%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ037-2 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:21:11 AM UTC 2026
% Result : Unsatisfiable 7.10s 3.33s
% Output : Refutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4178 ( 38 ~; 36 |; 0 &;4104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 111 ( 103 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 7 con; 0-54 aty)
% Number of variables : 1944 ( 0 ^;1944 !; 0 ?;1944 :)
% Comments :
%------------------------------------------------------------------------------
thf(state_decl,type,
state: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(r_decl,type,
r: $i ).
thf(g_decl,type,
g: $i ).
thf(o_decl,type,
o: $i ).
thf(y_decl,type,
y: $i ).
thf(w_decl,type,
w: $i ).
thf(19,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZM @ ( ZZA @ ( ZZ @ ( ZA @ ( ZX @ ( ZW @ ( O @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZV @ ( ZN @ ( ZB @ ( P @ ( I @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZY @ ( ZO @ ( ZC @ ( Q @ ( F @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( ZZB @ ( ZP @ ( ZD @ ( R @ ( C @ ( N @ ( M @ ( L @ ( K @ ( J @ ( S @ ( H @ ( G @ ( ZE @ ( E @ ( D @ ( ZQ @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rxz) ).
thf(56,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZM @ ( ZZA @ ( ZZ @ ( ZA @ ( ZX @ ( ZW @ ( O @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZV @ ( ZN @ ( ZB @ ( P @ ( I @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZY @ ( ZO @ ( ZC @ ( Q @ ( F @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( ZZB @ ( ZP @ ( ZD @ ( R @ ( C @ ( N @ ( M @ ( L @ ( K @ ( J @ ( S @ ( H @ ( G @ ( ZE @ ( E @ ( D @ ( ZQ @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZH @ ( V @ ( J @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( U @ ( ZG @ ( ZS @ ( ZZ @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( A @ ( T @ ( ZF @ ( ZR @ ( ZZA @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( B @ ( S @ ( ZE @ ( ZQ @ ( ZZB @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( ZP @ ( ZD @ ( R @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bzy) ).
thf(52,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZH @ ( V @ ( J @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( U @ ( ZG @ ( ZS @ ( ZZ @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( A @ ( T @ ( ZF @ ( ZR @ ( ZZA @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( B @ ( S @ ( ZE @ ( ZQ @ ( ZZB @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( ZP @ ( ZD @ ( R @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( S @ ( ZZA @ ( ZZ @ ( ZE @ ( ZX @ ( ZW @ ( ZQ @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( C @ ( R @ ( ZD @ ( ZP @ ( ZZB @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( F @ ( Q @ ( ZC @ ( ZO @ ( ZY @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( I @ ( P @ ( ZB @ ( ZN @ ( ZV @ ( N @ ( M @ ( L @ ( K @ ( J @ ( ZM @ ( H @ ( G @ ( ZA @ ( E @ ( D @ ( O @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rzx) ).
thf(54,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( S @ ( ZZA @ ( ZZ @ ( ZE @ ( ZX @ ( ZW @ ( ZQ @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( C @ ( R @ ( ZD @ ( ZP @ ( ZZB @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( F @ ( Q @ ( ZC @ ( ZO @ ( ZY @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( I @ ( P @ ( ZB @ ( ZN @ ( ZV @ ( N @ ( M @ ( L @ ( K @ ( J @ ( ZM @ ( H @ ( G @ ( ZA @ ( E @ ( D @ ( O @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
g @ ( w @ ( g @ ( g @ ( w @ ( g @ ( g @ ( w @ ( g @ ( w @ ( y @ ( w @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( w @ ( y @ ( w @ ( w @ ( y @ ( w @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( y @ ( b @ ( y @ ( y @ ( b @ ( y @ ( y @ ( b @ ( y @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_with_this) ).
thf(35,plain,
g @ ( w @ ( g @ ( g @ ( w @ ( g @ ( g @ ( w @ ( g @ ( w @ ( y @ ( w @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( w @ ( y @ ( w @ ( w @ ( y @ ( w @ ( o @ ( o @ ( o @ ( b @ ( g @ ( b @ ( r @ ( r @ ( r @ ( y @ ( b @ ( y @ ( y @ ( b @ ( y @ ( y @ ( b @ ( y @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( P @ ( ZB @ ( ZN @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( I @ ( O @ ( ZA @ ( ZM @ ( ZV @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( H @ ( N @ ( Z @ ( ZL @ ( ZU @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( G @ ( M @ ( Y @ ( ZK @ ( ZT @ ( K @ ( J @ ( L @ ( X @ ( ZJ @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fyz) ).
thf(48,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( P @ ( ZB @ ( ZN @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( I @ ( O @ ( ZA @ ( ZM @ ( ZV @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( H @ ( N @ ( Z @ ( ZL @ ( ZU @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( G @ ( M @ ( Y @ ( ZK @ ( ZT @ ( K @ ( J @ ( L @ ( X @ ( ZJ @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( R @ ( ZD @ ( ZP @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZQ @ ( ZE @ ( S @ ( C @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZZB @ ( ZR @ ( ZF @ ( T @ ( B @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( ZZA @ ( ZS @ ( ZG @ ( U @ ( A @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( ZZ @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( J @ ( V @ ( ZH @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',byz) ).
thf(58,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( R @ ( ZD @ ( ZP @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZQ @ ( ZE @ ( S @ ( C @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZZB @ ( ZR @ ( ZF @ ( T @ ( B @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( ZZA @ ( ZS @ ( ZG @ ( U @ ( A @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( ZZ @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( J @ ( V @ ( ZH @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZ @ ( ZW @ ( ZT @ ( ZZA @ ( ZX @ ( ZU @ ( ZZB @ ( ZY @ ( ZV @ ( ZJ @ ( ZI @ ( ZH @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bxy) ).
thf(36,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZ @ ( ZW @ ( ZT @ ( ZZA @ ( ZX @ ( ZU @ ( ZZB @ ( ZY @ ( ZV @ ( ZJ @ ( ZI @ ( ZH @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( U @ ( ZY @ ( ZX @ ( ZG @ ( ZV @ ( ZU @ ( ZS @ ( A @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZZ @ ( ZH @ ( V @ ( J @ ( D @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( ZW @ ( ZI @ ( W @ ( K @ ( G @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( ZT @ ( ZJ @ ( X @ ( L @ ( I @ ( H @ ( ZK @ ( F @ ( E @ ( Y @ ( C @ ( B @ ( M @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lzx) ).
thf(42,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( U @ ( ZY @ ( ZX @ ( ZG @ ( ZV @ ( ZU @ ( ZS @ ( A @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZZ @ ( ZH @ ( V @ ( J @ ( D @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( ZW @ ( ZI @ ( W @ ( K @ ( G @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( ZT @ ( ZJ @ ( X @ ( L @ ( I @ ( H @ ( ZK @ ( F @ ( E @ ( Y @ ( C @ ( B @ ( M @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( L @ ( K @ ( J @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( C @ ( F @ ( I @ ( B @ ( E @ ( H @ ( A @ ( D @ ( G @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',txy) ).
thf(25,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( L @ ( K @ ( J @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( C @ ( F @ ( I @ ( B @ ( E @ ( H @ ( A @ ( D @ ( G @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( U @ ( T @ ( S @ ( G @ ( D @ ( A @ ( H @ ( E @ ( B @ ( I @ ( F @ ( C @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tyx) ).
thf(46,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( U @ ( T @ ( S @ ( G @ ( D @ ( A @ ( H @ ( E @ ( B @ ( I @ ( F @ ( C @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZV @ ( ZY @ ( ZZB @ ( ZU @ ( ZX @ ( ZZA @ ( ZT @ ( ZW @ ( ZZ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZS @ ( ZR @ ( ZQ @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',byx) ).
thf(29,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZV @ ( ZY @ ( ZZB @ ( ZU @ ( ZX @ ( ZZA @ ( ZT @ ( ZW @ ( ZZ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZS @ ( ZR @ ( ZQ @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZL @ ( ZZ @ ( ZY @ ( Z @ ( ZW @ ( ZV @ ( N @ ( ZT @ ( ZS @ ( ZU @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( H @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZX @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( E @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( ZZA @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( B @ ( M @ ( L @ ( K @ ( J @ ( I @ ( T @ ( G @ ( F @ ( ZF @ ( D @ ( C @ ( ZR @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxz) ).
thf(38,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZL @ ( ZZ @ ( ZY @ ( Z @ ( ZW @ ( ZV @ ( N @ ( ZT @ ( ZS @ ( ZU @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( H @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZX @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( E @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( ZZA @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( B @ ( M @ ( L @ ( K @ ( J @ ( I @ ( T @ ( G @ ( F @ ( ZF @ ( D @ ( C @ ( ZR @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
~ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_like_this) ).
thf(21,plain,
~ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( w @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( y @ ( y @ ( y @ ( o @ ( o @ ( o @ ( g @ ( g @ ( g @ ( r @ ( r @ ( r @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ ( b @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZJ @ ( X @ ( L @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZT @ ( ZK @ ( Y @ ( M @ ( G @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZU @ ( ZL @ ( Z @ ( N @ ( H @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( ZV @ ( ZM @ ( ZA @ ( O @ ( I @ ( K @ ( J @ ( ZN @ ( ZB @ ( P @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fzy) ).
thf(33,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZJ @ ( X @ ( L @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZT @ ( ZK @ ( Y @ ( M @ ( G @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZU @ ( ZL @ ( Z @ ( N @ ( H @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( ZV @ ( ZM @ ( ZA @ ( O @ ( I @ ( K @ ( J @ ( ZN @ ( ZB @ ( P @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( ZG @ ( ZF @ ( ZE @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',myx) ).
thf(44,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( ZG @ ( ZF @ ( ZE @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZI @ ( W @ ( K @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZW @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( D @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZX @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( E @ ( V @ ( U @ ( T @ ( S @ ( R @ ( ZY @ ( P @ ( O @ ( N @ ( M @ ( L @ ( F @ ( J @ ( I @ ( H @ ( G @ ( ZO @ ( ZC @ ( Q @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mzy) ).
thf(27,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZI @ ( W @ ( K @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZW @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( D @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZX @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( E @ ( V @ ( U @ ( T @ ( S @ ( R @ ( ZY @ ( P @ ( O @ ( N @ ( M @ ( L @ ( F @ ( J @ ( I @ ( H @ ( G @ ( ZO @ ( ZC @ ( Q @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZK @ ( ZY @ ( ZX @ ( Y @ ( ZV @ ( ZU @ ( M @ ( ZT @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( G @ ( L @ ( X @ ( ZJ @ ( ZW @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( D @ ( K @ ( W @ ( ZI @ ( ZZ @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( A @ ( J @ ( V @ ( ZH @ ( I @ ( H @ ( U @ ( F @ ( E @ ( ZG @ ( C @ ( B @ ( ZS @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lxz) ).
thf(50,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZK @ ( ZY @ ( ZX @ ( Y @ ( ZV @ ( ZU @ ( M @ ( ZT @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( G @ ( L @ ( X @ ( ZJ @ ( ZW @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( D @ ( K @ ( W @ ( ZI @ ( ZZ @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( A @ ( J @ ( V @ ( ZH @ ( I @ ( H @ ( U @ ( F @ ( E @ ( ZG @ ( C @ ( B @ ( ZS @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( Q @ ( ZC @ ( ZO @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( F @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZY @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( E @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( ZX @ ( V @ ( U @ ( T @ ( S @ ( R @ ( D @ ( P @ ( O @ ( N @ ( M @ ( L @ ( ZW @ ( J @ ( I @ ( H @ ( G @ ( K @ ( W @ ( ZI @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',myz) ).
thf(31,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( Q @ ( ZC @ ( ZO @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( F @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZY @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( E @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( ZX @ ( V @ ( U @ ( T @ ( S @ ( R @ ( D @ ( P @ ( O @ ( N @ ( M @ ( L @ ( ZW @ ( J @ ( I @ ( H @ ( G @ ( K @ ( W @ ( ZI @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( T @ ( ZZ @ ( ZY @ ( ZF @ ( ZW @ ( ZV @ ( ZR @ ( ZT @ ( ZS @ ( B @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZZA @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( E @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( ZX @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( H @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( ZU @ ( M @ ( L @ ( K @ ( J @ ( I @ ( ZL @ ( G @ ( F @ ( Z @ ( D @ ( C @ ( N @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mzx) ).
thf(40,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( T @ ( ZZ @ ( ZY @ ( ZF @ ( ZW @ ( ZV @ ( ZR @ ( ZT @ ( ZS @ ( B @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZZA @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( E @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( ZX @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( H @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( ZU @ ( M @ ( L @ ( K @ ( J @ ( I @ ( ZL @ ( G @ ( F @ ( Z @ ( D @ ( C @ ( N @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( X @ ( W @ ( V @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxy) ).
thf(23,plain,
! [ZZB: $i,ZZA: $i,ZZ: $i,ZY: $i,ZX: $i,ZW: $i,ZV: $i,ZU: $i,ZT: $i,ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( X @ ( W @ ( V @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ZZB @ ( ZZA @ ( ZZ @ ( ZY @ ( ZX @ ( ZW @ ( ZV @ ( ZU @ ( ZT @ ( ZS @ ( ZR @ ( ZQ @ ( ZP @ ( ZO @ ( ZN @ ( ZM @ ( ZL @ ( ZK @ ( ZJ @ ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ ( Y @ ( X @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ state ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,plain,
$false,
inference(e,[status(thm)],[56,52,54,35,48,58,36,42,25,46,29,38,21,33,44,27,50,31,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ037-2 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 05:07:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.23 % [INFO] Parsing done (234ms).
% 1.38/1.25 % [INFO] Running in sequential loop mode.
% 2.18/1.65 % [INFO] eprover registered as external prover.
% 2.18/1.66 % [INFO] Scanning for conjecture ...
% 2.37/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.55/1.83 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.83/1.92 % [INFO] Problem is propositional (TPTP CNF).
% 2.83/1.93 % [INFO] Type checking passed.
% 2.83/1.94 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.10/3.32 % External prover 'e' found a proof!
% 7.10/3.32 % [INFO] Killing All external provers ...
% 7.10/3.33 % Time passed: 2786ms (effective reasoning time: 2072ms)
% 7.10/3.33 % Axioms used in derivation (19): myz, start_with_this, mxy, txy, byz, rzx, fzy, tyx, mzx, lxz, rxz, lzx, bzy, myx, mxz, bxy, mzy, byx, fyz
% 7.10/3.33 % No. of inferences in proof: 41
% 7.10/3.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2786 ms resp. 2072 ms w/o parsing
% 7.47/3.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.47/3.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------