0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n005.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 : 1200 0.13/0.34 % DateTime : Tue Jul 13 15:21:03 EDT 2021 0.19/0.34 % CPUTime : 0.82/1.18 ============================== Prover9 =============================== 0.82/1.18 Prover9 (32) version 2009-11A, November 2009. 0.82/1.18 Process 2111 was started by sandbox on n005.cluster.edu, 0.82/1.18 Tue Jul 13 15:21:04 2021 0.82/1.18 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_1948_n005.cluster.edu". 0.82/1.18 ============================== end of head =========================== 0.82/1.18 0.82/1.18 ============================== INPUT ================================= 0.82/1.18 0.82/1.18 % Reading from file /tmp/Prover9_1948_n005.cluster.edu 0.82/1.18 0.82/1.18 set(prolog_style_variables). 0.82/1.18 set(auto2). 0.82/1.18 % set(auto2) -> set(auto). 0.82/1.18 % set(auto) -> set(auto_inference). 0.82/1.18 % set(auto) -> set(auto_setup). 0.82/1.18 % set(auto_setup) -> set(predicate_elim). 0.82/1.18 % set(auto_setup) -> assign(eq_defs, unfold). 0.82/1.18 % set(auto) -> set(auto_limits). 0.82/1.18 % set(auto_limits) -> assign(max_weight, "100.000"). 0.82/1.18 % set(auto_limits) -> assign(sos_limit, 20000). 0.82/1.18 % set(auto) -> set(auto_denials). 0.82/1.18 % set(auto) -> set(auto_process). 0.82/1.18 % set(auto2) -> assign(new_constants, 1). 0.82/1.18 % set(auto2) -> assign(fold_denial_max, 3). 0.82/1.18 % set(auto2) -> assign(max_weight, "200.000"). 0.82/1.18 % set(auto2) -> assign(max_hours, 1). 0.82/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.82/1.18 % set(auto2) -> assign(max_seconds, 0). 0.82/1.18 % set(auto2) -> assign(max_minutes, 5). 0.82/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.82/1.18 % set(auto2) -> set(sort_initial_sos). 0.82/1.18 % set(auto2) -> assign(sos_limit, -1). 0.82/1.18 % set(auto2) -> assign(lrs_ticks, 3000). 0.82/1.18 % set(auto2) -> assign(max_megs, 400). 0.82/1.18 % set(auto2) -> assign(stats, some). 0.82/1.18 % set(auto2) -> clear(echo_input). 0.82/1.18 % set(auto2) -> set(quiet). 0.82/1.18 % set(auto2) -> clear(print_initial_clauses). 0.82/1.18 % set(auto2) -> clear(print_given). 0.82/1.18 assign(lrs_ticks,-1). 0.82/1.18 assign(sos_limit,10000). 0.82/1.18 assign(order,kbo). 0.82/1.18 set(lex_order_vars). 0.82/1.18 clear(print_given). 0.82/1.18 0.82/1.18 % formulas(sos). % not echoed (31 formulas) 0.82/1.18 0.82/1.18 ============================== end of input ========================== 0.82/1.18 0.82/1.18 % From the command line: assign(max_seconds, 1200). 0.82/1.18 0.82/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.82/1.18 0.82/1.18 % Formulas that are not ordinary clauses: 0.82/1.18 1 (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_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 2 (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]. 0.82/1.18 3 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 4 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 5 (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]. 0.82/1.18 6 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 7 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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]. 0.82/1.18 8 (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_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 9 (all A_27a all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 10 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 11 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_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_3F_2E0),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]. 0.82/1.18 12 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 13 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 14 (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]. 0.82/1.18 15 (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]. 0.82/1.18 16 (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]. 0.82/1.18 17 (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]. 0.82/1.18 18 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 19 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_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]. 0.82/1.18 20 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 21 (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_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 22 (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_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(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]. 0.82/1.18 23 (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]. 0.82/1.18 24 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 0.82/1.18 25 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 26 (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_2Ebool_2E_2F_5C_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_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 27 (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),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 28 (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]. 0.87/1.59 29 -(all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture) # label(non_clause). [assumption]. 0.87/1.59 0.87/1.59 ============================== end of process non-clausal formulas === 0.87/1.59 0.87/1.59 ============================== PROCESS INITIAL CLAUSES =============== 0.87/1.59 0.87/1.59 ============================== PREDICATE ELIMINATION ================= 0.87/1.59 0.87/1.59 ============================== end predicate elimination ============= 0.87/1.59 0.87/1.59 Auto_denials: (non-Horn, no changes). 0.87/1.59 0.87/1.59 Term ordering decisions: 0.87/1.59 Function symbol KB weights: tyop_2Emin_2Ebool=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_2ET_2E0=1. c_2Emin_2E_3D_2E0=1. c_2Ebool_2EF_2E0=1. c_2Ebool_2EIN_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. c_2Ebool_2E_7E_2E0=1. c_2Epred__set_2ECHOICE_2E0=1. c_2Epred__set_2EDELETE_2E0=1. c_2Epred__set_2EREST_2E0=1. c_2Epred__set_2ESUBSET_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c1=1. c2=1. s=1. tyop_2Emin_2Efun=1. app_2E2=1. c_2Ebool_2EIN_2E2=1. c_2Epred__set_2EDELETE_2E2=1. c_2Epred__set_2ESUBSET_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_2Emin_2E_3D_2E2=1. f1=1. f2=1. c_2Ebool_2E_21_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Epred__set_2ECHOICE_2E1=1. c_2Epred__set_2EREST_2E1=1. c_2Ebool_2E_7E_2E1=1. f3=1. f4=1. 0.87/1.59 0.87/1.59 ============================== end of process initial clauses ======== 0.87/1.59 0.87/1.59 ============================== CLAUSES FOR SEARCH ==================== 0.87/1.59 0.87/1.59 ============================== end of clauses for search ============= 0.87/1.59 0.87/1.59 ============================== SEARCH ================================ 0.87/1.59 0.87/1.59 % Starting search at 0.02 seconds. 0.87/1.59 0.87/1.59 ============================== PROOF ================================= 0.87/1.59 % SZS status Theorem 0.87/1.59 % SZS output start Refutation 0.87/1.59 0.87/1.59 % Proof 1 at 0.42 (+ 0.01) seconds. 0.87/1.59 % Length of proof is 18. 0.87/1.59 % Level of proof is 5. 0.87/1.59 % Maximum clause weight is 32.000. 0.87/1.59 % Given clauses 132. 0.87/1.59 0.87/1.59 4 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 18 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 24 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 0.87/1.59 28 (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]. 0.87/1.59 29 -(all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture) # label(non_clause). [assumption]. 0.87/1.59 35 p(s(tyop_2Emin_2Ebool,A)) | p(s(tyop_2Emin_2Ebool,B)) | s(tyop_2Emin_2Ebool,B) = s(tyop_2Emin_2Ebool,A) # label(reserved_2Eho_2Eboolext) # label(axiom). [clausify(28)]. 0.87/1.59 45 s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(A,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))))) = s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B))) # label(thm_2Epred__set_2EREST__DEF) # label(axiom). [clausify(4)]. 0.87/1.59 46 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,f3(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B)))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom). [clausify(24)]. 0.87/1.59 57 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(reserved_2Eho_2Enotfalse) # label(axiom). [assumption]. 0.87/1.59 60 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2))),s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)))) # label(thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture). [clausify(29)]. 0.87/1.59 84 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) | -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,f3(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom). [clausify(24)]. 0.87/1.59 88 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C),s(A,D)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A,B),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom). [clausify(18)]. 0.87/1.59 202 p(s(tyop_2Emin_2Ebool,A)) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,A). [resolve(57,a,35,b)]. 0.87/1.59 540 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f3(c1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)),c2)),s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)))). [ur(84,a,60,a)]. 0.87/1.59 1779 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2))),s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0). [resolve(202,a,60,a),flip(a)]. 0.87/1.59 1863 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f3(c1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)),c2)),s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2),s(c1,A)))))). [ur(88,b,540,a)]. 0.87/1.59 2059 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f3(c1,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)),c2)),s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(c1,tyop_2Emin_2Ebool),c2)))))). [para(45(a,1),1863(a,1,2,2))]. 0.87/1.59 2127 $F. [resolve(2059,a,46,b),rewrite([1779(18)]),unit_del(a,57)]. 0.87/1.59 0.87/1.59 % SZS output end Refutation 0.87/1.59 ============================== end of proof ========================== 0.87/1.59 0.87/1.59 ============================== STATISTICS ============================ 0.87/1.59 0.87/1.59 Given=132. Generated=8761. Kept=2089. proofs=1. 0.87/1.59 Usable=91. Sos=1163. Demods=53. Limbo=1, Disabled=888. Hints=0. 0.87/1.59 Megabytes=5.89. 0.87/1.59 User_CPU=0.42, System_CPU=0.01, Wall_clock=0. 0.87/1.59 0.87/1.59 ============================== end of statistics ===================== 0.87/1.59 0.87/1.59 ============================== end of search ========================= 0.87/1.59 0.87/1.59 THEOREM PROVED 0.87/1.59 % SZS status Theorem 0.87/1.59 0.87/1.59 Exiting with 1 proof. 0.87/1.59 0.87/1.59 Process 2111 exit (max_proofs) Tue Jul 13 15:21:04 2021 0.87/1.59 Prover9 interrupted 0.87/1.59 EOF