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