TSTP Solution File: SYN986+1.002 by Goeland---1.0.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Goeland---1.0.0
% Problem  : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : goeland -dmt -presko -proof %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 22:25:13 EDT 2022

% Result   : Theorem 25.96s 15.28s
% Output   : Proof 25.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command    : goeland -dmt -presko -proof %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Sep  5 09:37:05 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  [DMT] DMT loaded with preskolemization
% 0.13/0.34  [EQ] equality loaded.
% 0.13/0.34  [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34  Conjecture not found
% 0.13/0.34  Start search
% 0.13/0.34  nb_step : 1 - limit : 3
% 0.13/0.34  Launch Gotab with destructive = true
% 0.13/0.37  nb_step : 2 - limit : 6
% 0.13/0.37  Launch Gotab with destructive = true
% 2.09/1.58  nb_step : 3 - limit : 12
% 2.09/1.58  Launch Gotab with destructive = true
% 25.91/15.28  % SZS output start Proof for theBenchmark.p
% 25.91/15.28  [437] ALPHA_AND : ((! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6))) & ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))) & ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13))))
% 25.91/15.28  	-> [438] (! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6))) & ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))), ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.91/15.28  
% 25.91/15.28  [438] ALPHA_AND : (! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6))) & ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10)))))
% 25.91/15.28  	-> [439] ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6))), ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.91/15.28  
% 25.91/15.28  [439] GAMMA_NOT_EXISTS : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.91/15.28  	-> [440] ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.91/15.28  
% 25.91/15.28  [440] BETA_NOT_AND : ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.91/15.28  	-> [441] ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.91/15.28  	-> [442] ~r(zero, zero, succ(zero))
% 25.91/15.28  
% 25.91/15.28  [442] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.91/15.28  	-> [445] r(Y6_0_1, zero, succ(Y6_0_1))
% 25.91/15.28  
% 25.91/15.28  [445] CLOSURE : r(Y6_0_1, zero, succ(Y6_0_1))
% 25.91/15.28  
% 25.91/15.28  [441] BETA_NOT_AND : ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.91/15.28  	-> [477] ~r(zero, zero, succ(zero))
% 25.91/15.28  	-> [478] ~r(zero, succ(zero), zero)
% 25.91/15.28  
% 25.91/15.28  [477] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.91/15.28  	-> [480] r(Y6_8_1, zero, succ(Y6_8_1))
% 25.91/15.28  
% 25.91/15.28  [480] CLOSURE : r(Y6_8_1, zero, succ(Y6_8_1))
% 25.91/15.28  
% 25.91/15.28  [478] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.91/15.28  	-> [479] r(zero, zero, succ(zero))
% 25.91/15.28  
% 25.91/15.28  [479] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [481] (r(zero, zero, succ(zero)) => (r(succ(zero), zero, zero) => r(zero, succ(zero), zero)))
% 25.96/15.28  
% 25.96/15.28  [481] BETA_IMPLY : (r(zero, zero, succ(zero)) => (r(succ(zero), zero, zero) => r(zero, succ(zero), zero)))
% 25.96/15.28  	-> [482] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [483] (r(succ(zero), zero, zero) => r(zero, succ(zero), zero))
% 25.96/15.28  
% 25.96/15.28  [482] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [483] BETA_IMPLY : (r(succ(zero), zero, zero) => r(zero, succ(zero), zero))
% 25.96/15.28  	-> [492] ~r(succ(zero), zero, zero)
% 25.96/15.28  	-> [493] r(zero, succ(zero), zero)
% 25.96/15.28  
% 25.96/15.28  [493] CLOSURE : r(zero, succ(zero), zero)
% 25.96/15.28  
% 25.96/15.28  [495] BETA_NOT_AND : ~((r(zero, zero, zero) & r(zero, zero, succ(zero))) & r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  	-> [502] ~(r(zero, zero, zero) & r(zero, zero, succ(zero)))
% 25.96/15.28  	-> [503] ~r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [502] BETA_NOT_AND : ~(r(zero, zero, zero) & r(zero, zero, succ(zero)))
% 25.96/15.28  	-> [504] ~r(zero, zero, zero)
% 25.96/15.28  	-> [505] ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [505] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [504]  : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [506] ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  
% 25.96/15.28  [506] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [507] r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [507] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [508] ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  
% 25.96/15.28  [508] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [509] (r(zero, zero, succ(zero)) => (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [509] BETA_IMPLY : (r(zero, zero, succ(zero)) => (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero)))))
% 25.96/15.28  	-> [510] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [511] (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  
% 25.96/15.28  [510] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [511] BETA_IMPLY : (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  	-> [720] ~r(succ(zero), zero, succ(succ(zero)))
% 25.96/15.28  	-> [721] r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [720]  : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [722] ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  
% 25.96/15.28  [722] GAMMA_NOT_EXISTS : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [723] ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [723] BETA_NOT_AND : ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  	-> [724] ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [725] ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [725] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [724] BETA_NOT_AND : ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [730] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [731] ~r(zero, succ(zero), zero)
% 25.96/15.28  
% 25.96/15.28  [731]  : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [732] ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  
% 25.96/15.28  [732] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [733] r(Y6_27_1, zero, succ(Y6_27_1))
% 25.96/15.28  
% 25.96/15.28  [733] CLOSURE : r(Y6_27_1, zero, succ(Y6_27_1))
% 25.96/15.28  
% 25.96/15.28  [730] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [721]  : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [1678] ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  
% 25.96/15.28  [1678] GAMMA_NOT_EXISTS : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [1679] ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [1679] BETA_NOT_AND : ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  	-> [1680] ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [1681] ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [1681] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [1680] BETA_NOT_AND : ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [2018] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [2019] ~r(zero, succ(zero), zero)
% 25.96/15.28  
% 25.96/15.28  [2018] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2023] BETA_IMPLY : (r(zero, succ(zero), succ(succ(zero))) => (r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))) => r(zero, succ(succ(zero)), succ(succ(succ(succ(zero)))))))
% 25.96/15.28  	-> [2448] ~r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  	-> [2449] (r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))) => r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))))
% 25.96/15.28  
% 25.96/15.28  [2448] CLOSURE : ~r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2449] BETA_IMPLY : (r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))) => r(zero, succ(succ(zero)), succ(succ(succ(succ(zero))))))
% 25.96/15.28  	-> [2804] ~r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero)))))
% 25.96/15.28  	-> [2805] r(zero, succ(succ(zero)), succ(succ(succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [2804]  : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [2806] ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  
% 25.96/15.28  [2806] GAMMA_NOT_EXISTS : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [2808] ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2808] BETA_NOT_AND : ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), zero)) & r(zero, zero, succ(zero)))
% 25.96/15.28  	-> [2810] ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [2811] ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2811] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2810] BETA_NOT_AND : ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), zero))
% 25.96/15.28  	-> [2844] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [2845] ~r(zero, succ(zero), zero)
% 25.96/15.28  
% 25.96/15.28  [2845]  : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [2846] ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  
% 25.96/15.28  [2846] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [2847] r(succ(succ(zero)), zero, succ(succ(succ(zero))))
% 25.96/15.28  
% 25.96/15.28  [2847] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [2848] ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  
% 25.96/15.28  [2848] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [2849] (r(succ(succ(zero)), zero, succ(succ(succ(zero)))) => (r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero))))) => r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero)))))))
% 25.96/15.28  
% 25.96/15.28  [2849] BETA_IMPLY : (r(succ(succ(zero)), zero, succ(succ(succ(zero)))) => (r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero))))) => r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero)))))))
% 25.96/15.28  	-> [2850] ~r(succ(succ(zero)), zero, succ(succ(succ(zero))))
% 25.96/15.28  	-> [2851] (r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero))))) => r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))))
% 25.96/15.28  
% 25.96/15.28  [2850] CLOSURE : ~r(succ(succ(zero)), zero, succ(succ(succ(zero))))
% 25.96/15.28  
% 25.96/15.28  [2851] BETA_IMPLY : (r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero))))) => r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero))))))
% 25.96/15.28  	-> [2868] ~r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero)))))
% 25.96/15.28  	-> [2869] r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [2868] CLOSURE : ~r(succ(succ(succ(zero))), zero, succ(succ(succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [2869] CLOSURE : r(succ(succ(zero)), succ(zero), succ(succ(succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [2844] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2805]  : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [2807] ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  
% 25.96/15.28  [2807] GAMMA_NOT_EXISTS : ~? [Z211_11, Z112_12, Z013_13] :  (((r(zero, zero, Z211_11) & r(zero, Z211_11, Z112_12)) & r(zero, Z112_12, Z013_13)))
% 25.96/15.28  	-> [2809] ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), succ(succ(zero)))) & r(zero, succ(succ(zero)), Z013_45_0))
% 25.96/15.28  
% 25.96/15.28  [2809] BETA_NOT_AND : ~((r(zero, zero, succ(zero)) & r(zero, succ(zero), succ(succ(zero)))) & r(zero, succ(succ(zero)), Z013_45_0))
% 25.96/15.28  	-> [2812] ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  	-> [2813] ~r(zero, succ(succ(zero)), Z013_45_0)
% 25.96/15.28  
% 25.96/15.28  [2813] CLOSURE : ~r(zero, succ(succ(zero)), Z013_45_0)
% 25.96/15.28  
% 25.96/15.28  [2812] BETA_NOT_AND : ~(r(zero, zero, succ(zero)) & r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  	-> [2886] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [2887] ~r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2886] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2887] CLOSURE : ~r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [503]  : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [2888] ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  
% 25.96/15.28  [2888] GAMMA_FORALL : ! [Y6_6] :  (r(Y6_6, zero, succ(Y6_6)))
% 25.96/15.28  	-> [2889] r(succ(zero), zero, succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2889] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [2890] ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  
% 25.96/15.28  [2890] GAMMA_FORALL : ! [Y7_7, X8_8, Z9_9, Z110_10] :  ((r(Y7_7, X8_8, Z9_9) => (r(Z9_9, X8_8, Z110_10) => r(Y7_7, succ(X8_8), Z110_10))))
% 25.96/15.28  	-> [2891] (r(zero, zero, succ(zero)) => (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero)))))
% 25.96/15.28  
% 25.96/15.28  [2891] BETA_IMPLY : (r(zero, zero, succ(zero)) => (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero)))))
% 25.96/15.28  	-> [2892] ~r(zero, zero, succ(zero))
% 25.96/15.28  	-> [2893] (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  
% 25.96/15.28  [2892] CLOSURE : ~r(zero, zero, succ(zero))
% 25.96/15.28  
% 25.96/15.28  [2893] BETA_IMPLY : (r(succ(zero), zero, succ(succ(zero))) => r(zero, succ(zero), succ(succ(zero))))
% 25.96/15.28  	-> [2896] ~r(succ(zero), zero, succ(succ(zero)))
% 25.96/15.28  	-> [2897] r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2897] CLOSURE : r(zero, succ(zero), succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  [2896] CLOSURE : ~r(succ(zero), zero, succ(succ(zero)))
% 25.96/15.28  
% 25.96/15.28  % SZS output end Proof for theBenchmark.p
% 25.96/15.28  [14.938989s][1][Res] 72927 goroutines created
% 25.96/15.28  ==== Result ====
% 25.96/15.28  [14.939043s][1][Res] VALID
% 25.96/15.28  % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------