%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : ITP010+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n022.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  : 600s
% DateTime : Sun Jul 17 01:27:10 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ITP010+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.10/0.13  % Command  : run_zenon %s %d
% 0.13/0.34  % Computer : n022.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  : 600
% 0.13/0.34  % DateTime : Fri Jun  3 23:15:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.50  Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EFORALL__SIMP
% 0.19/0.50  Zenon warning: unused variable (V1x_2E0 : zenon_U) in thm_2Ebool_2EFORALL__SIMP
% 0.19/0.50  (* PROOF-FOUND *)
% 0.19/0.50  % SZS status Theorem
% 0.19/0.50  (* BEGIN-PROOF *)
% 0.19/0.50  % SZS output start Proof
% 0.19/0.50  Theorem thm_2Ecardinal_2ECARD__NOT__LE : (forall A_27a : zenon_U, (forall A_27b : zenon_U, (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))))))).
% 0.19/0.50  Proof.
% 0.19/0.50  apply NNPP. intro zenon_G.
% 0.19/0.50  apply (zenon_notallex_s (fun A_27a : zenon_U => (forall A_27b : zenon_U, (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))))))) zenon_G); [ zenon_intro zenon_H27; idtac ].
% 0.19/0.50  elim zenon_H27. zenon_intro zenon_TA_27a_bo. zenon_intro zenon_H29.
% 0.19/0.50  apply (zenon_notallex_s (fun A_27b : zenon_U => (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0))))))))) zenon_H29); [ zenon_intro zenon_H2a; idtac ].
% 0.19/0.50  elim zenon_H2a. zenon_intro zenon_TA_27b_br. zenon_intro zenon_H2c.
% 0.19/0.50  apply (zenon_notallex_s (fun V0s_2E0 : zenon_U => (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))))) zenon_H2c); [ zenon_intro zenon_H2d; idtac ].
% 0.19/0.50  elim zenon_H2d. zenon_intro zenon_TV0s_2E0_bu. zenon_intro zenon_H2f.
% 0.19/0.50  apply (zenon_notallex_s (fun V1t_2E0 : zenon_U => ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_bu) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_bu) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0))))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ].
% 0.19/0.50  elim zenon_H30. zenon_intro zenon_TV1t_2E0_bx. zenon_intro zenon_H32.
% 0.19/0.50  apply (zenon_notequiv_s _ _ zenon_H32); [ zenon_intro zenon_H33; zenon_intro zenon_H34 | zenon_intro zenon_H34; zenon_intro zenon_H33 ].
% 0.19/0.50  exact (zenon_H33 zenon_H34).
% 0.19/0.50  exact (zenon_H33 zenon_H34).
% 0.19/0.50  Qed.
% 0.19/0.50  % SZS output end Proof
% 0.19/0.50  (* END-PROOF *)
% 0.19/0.50  nodes searched: 13
% 0.19/0.50  max branch formulas: 52
% 0.19/0.50  proof nodes created: 8
% 0.19/0.50  formulas created: 1064
% 0.19/0.50  
%------------------------------------------------------------------------------