))
% 0.65/0.84 [55]~E(x551,x552)+E(f20(x551,x553,x554,x555,x556,x557),f20(x552,x553,x554,x555,x556,x557))
% 0.65/0.84 [56]~E(x561,x562)+E(f20(x563,x561,x564,x565,x566,x567),f20(x563,x562,x564,x565,x566,x567))
% 0.65/0.84 [57]~E(x571,x572)+E(f20(x573,x574,x571,x575,x576,x577),f20(x573,x574,x572,x575,x576,x577))
% 0.65/0.84 [58]~E(x581,x582)+E(f20(x583,x584,x585,x581,x586,x587),f20(x583,x584,x585,x582,x586,x587))
% 0.65/0.84 [59]~E(x591,x592)+E(f20(x593,x594,x595,x596,x591,x597),f20(x593,x594,x595,x596,x592,x597))
% 0.65/0.84 [60]~E(x601,x602)+E(f20(x603,x604,x605,x606,x607,x601),f20(x603,x604,x605,x606,x607,x602))
% 0.65/0.84 [61]~E(x611,x612)+E(f10(x611,x613,x614,x615,x616,x617,x618),f10(x612,x613,x614,x615,x616,x617,x618))
% 0.65/0.84 [62]~E(x621,x622)+E(f10(x623,x621,x624,x625,x626,x627,x628),f10(x623,x622,x624,x625,x626,x627,x628))
% 0.65/0.84 [63]~E(x631,x632)+E(f10(x633,x634,x631,x635,x636,x637,x638),f10(x633,x634,x632,x635,x636,x637,x638))
% 0.65/0.84 [64]~E(x641,x642)+E(f10(x643,x644,x645,x641,x646,x647,x648),f10(x643,x644,x645,x642,x646,x647,x648))
% 0.65/0.84 [65]~E(x651,x652)+E(f10(x653,x654,x655,x656,x651,x657,x658),f10(x653,x654,x655,x656,x652,x657,x658))
% 0.65/0.84 [66]~E(x661,x662)+E(f10(x663,x664,x665,x666,x667,x661,x668),f10(x663,x664,x665,x666,x667,x662,x668))
% 0.65/0.84 [67]~E(x671,x672)+E(f10(x673,x674,x675,x676,x677,x678,x671),f10(x673,x674,x675,x676,x677,x678,x672))
% 0.65/0.84 [68]~P1(x681)+P1(x682)+~E(x681,x682)
% 0.65/0.84 [69]~P2(x691)+P2(x692)+~E(x691,x692)
% 0.65/0.84 [70]~P3(x701)+P3(x702)+~E(x701,x702)
% 0.65/0.84
% 0.65/0.84 %-------------------------------------------
% 0.65/0.85 cnf(146,plain,
% 0.65/0.85 (E(f31(a4,a7),f31(a4,x1461))),
% 0.65/0.85 inference(scs_inference,[],[82,2])).
% 0.65/0.85 cnf(164,plain,
% 0.65/0.85 (~E(f31(a4,a14),f31(a4,a15))),
% 0.65/0.85 inference(scs_inference,[],[82,76,103,79,85,91,100,102,2,125,126,129,139,140,69,3,131,108])).
% 0.65/0.85 cnf(233,plain,
% 0.65/0.85 (~P2(f22(f24(x2331),a1,f22(f24(x2331),f11(f24(x2331),a1),f8(f24(x2331)),f31(a4,a14)),f31(a4,a15)))),
% 0.65/0.85 inference(scs_inference,[],[82,75,76,103,79,85,91,100,102,2,125,126,129,139,140,69,3,131,108,112,107,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,124])).
% 0.65/0.85 cnf(253,plain,
% 0.65/0.85 (~P2(f22(f24(x2531),a1,f22(f24(x2531),f11(f24(x2531),a1),f8(f24(x2531)),f31(a4,a14)),f22(f11(f30(f32(a2,f11(x2531,f11(a4,a1))),f32(a4,x2531)),a1),f24(x2531),f25(x2531),f16(x2531,f31(a4,a15),f22(f24(x2531),f11(f24(x2531),a1),f8(f24(x2531)),f31(a4,a14))))))),
% 0.65/0.85 inference(scs_inference,[],[82,71,75,76,103,79,85,91,100,102,2,125,126,129,139,140,69,3,131,108,112,107,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,124,118,105,114,113,123,121,120,116,115,127])).
% 0.65/0.85 cnf(260,plain,
% 0.65/0.85 (P3(f11(a1,a1))),
% 0.65/0.85 inference(scs_inference,[],[82,71,75,76,77,103,79,85,91,100,102,2,125,126,129,139,140,69,3,131,108,112,107,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,124,118,105,114,113,123,121,120,116,115,127,137,70,111,110])).
% 0.65/0.85 cnf(291,plain,
% 0.65/0.85 (P2(f22(f11(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),a1),a1,f22(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),f11(f11(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),a1),a1),f29(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1)),f22(f24(x2911),f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),f26(x2911),x2912)),f22(f11(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),a1),f11(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1),a1),f3(f11(f30(f32(a2,f11(x2911,f11(a4,a1))),f32(a4,x2911)),a1)),f23(x2911))))),
% 0.65/0.85 inference(rename_variables,[],[101])).
% 0.65/0.85 cnf(301,plain,
% 0.65/0.85 ($false),
% 0.65/0.85 inference(scs_inference,[],[82,101,291,103,102,260,253,233,146,164,125,126,111,131,128,2,6,118,69,3]),
% 0.65/0.85 ['proof']).
% 0.65/0.85 % SZS output end Proof
% 0.65/0.85 % Total time :0.180000s
%------------------------------------------------------------------------------