0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n005.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1200 0.11/0.32 % DateTime : Tue Jul 13 15:32:48 EDT 2021 0.11/0.32 % CPUTime : 0.39/1.14 ============================== Prover9 =============================== 0.39/1.14 Prover9 (32) version 2009-11A, November 2009. 0.39/1.14 Process 18310 was started by sandbox2 on n005.cluster.edu, 0.39/1.14 Tue Jul 13 15:32:49 2021 0.39/1.14 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_18131_n005.cluster.edu". 0.39/1.14 ============================== end of head =========================== 0.39/1.14 0.39/1.14 ============================== INPUT ================================= 0.39/1.14 0.39/1.14 % Reading from file /tmp/Prover9_18131_n005.cluster.edu 0.39/1.14 0.39/1.14 set(prolog_style_variables). 0.39/1.14 set(auto2). 0.39/1.14 % set(auto2) -> set(auto). 0.39/1.14 % set(auto) -> set(auto_inference). 0.39/1.14 % set(auto) -> set(auto_setup). 0.39/1.14 % set(auto_setup) -> set(predicate_elim). 0.39/1.14 % set(auto_setup) -> assign(eq_defs, unfold). 0.39/1.14 % set(auto) -> set(auto_limits). 0.39/1.14 % set(auto_limits) -> assign(max_weight, "100.000"). 0.39/1.14 % set(auto_limits) -> assign(sos_limit, 20000). 0.39/1.14 % set(auto) -> set(auto_denials). 0.39/1.14 % set(auto) -> set(auto_process). 0.39/1.14 % set(auto2) -> assign(new_constants, 1). 0.39/1.14 % set(auto2) -> assign(fold_denial_max, 3). 0.39/1.14 % set(auto2) -> assign(max_weight, "200.000"). 0.39/1.14 % set(auto2) -> assign(max_hours, 1). 0.39/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.39/1.14 % set(auto2) -> assign(max_seconds, 0). 0.39/1.14 % set(auto2) -> assign(max_minutes, 5). 0.39/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.39/1.14 % set(auto2) -> set(sort_initial_sos). 0.39/1.14 % set(auto2) -> assign(sos_limit, -1). 0.39/1.14 % set(auto2) -> assign(lrs_ticks, 3000). 0.39/1.14 % set(auto2) -> assign(max_megs, 400). 0.39/1.14 % set(auto2) -> assign(stats, some). 0.39/1.14 % set(auto2) -> clear(echo_input). 0.39/1.14 % set(auto2) -> set(quiet). 0.39/1.14 % set(auto2) -> clear(print_initial_clauses). 0.39/1.14 % set(auto2) -> clear(print_given). 0.39/1.14 assign(lrs_ticks,-1). 0.39/1.14 assign(sos_limit,10000). 0.39/1.14 assign(order,kbo). 0.39/1.14 set(lex_order_vars). 0.39/1.14 clear(print_given). 0.39/1.14 0.39/1.14 % formulas(sos). % not echoed (43 formulas) 0.39/1.14 0.39/1.14 ============================== end of input ========================== 0.39/1.14 0.39/1.14 % From the command line: assign(max_seconds, 1200). 0.39/1.14 0.39/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.39/1.14 0.39/1.14 % Formulas that are not ordinary clauses: 0.39/1.14 1 (all V0t_2E0 ((s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)) & (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 2 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 3 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 4 (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]. 0.39/1.14 5 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))) # label(thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 6 (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]. 0.39/1.14 7 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 8 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 9 (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]. 0.39/1.14 10 (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]. 0.39/1.14 11 (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]. 0.39/1.14 12 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 13 (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]. 0.39/1.14 14 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2Erespects_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0)) # label(thm_2Equotient_2Erespects__def) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 15 (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]. 0.39/1.14 16 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 17 (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),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(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]. 0.39/1.14 18 (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]. 0.39/1.14 19 (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]. 0.39/1.14 20 (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]. 0.39/1.14 21 (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]. 0.39/1.14 22 (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]. 0.39/1.14 23 (all A_27a all A_27b all V0R_2E0 all V1abs_2E0 all V2rep_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))) -> (all V3r_2E0 all V4s_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)),V0R_2E0),s(A_27a,V4s_2E0))),s(A_27a,V4s_2E0)))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V3r_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V4s_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)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V3r_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)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V4s_2E0)))))))) # label(thm_2Equotient_2EQUOTIENT__REL) # label(axiom) # label(non_clause). [assumption]. 0.39/1.14 24 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_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]. 0.39/1.14 25 (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]. 0.39/1.14 26 (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]. 0.39/1.14 27 (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]. 0.39/1.15 28 (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]. 0.39/1.15 29 (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]. 0.39/1.15 30 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 31 (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,V1t2_2E0) = s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 32 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 33 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 34 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 35 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 36 (all A_27a all A_27b all A_27c all A_27d all V0R1_2E0 all V1abs1_2E0 all V2rep1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))) -> (all V3R2_2E0 all V4abs2_2E0 all V5rep2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))))))) # label(thm_2Equotient_2EFUN__QUOTIENT) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 37 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 38 (all A_27b all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 0.39/1.15 39 (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]. 0.39/1.15 40 -(all A_27a all A_27b all A_27c all A_27d all V0R1_2E0 all V1abs1_2E0 all V2rep1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))) -> (all V3R2_2E0 all V4abs2_2E0 all V5rep2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))) -> (all V6f_2E0 all V7g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))) & s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0))))))))) # label(thm_2Equotient_2EFUN__REL__EQ__REL) # label(negated_conjecture) # label(non_clause). [assumption]. 0.39/1.15 0.39/1.15 ============================== end of process non-clausal formulas === 0.39/1.15 0.39/1.15 ============================== PROCESS INITIAL CLAUSES =============== 7.86/8.14 7.86/8.14 ============================== PREDICATE ELIMINATION ================= 7.86/8.14 7.86/8.14 ============================== end predicate elimination ============= 7.86/8.14 7.86/8.14 Auto_denials: (non-Horn, no changes). 7.86/8.14 7.86/8.14 Term ordering decisions: 7.86/8.14 Function symbol KB weights: tyop_2Emin_2Ebool=1. c_2Ebool_2ET_2E0=1. c_2Equotient_2EQUOTIENT_2E0=1. c_2Ebool_2EF_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_2Equotient_2E_2D_2D_3E_2E0=1. c_2Ecombin_2EW_2E0=1. c_2Emin_2E_3D_2E0=1. c_2Equotient_2E_3D_3D_3D_3E_2E0=1. c_2Equotient_2Erespects_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. c_2Ebool_2E_7E_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. tyop_2Emin_2Efun=1. s=1. app_2E2=1. c_2Equotient_2E_2D_2D_3E_2E2=1. c_2Equotient_2E_3D_3D_3D_3E_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_2Equotient_2Erespects_2E2=1. c_2Ecombin_2EW_2E2=1. c_2Emin_2E_3D_2E2=1. f2=1. f3=1. c_2Ebool_2E_21_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Ebool_2E_7E_2E1=1. c_2Equotient_2EQUOTIENT_2E3=1. c_2Equotient_2E_2D_2D_3E_2E3=1. c_2Equotient_2E_3D_3D_3D_3E_2E4=1. f1=1. 7.86/8.14 7.86/8.14 ============================== end of process initial clauses ======== 7.86/8.14 7.86/8.14 ============================== CLAUSES FOR SEARCH ==================== 7.86/8.14 7.86/8.14 ============================== end of clauses for search ============= 7.86/8.14 7.86/8.14 ============================== SEARCH ================================ 7.86/8.14 7.86/8.14 % Starting search at 0.02 seconds. 7.86/8.14 7.86/8.14 Low Water (keep): wt=157.000, iters=3355 7.86/8.14 7.86/8.14 Low Water (keep): wt=132.000, iters=3390 7.86/8.14 7.86/8.14 Low Water (keep): wt=131.000, iters=3388 7.86/8.14 7.86/8.14 Low Water (keep): wt=123.000, iters=3341 7.86/8.14 7.86/8.14 Low Water (keep): wt=121.000, iters=3424 7.86/8.14 7.86/8.14 Low Water (keep): wt=118.000, iters=3451 7.86/8.14 7.86/8.14 Low Water (keep): wt=112.000, iters=3375 7.86/8.14 7.86/8.14 Low Water (keep): wt=108.000, iters=3580 7.86/8.14 7.86/8.14 Low Water (keep): wt=107.000, iters=3541 7.86/8.14 7.86/8.14 Low Water (keep): wt=100.000, iters=3343 7.86/8.14 7.86/8.14 Low Water (keep): wt=97.000, iters=3345 7.86/8.14 7.86/8.14 Low Water (keep): wt=96.000, iters=3371 7.86/8.14 7.86/8.14 Low Water (keep): wt=95.000, iters=3541 7.86/8.14 7.86/8.14 Low Water (keep): wt=93.000, iters=3345 7.86/8.14 7.86/8.14 Low Water (keep): wt=92.000, iters=3358 7.86/8.14 7.86/8.14 Low Water (keep): wt=89.000, iters=3542 7.86/8.14 7.86/8.14 Low Water (keep): wt=88.000, iters=3495 7.86/8.14 7.86/8.14 Low Water (keep): wt=87.000, iters=3420 7.86/8.14 7.86/8.14 Low Water (keep): wt=84.000, iters=3380 7.86/8.14 7.86/8.14 Low Water (keep): wt=83.000, iters=3499 7.86/8.14 7.86/8.14 Low Water (keep): wt=78.000, iters=3353 7.86/8.14 7.86/8.14 Low Water (keep): wt=75.000, iters=3364 7.86/8.14 7.86/8.14 Low Water (keep): wt=71.000, iters=3358 7.86/8.14 7.86/8.14 Low Water (keep): wt=70.000, iters=3479 7.86/8.14 7.86/8.14 Low Water (keep): wt=68.000, iters=3405 7.86/8.14 7.86/8.14 Low Water (keep): wt=67.000, iters=3364 7.86/8.14 7.86/8.14 Low Water (keep): wt=66.000, iters=3340 7.86/8.14 7.86/8.14 Low Water (keep): wt=65.000, iters=3426 7.86/8.14 7.86/8.14 Low Water (keep): wt=64.000, iters=3503 7.86/8.14 7.86/8.14 Low Water (keep): wt=62.000, iters=3514 7.86/8.14 7.86/8.14 Low Water (keep): wt=57.000, iters=3366 7.86/8.14 7.86/8.14 Low Water (keep): wt=56.000, iters=3393 7.86/8.14 7.86/8.14 Low Water (keep): wt=53.000, iters=3335 7.86/8.14 7.86/8.14 Low Water (keep): wt=52.000, iters=3373 7.86/8.14 7.86/8.14 Low Water (keep): wt=50.000, iters=3352 7.86/8.14 7.86/8.14 Low Water (keep): wt=49.000, iters=3366 7.86/8.14 7.86/8.14 Low Water (keep): wt=46.000, iters=3349 7.86/8.14 7.86/8.14 Low Water (keep): wt=45.000, iters=3526 7.86/8.14 7.86/8.14 Low Water (keep): wt=44.000, iters=3463 7.86/8.14 7.86/8.14 Low Water (keep): wt=43.000, iters=3351 7.86/8.14 7.86/8.14 Low Water (keep): wt=41.000, iters=3349 7.86/8.14 7.86/8.14 Low Water (keep): wt=40.000, iters=3352 7.86/8.14 7.86/8.14 Low Water (displace): id=3646, wt=199.000 7.86/8.14 7.86/8.14 Low Water (displace): id=1551, wt=198.000 7.86/8.14 7.86/8.14 Low Water (keep): wt=39.000, iters=3351 7.86/8.14 7.86/8.14 Low Water (displace): id=8390, wt=197.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8367, wt=196.000 7.86/8.14 7.86/8.14 Low Water (displace): id=6252, wt=195.000 7.86/8.14 7.86/8.14 Low Water (displace): id=10459, wt=194.000 7.86/8.14 7.86/8.14 Low Water (displace): id=10449, wt=193.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8246, wt=192.000 7.86/8.14 7.86/8.14 Low Water (keep): wt=38.000, iters=3341 7.86/8.14 7.86/8.14 Low Water (displace): id=8276, wt=191.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8304, wt=190.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8244, wt=189.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8218, wt=188.000 7.86/8.14 7.86/8.14 Low Water (displace): id=4129, wt=187.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8343, wt=186.000 7.86/8.14 7.86/8.14 Low Water (displace): id=7008, wt=185.000 7.86/8.14 7.86/8.14 Low Water (displace): id=8290, wt=184.000 7.86/8.14 7.86/8.14 Low Water (displace): id=10727, wt=183.000 7.86/8.14 7.86/8.14 Low Water (displace): id=10725, wt=182.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10717, wt=181.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8158, wt=180.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10774, wt=179.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10407, wt=178.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10762, wt=177.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10580, wt=176.000 94.83/95.17 94.83/95.17 Low Water (displace): id=7405, wt=175.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10750, wt=174.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8645, wt=173.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10704, wt=172.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10703, wt=171.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10696, wt=170.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10695, wt=169.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8334, wt=168.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10688, wt=167.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10687, wt=166.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10493, wt=165.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8647, wt=164.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10590, wt=163.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10594, wt=162.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10585, wt=161.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10430, wt=160.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8289, wt=159.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10582, wt=158.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8615, wt=157.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10773, wt=156.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10406, wt=155.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10761, wt=154.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10732, wt=153.000 94.83/95.17 94.83/95.17 Low Water (displace): id=11518, wt=152.000 94.83/95.17 94.83/95.17 Low Water (keep): wt=37.000, iters=3340 94.83/95.17 94.83/95.17 Low Water (keep): wt=36.000, iters=3342 94.83/95.17 94.83/95.17 Low Water (displace): id=10749, wt=151.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10596, wt=150.000 94.83/95.17 94.83/95.17 Low Water (displace): id=12208, wt=149.000 94.83/95.17 94.83/95.17 Low Water (displace): id=12673, wt=148.000 94.83/95.17 94.83/95.17 Low Water (displace): id=7952, wt=147.000 94.83/95.17 94.83/95.17 Low Water (displace): id=12974, wt=146.000 94.83/95.17 94.83/95.17 Low Water (keep): wt=35.000, iters=3371 94.83/95.17 94.83/95.17 Low Water (displace): id=12768, wt=145.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10504, wt=144.000 94.83/95.17 94.83/95.17 Low Water (displace): id=12216, wt=143.000 94.83/95.17 94.83/95.17 Low Water (displace): id=10776, wt=142.000 94.83/95.17 94.83/95.17 Low Water (displace): id=8171, wt=141.000 94.83/95.17 94.83/95.17 Low Water (displace): id=13700, wt=140.000 94.83/95.17 94.83/95.17 Low Water (displace): id=13946, wt=33.000 94.83/95.17 94.83/95.17 Low Water (keep): wt=34.000, iters=3403 94.83/95.17 94.83/95.17 Low Water (keep): wt=33.000, iters=3336 94.83/95.17 94.83/95.17 Low Water (displace): id=14624, wt=32.000 94.83/95.17 94.83/95.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 101 (0.00 of 14.07 sec). 94.83/95.17 94.83/95.17 Low Water (keep): wt=32.000, iters=3370 94.83/95.17 94.83/95.17 Low Water (displace): id=16323, wt=31.000 94.83/95.17 94.83/95.17 Low Water (displace): id=16355, wt=30.000 94.83/95.17 94.83/95.17 Low Water (displace): id=19549, wt=29.000 94.83/95.17 94.83/95.17 Low Water (keep): wt=31.000, iters=3334 94.83/95.17 94.83/95.17 Low Water (keep): wt=30.000, iters=3334 94.83/95.17 94.83/95.17 Low Water (displace): id=31391, wt=28.000 94.83/95.17 94.83/95.17 Low Water (displace): id=36508, wt=27.000 94.83/95.17 94.83/95.17 Low Water (keep): wt=29.000, iters=3336 94.83/95.17 94.83/95.17 ============================== STATISTICS ============================ 94.83/95.17 94.83/95.17 Given=1097. Generated=617076. Kept=117418. proofs=0. 94.83/95.17 Usable=844. Sos=10000. Demods=106. Limbo=85, Disabled=106563. Hints=0. 94.83/95.17 Kept_by_rule=0, Deleted_by_rule=114174. 94.83/95.17 Forward_subsumed=165397. Back_subsumed=153. 94.83/95.17 Sos_limit_deleted=220087. Sos_displaced=100681. Sos_removed=0. 94.83/95.17 New_demodulators=212 (0 lex), Back_demodulated=5654. Back_unit_deleted=1. 94.83/95.17 Demod_attempts=61620615. Demod_rewrites=250128. 94.83/95.17 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 94.83/95.17 Nonunit_fsub_feature_tests=457876. Nonunit_bsub_feature_tests=42046. 94.83/95.17 Megabytes=419.43. 94.83/95.17 User_CPU=93.41, System_CPU=0.62, Wall_clock=94. 94.83/95.17 94.83/95.17 Megs malloced by palloc(): 400. 94.83/95.17 type (bytes each) gets frees in use bytes 94.83/95.17 chunk ( 104) 3234 3234 0 0.0 K 94.83/95.17 string_buf ( 8) 2737 2737 0 0.0 K 94.83/95.17 token ( 20) 7141 7141 0 0.0 K 94.83/95.17 pterm ( 16) 4763 4763 0 0.0 K 94.83/95.17 hashtab ( 8) 40 40 0 0.0 K 94.83/95.17 hashnode ( 8) 138 138 0 0.0 K 94.83/95.17 term ( 20) 105870814 91912338 13958476 272626.5 K 94.83/95.17 term arg arrays: 59489.0 K 94.83/95.17 attribute ( 12) 378 10 368 4.3 K 94.83/95.17 ilist ( 8) 481938619 481165662 772957 6038.7 K 94.83/95.17 plist ( 8) 14181929 14051379 130550 1019.9 K 94.83/95.17 i2list ( 12) 7455516 7455516 0 0.0 K 94.83/95.18 just ( 12) 909865 778600 131265 1538.3 K 94.83/95.18 parajust ( 16) 430382 420700 9682 151.3 K 94.83/95.18 instancejust ( 8) 0 0 0 0.0 K 94.83/95.18 ivyjust ( 24) 0 0 0 0.0 K 94.83/95.18 formula ( 28) 2133 1503 630 17.2 K 94.83/95.18 formula arg arrays: 2.1 K 94.83/95.18 topform ( 52) 617190 499658 117532 5968.4 K 94.83/95.18 clist_pos ( 20) 342697 225099 117598 2296.8 K 94.83/95.18 clist ( 16) 8 1 7 0.1 K 94.83/95.18 context ( 808) 3763942 3763942 0 0.0 K 94.83/95.18 trail ( 12) 3370003 3370003 0 0.0 K 94.83/95.18 ac_match_pos (70044) 0 0 0 0.0 K 94.83/95.18 ac_match_free_vars_pos (20020) 94.83/95.18 0 0 0 0.0 K 94.83/95.18 btm_state ( 60) 0 0 0 0.0 K 94.83/95.18 btu_state ( 60) 0 0 0 0.0 K 94.83/95.18 ac_position (285432) 0 0 0 0.0 K 94.83/95.18 fpa_trie ( 20) 1556674 1305692 250982 4902.0 K 94.83/95.18 fpa_state ( 28) 2684187 2684187 0 0.0 K 94.83/95.18 fpa_index ( 12) 10 0 10 0.1 K 94.83/95.18 fpa_chunk ( 20) 3560932 3465984 94948 1854.5 K 94.83/95.18 fpa_list ( 16) 1352550 0 1352550 21133.6 K 94.83/95.18 fpa_list chunks: 11875.0 K 94.83/95.18 discrim ( 12) 4981861 4884166 97695 1144.9 K 94.83/95.18 discrim_pos ( 16) 351740 351740 0 0.0 K 94.83/95.18 flat2 ( 32) 28684024 28684024 0 0.0 K 94.83/95.18 flat ( 48) 0 0 0 0.0 K 94.83/95.18 flatterm ( 32) 90012588 90012588 0 0.0 K 94.83/95.18 mindex ( 28) 13 0 13 0.4 K 94.83/95.18 mindex_pos ( 56) 2282107 2282107 0 0.0 K 94.83/95.18 lindex ( 12) 5 0 5 0.1 K 94.83/95.18 clash ( 40) 32444 32444 0 0.0 K 94.83/95.18 di_tree ( 12) 1934861 1088349 846512 9920.1 K 94.83/95.18 avl_node ( 20) 234596 214596 20000 390.6 K 94.83/95.18 94.83/95.18 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 94.83/95.18 List 1, length 44, 0.2 K 94.83/95.18 List 2, length 327, 2.6 K 94.83/95.18 List 3, length 206239, 2416.9 K 94.83/95.18 List 5, length 1413, 27.6 K 94.83/95.18 List 6, length 1, 0.0 K 94.83/95.18 List 7, length 477, 13.0 K 94.83/95.18 List 8, length 11228, 350.9 K 94.83/95.18 List 9, length 6, 0.2 K 94.83/95.18 List 10, length 5, 0.2 K 94.83/95.18 List 13, length 1, 0.1 K 94.83/95.18 List 14, length 4, 0.2 K 94.83/95.18 List 16, length 11923, 745.2 K 94.83/95.18 List 26, length 240, 24.4 K 94.83/95.18 List 32, length 6454, 806.8 K 94.83/95.18 List 64, length 7390, 1847.5 K 94.83/95.18 List 128, length 5250, 2625.0 K 94.83/95.18 List 202, length 5, 3.9 K 94.83/95.18 List 256, length 863, 863.0 K 94.83/95.18 94.83/95.18 ============================== SELECTOR REPORT ======================= 94.83/95.18 Sos_deleted=220087, Sos_displaced=100681, Sos_size=10000 94.83/95.18 SELECTOR PART PRIORITY ORDER SIZE SELECTED 94.83/95.18 I 2147483647 high age 0 70 94.83/95.18 H 1 high weight 0 0 94.83/95.18 A 1 low age 10000 115 94.83/95.18 F 4 low weight 2201 456 94.83/95.18 T 4 low weight 7799 456 94.83/95.18 ============================== end of selector report ================ 94.83/95.18 94.83/95.18 ============================== end of statistics ===================== 94.83/95.18 94.83/95.18 Exiting with failure. 94.83/95.18 94.83/95.18 Process 18310 exit (max_megs) Tue Jul 13 15:34:23 2021 94.83/95.18 Prover9 interrupted 94.83/95.18 EOF