0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n003.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 : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 04:20:51 EDT 2022 0.13/0.34 % CPUTime : 0.44/1.05 ============================== Prover9 =============================== 0.44/1.05 Prover9 (32) version 2009-11A, November 2009. 0.44/1.05 Process 15884 was started by sandbox on n003.cluster.edu, 0.44/1.05 Tue Aug 9 04:20:51 2022 0.44/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_15690_n003.cluster.edu". 0.44/1.05 ============================== end of head =========================== 0.44/1.05 0.44/1.05 ============================== INPUT ================================= 0.44/1.05 0.44/1.05 % Reading from file /tmp/Prover9_15690_n003.cluster.edu 0.44/1.05 0.44/1.05 set(prolog_style_variables). 0.44/1.05 set(auto2). 0.44/1.05 % set(auto2) -> set(auto). 0.44/1.05 % set(auto) -> set(auto_inference). 0.44/1.05 % set(auto) -> set(auto_setup). 0.44/1.05 % set(auto_setup) -> set(predicate_elim). 0.44/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.44/1.05 % set(auto) -> set(auto_limits). 0.44/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.44/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.44/1.05 % set(auto) -> set(auto_denials). 0.44/1.05 % set(auto) -> set(auto_process). 0.44/1.05 % set(auto2) -> assign(new_constants, 1). 0.44/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.44/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.44/1.05 % set(auto2) -> assign(max_hours, 1). 0.44/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.44/1.05 % set(auto2) -> assign(max_seconds, 0). 0.44/1.05 % set(auto2) -> assign(max_minutes, 5). 0.44/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.44/1.05 % set(auto2) -> set(sort_initial_sos). 0.44/1.05 % set(auto2) -> assign(sos_limit, -1). 0.44/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.44/1.05 % set(auto2) -> assign(max_megs, 400). 0.44/1.05 % set(auto2) -> assign(stats, some). 0.44/1.05 % set(auto2) -> clear(echo_input). 0.44/1.05 % set(auto2) -> set(quiet). 0.44/1.05 % set(auto2) -> clear(print_initial_clauses). 0.44/1.05 % set(auto2) -> clear(print_given). 0.44/1.05 assign(lrs_ticks,-1). 0.44/1.05 assign(sos_limit,10000). 0.44/1.05 assign(order,kbo). 0.44/1.05 set(lex_order_vars). 0.44/1.05 clear(print_given). 0.44/1.05 0.44/1.05 % formulas(sos). % not echoed (50 formulas) 0.44/1.05 0.44/1.05 ============================== end of input ========================== 0.44/1.05 0.44/1.05 % From the command line: assign(max_seconds, 960). 0.44/1.05 0.44/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.44/1.05 0.44/1.05 % Formulas that are not ordinary clauses: 0.44/1.05 1 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.05 2 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 0.44/1.05 3 (all A_27a all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))) <-> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Ewords_2En2w__11) # label(axiom) # label(non_clause). [assumption]. 0.44/1.05 4 (all X0_2E0 s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint),c_2Einteger_2Eint__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.05 5 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 6 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1m_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))))) # label(thm_2Einteger_2EINT__LT__CALCULATE) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 7 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Einteger_2ENUM__OF__INT) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 8 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 9 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 10 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),c_2Einteger_2Eint__lt_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0)))) # label(arityeq2_2Ec_2Einteger_2Eint__lt_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 11 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 12 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 all V3x_27_2E0 all V4y_2E0 all V5y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V5y_27_2E0) = s(A_27a,V4y_2E0)) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0)) & s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1Q_2E0) -> s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1Q_2E0),s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))))) # label(thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 13 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 14 (all A_27a all V0x_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 15 (all A_27a all X0_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Einteger__word_2Ei2w_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X0_2E0)))) # label(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 16 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 17 (all A_27a ((all V2t1_2E0 all V3t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)) & (all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))))) # label(thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 18 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 19 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 20 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X0_2E0) = s(A_27a,X1_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 21 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 22 (all A_27a all X0_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 23 (all A_27a all V0i_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,V0i_2E0)))))))) # label(thm_2Einteger__word_2Ei2w__def) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 24 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 25 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X2_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 26 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 27 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Eprim__rec_2ENOT__LESS__0) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 28 (all X0_2E0 s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__neg_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,X0_2E0)))) # label(arityeq1_2Ec_2Einteger_2Eint__neg_2E1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 29 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 30 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 31 (all A_27a all X0_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 32 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) -> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 33 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 34 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 35 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Ewords_2Edimword_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 36 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 37 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 38 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 39 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 40 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 41 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0)))))) # label(thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 42 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.06 43 (all A_27a s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Ewords_2EWORD__NEG__0) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 44 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 45 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum),c_2Einteger_2ENum_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X0_2E0)))) # label(arityeq1_2Ec_2Einteger_2ENum_2E1) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 46 -(all A_27a s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Einteger__word_2Ei2w__0) # label(negated_conjecture) # label(non_clause). [assumption]. 0.79/1.10 0.79/1.10 ============================== end of process non-clausal formulas === 0.79/1.10 0.79/1.10 ============================== PROCESS INITIAL CLAUSES =============== 0.79/1.10 0.79/1.10 ============================== PREDICATE ELIMINATION ================= 0.79/1.10 0.79/1.10 ============================== end predicate elimination ============= 0.79/1.10 0.79/1.10 Auto_denials: (non-Horn, no changes). 0.79/1.10 0.79/1.10 Term ordering decisions: 0.79/1.10 Function symbol KB weights: tyop_2Emin_2Ebool=1. tyop_2Enum_2Enum=1. tyop_2Einteger_2Eint=1. c_2Enum_2E0_2E0=1. c_2Ebool_2ET_2E0=1. c_2Ebool_2EF_2E0=1. c_2Ebool_2Ethe__value_2E0=1. c_2Ebool_2E_2F_5C_2E0=1. c_2Ebool_2E_5C_2F_2E0=1. c_2Emin_2E_3D_3D_3E_2E0=1. c_2Ebool_2ECOND_2E0=1. c_2Emin_2E_3D_2E0=1. c_2Earithmetic_2EMOD_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. c_2Ebool_2E_7E_2E0=1. c_2Einteger_2ENum_2E0=1. c_2Einteger_2Eint__lt_2E0=1. c_2Einteger_2Eint__neg_2E0=1. c_2Einteger_2Eint__of__num_2E0=1. c_2Einteger__word_2Ei2w_2E0=1. c_2Eprim__rec_2E_3C_2E0=1. c_2Ewords_2Edimword_2E0=1. c_2Ewords_2En2w_2E0=1. c_2Ewords_2Eword__2comp_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c1=1. s=1. tyop_2Emin_2Efun=1. app_2E2=1. tyop_2Efcp_2Ecart=1. c_2Einteger_2Eint__lt_2E2=1. c_2Earithmetic_2EMOD_2E2=1. c_2Ebool_2E_2F_5C_2E2=1. c_2Ebool_2E_5C_2F_2E2=1. c_2Emin_2E_3D_3D_3E_2E2=1. c_2Eprim__rec_2E_3C_2E2=1. c_2Emin_2E_3D_2E2=1. f2=1. f3=1. c_2Einteger_2Eint__of__num_2E1=1. c_2Ewords_2En2w_2E1=1. c_2Einteger_2Eint__neg_2E1=1. tyop_2Ebool_2Eitself=1. c_2Ewords_2Edimword_2E1=1. c_2Einteger_2ENum_2E1=1. c_2Ebool_2E_21_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Ewords_2Eword__2comp_2E1=1. c_2Einteger__word_2Ei2w_2E1=1. c_2Ebool_2E_7E_2E1=1. c_2Ebool_2ECOND_2E3=1. f1=1. 0.79/1.10 0.79/1.10 ============================== end of process initial clauses ======== 0.79/1.10 0.79/1.10 ============================== CLAUSES FOR SEARCH ==================== 0.79/1.10 0.79/1.10 ============================== end of clauses for search ============= 0.79/1.10 0.79/1.10 ============================== SEARCH ================================ 0.79/1.10 0.79/1.10 % Starting search at 0.03 seconds. 0.79/1.10 0.79/1.10 ============================== PROOF ================================= 0.79/1.10 % SZS status Theorem 0.79/1.10 % SZS output start Refutation 0.79/1.10 0.79/1.10 % Proof 1 at 0.06 (+ 0.00) seconds. 0.79/1.10 % Length of proof is 16. 0.79/1.10 % Level of proof is 4. 0.79/1.10 % Maximum clause weight is 56.000. 0.79/1.10 % Given clauses 33. 0.79/1.10 0.79/1.10 6 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1m_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))))) # label(thm_2Einteger_2EINT__LT__CALCULATE) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 7 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Einteger_2ENUM__OF__INT) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 17 (all A_27a ((all V2t1_2E0 all V3t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)) & (all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))))) # label(thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 23 (all A_27a all V0i_2E0 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,V0i_2E0)))))))) # label(thm_2Einteger__word_2Ei2w__def) # label(axiom) # label(non_clause). [assumption]. 0.79/1.10 46 -(all A_27a s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Einteger__word_2Ei2w__0) # label(negated_conjecture) # label(non_clause). [assumption]. 0.79/1.10 49 s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,A))))) = s(tyop_2Enum_2Enum,A) # label(thm_2Einteger_2ENUM__OF__INT) # label(axiom). [clausify(7)]. 0.79/1.10 55 s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Einteger_2EINT__NEG__0) # label(axiom). [assumption]. 0.79/1.10 56 s(A,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A,B),s(A,C))) = s(A,C) # label(thm_2Ebool_2Ebool__case__thm) # label(axiom). [clausify(17)]. 0.79/1.10 67 s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,A))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,B))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) # label(thm_2Einteger_2EINT__LT__CALCULATE) # label(axiom). [clausify(6)]. 0.79/1.10 77 s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,A))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,B))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,A),s(tyop_2Enum_2Enum,B))) # label(thm_2Einteger_2EINT__LT__CALCULATE) # label(axiom). [clausify(6)]. 0.79/1.10 95 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,B))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,B),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,B))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,B))))))) # label(thm_2Einteger__word_2Ei2w__def) # label(axiom). [clausify(23)]. 0.79/1.10 96 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,B),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,B))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,B))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,B))). [copy(95),flip(a)]. 0.79/1.10 104 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,c1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,c1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Einteger__word_2Ei2w__0) # label(negated_conjecture). [clausify(46)]. 0.79/1.10 170 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,A),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0). [para(55(a,1),67(a,1,2,2)),rewrite([77(14)])]. 0.79/1.10 195 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,B))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,B))). [para(49(a,1),96(a,1,2,3,2,1)),rewrite([77(16),170(10),56(32)]),flip(a)]. 0.79/1.10 196 $F. [resolve(195,a,104,a)]. 0.79/1.10 0.79/1.10 % SZS output end Refutation 0.79/1.10 ============================== end of proof ========================== 0.79/1.10 0.79/1.10 ============================== STATISTICS ============================ 0.79/1.10 0.79/1.10 Given=33. Generated=1098. Kept=128. proofs=1. 0.79/1.10 Usable=33. Sos=85. Demods=26. Limbo=0, Disabled=87. Hints=0. 0.79/1.10 Megabytes=0.63. 0.79/1.10 User_CPU=0.06, System_CPU=0.00, Wall_clock=0. 0.79/1.10 0.79/1.10 ============================== end of statistics ===================== 0.79/1.10 0.79/1.10 ============================== end of search ========================= 0.79/1.10 0.79/1.10 THEOREM PROVED 0.79/1.10 % SZS status Theorem 0.79/1.10 0.79/1.10 Exiting with 1 proof. 0.79/1.10 0.79/1.10 Process 15884 exit (max_proofs) Tue Aug 9 04:20:51 2022 0.79/1.10 Prover9 interrupted 0.79/1.11 EOF