TSTP Solution File: ITP010+4 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : ITP010+4 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n027.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 01:27:11 EDT 2022
% Result : Theorem 2.48s 2.68s
% Output : Proof 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP010+4 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 3 10:10:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.00 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Ebool_2EABS__SIMP
% 1.80/2.00 Zenon warning: unused variable (V1t2_2E0 : zenon_U) in thm_2Ebool_2EABS__SIMP
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EFORALL__SIMP
% 1.80/2.00 Zenon warning: unused variable (V1x_2E0 : zenon_U) in thm_2Ebool_2EFORALL__SIMP
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EEXISTS__SIMP
% 1.80/2.00 Zenon warning: unused variable (V1x_2E0 : zenon_U) in thm_2Ebool_2EEXISTS__SIMP
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__AND__THM
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__AND__THM
% 1.80/2.00 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__AND__THM
% 1.80/2.00 Zenon warning: unused variable (V4x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__AND__THM
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EBOTH__FORALL__OR__THM
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__OR__THM
% 1.80/2.00 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__OR__THM
% 1.80/2.00 Zenon warning: unused variable (V4x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__OR__THM
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EBOTH__FORALL__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V4x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__FORALL__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (V4x_2E0 : zenon_U) in thm_2Ebool_2EBOTH__EXISTS__IMP__THM
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER
% 1.80/2.00 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER
% 1.80/2.00 Zenon warning: unused variable (V1f1_2E0 : zenon_U) in thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER
% 1.80/2.00 Zenon warning: unused variable (V2f2_2E0 : zenon_U) in thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Epred__set_2ESUBSET__MIN__SET
% 1.80/2.00 Zenon warning: unused variable (V2n_2E0 : zenon_U) in thm_2Epred__set_2ESUBSET__MIN__SET
% 1.80/2.00 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Elist_2Elupdate__append2
% 1.80/2.00 Zenon warning: unused variable (V4l3_2E0 : zenon_U) in thm_2Elist_2Elupdate__append2
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Enumeral__bit_2Enumeral__imod__2exp
% 1.80/2.00 Zenon warning: unused variable (V2n_2E0 : zenon_U) in thm_2Enumeral__bit_2Enumeral__imod__2exp
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Enumeral__bit_2ENUMERAL__BITWISE
% 1.80/2.00 Zenon warning: unused variable (V2a_2E0 : zenon_U) in thm_2Enumeral__bit_2ENUMERAL__BITWISE
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING
% 1.80/2.00 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING
% 1.80/2.00 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T
% 1.80/2.00 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T
% 1.80/2.00 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T
% 1.80/2.00 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F
% 1.80/2.00 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F
% 1.80/2.00 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F
% 1.80/2.00 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F
% 2.48/2.68 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__DIFF
% 2.48/2.68 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__DIFF
% 2.48/2.68 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__T
% 2.48/2.68 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__T
% 2.48/2.68 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__T
% 2.48/2.68 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__T
% 2.48/2.68 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__F
% 2.48/2.68 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__F
% 2.48/2.68 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__F
% 2.48/2.68 Zenon warning: unused variable (V1s_2E0 : zenon_U) in thm_2Eres__quan_2ERES__EXISTS__F
% 2.48/2.68 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Eres__quan_2ERES__FORALL__DIFF
% 2.48/2.68 Zenon warning: unused variable (V3x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__DIFF
% 2.48/2.68 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__FORALL__F
% 2.48/2.68 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__FORALL__F
% 2.48/2.68 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__F
% 2.48/2.68 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__F
% 2.48/2.68 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Eres__quan_2ERES__FORALL__T
% 2.48/2.68 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Eres__quan_2ERES__FORALL__T
% 2.48/2.68 Zenon warning: unused variable (V0P_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__T
% 2.48/2.68 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__T
% 2.48/2.68 Zenon warning: unused variable (V2x_2E0 : zenon_U) in thm_2Eres__quan_2ERES__FORALL__FORALL
% 2.48/2.68 Zenon warning: unused variable (A_27c : zenon_U) in thm_2Efcp_2Efcp__subst__comp
% 2.48/2.68 Zenon warning: unused variable (A_27d : zenon_U) in thm_2Efcp_2Efcp__subst__comp
% 2.48/2.68 Zenon warning: unused variable (V2a_2E0 : zenon_U) in thm_2Efcp_2Efcp__subst__comp
% 2.48/2.68 Zenon warning: unused variable (V3b_2E0 : zenon_U) in thm_2Efcp_2Efcp__subst__comp
% 2.48/2.68 Zenon warning: unused variable (A_27b : zenon_U) in thm_2Ellist_2ELFLATTEN__THM
% 2.48/2.68 Zenon warning: unused variable (V1tl_2E0 : zenon_U) in thm_2Ellist_2ELFLATTEN__THM
% 2.48/2.68 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Esorting_2Esorted__perm__count__list
% 2.48/2.68 Zenon warning: unused variable (V0y_2E0 : zenon_U) in thm_2Esorting_2Esorted__perm__count__list
% 2.48/2.68 (* PROOF-FOUND *)
% 2.48/2.68 % SZS status Theorem
% 2.48/2.68 (* BEGIN-PROOF *)
% 2.48/2.68 % SZS output start Proof
% 2.48/2.68 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)))))))))).
% 2.48/2.68 Proof.
% 2.48/2.68 apply NNPP. intro zenon_G.
% 2.48/2.68 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_H1df8; idtac ].
% 2.48/2.68 elim zenon_H1df8. zenon_intro zenon_TA_27a_ljd. zenon_intro zenon_H1dfa.
% 2.48/2.68 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_ljd (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_ljd (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0))))))))) zenon_H1dfa); [ zenon_intro zenon_H1dfb; idtac ].
% 2.48/2.68 elim zenon_H1dfb. zenon_intro zenon_TA_27b_ljg. zenon_intro zenon_H1dfd.
% 2.48/2.68 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_ljd (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_ljg (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_ljd (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_ljg (tyop_2Emin_2Ebool)) V1t_2E0)))))))) zenon_H1dfd); [ zenon_intro zenon_H1dfe; idtac ].
% 2.48/2.68 elim zenon_H1dfe. zenon_intro zenon_TV0s_2E0_ljj. zenon_intro zenon_H1e00.
% 2.48/2.68 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_ljd (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_ljj) (s (tyop_2Emin_2Efun zenon_TA_27b_ljg (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_ljd (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_ljj) (s (tyop_2Emin_2Efun zenon_TA_27b_ljg (tyop_2Emin_2Ebool)) V1t_2E0))))))) zenon_H1e00); [ zenon_intro zenon_H1e01; idtac ].
% 2.48/2.68 elim zenon_H1e01. zenon_intro zenon_TV1t_2E0_ljm. zenon_intro zenon_H1e03.
% 2.48/2.68 apply (zenon_notequiv_s _ _ zenon_H1e03); [ zenon_intro zenon_H1e04; zenon_intro zenon_H1e05 | zenon_intro zenon_H1e05; zenon_intro zenon_H1e04 ].
% 2.48/2.68 exact (zenon_H1e04 zenon_H1e05).
% 2.48/2.68 exact (zenon_H1e04 zenon_H1e05).
% 2.48/2.68 Qed.
% 2.48/2.68 % SZS output end Proof
% 2.48/2.68 (* END-PROOF *)
% 2.48/2.68 nodes searched: 102
% 2.48/2.68 max branch formulas: 7937
% 2.48/2.68 proof nodes created: 8
% 2.48/2.68 formulas created: 416092
% 2.48/2.68
%------------------------------------------------------------------------------