0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n005.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % DateTime : Thu Jul 2 09:22:06 EDT 2020 0.12/0.33 % CPUTime : 0.76/1.03 ============================== Prover9 =============================== 0.76/1.03 Prover9 (32) version 2009-11A, November 2009. 0.76/1.03 Process 19745 was started by sandbox2 on n005.cluster.edu, 0.76/1.03 Thu Jul 2 09:22:06 2020 0.76/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_19592_n005.cluster.edu". 0.76/1.03 ============================== end of head =========================== 0.76/1.03 0.76/1.03 ============================== INPUT ================================= 0.76/1.03 0.76/1.03 % Reading from file /tmp/Prover9_19592_n005.cluster.edu 0.76/1.03 0.76/1.03 set(prolog_style_variables). 0.76/1.03 set(auto2). 0.76/1.03 % set(auto2) -> set(auto). 0.76/1.03 % set(auto) -> set(auto_inference). 0.76/1.03 % set(auto) -> set(auto_setup). 0.76/1.03 % set(auto_setup) -> set(predicate_elim). 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.76/1.03 % set(auto) -> set(auto_limits). 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.76/1.03 % set(auto) -> set(auto_denials). 0.76/1.03 % set(auto) -> set(auto_process). 0.76/1.03 % set(auto2) -> assign(new_constants, 1). 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.76/1.03 % set(auto2) -> assign(max_hours, 1). 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.76/1.03 % set(auto2) -> assign(max_seconds, 0). 0.76/1.03 % set(auto2) -> assign(max_minutes, 5). 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.76/1.03 % set(auto2) -> set(sort_initial_sos). 0.76/1.03 % set(auto2) -> assign(sos_limit, -1). 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.76/1.03 % set(auto2) -> assign(max_megs, 400). 0.76/1.03 % set(auto2) -> assign(stats, some). 0.76/1.03 % set(auto2) -> clear(echo_input). 0.76/1.03 % set(auto2) -> set(quiet). 0.76/1.03 % set(auto2) -> clear(print_initial_clauses). 0.76/1.03 % set(auto2) -> clear(print_given). 0.76/1.03 assign(lrs_ticks,-1). 0.76/1.03 assign(sos_limit,10000). 0.76/1.03 assign(order,kbo). 0.76/1.03 set(lex_order_vars). 0.76/1.03 clear(print_given). 0.76/1.03 0.76/1.03 % formulas(sos). % not echoed (43 formulas) 0.76/1.03 0.76/1.03 ============================== end of input ========================== 0.76/1.03 0.76/1.03 % From the command line: assign(max_seconds, 960). 0.76/1.03 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.76/1.03 0.76/1.03 % Formulas that are not ordinary clauses: 0.76/1.03 1 (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]. 0.76/1.03 2 (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,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 0.76/1.03 3 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 0.76/1.03 4 (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]. 0.76/1.03 5 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 0.76/1.03 6 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # 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]. 0.76/1.03 7 (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]. 0.76/1.03 8 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 0.76/1.03 9 (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,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 0.76/1.03 10 (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),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))) = 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)))) # 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]. 0.76/1.04 11 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (p(s(tyop_2Emin_2Ebool,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) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 12 (all A_27a all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 13 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 14 (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]. 0.76/1.04 15 (all V0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 16 (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]. 0.76/1.04 17 (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]. 0.76/1.04 18 (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]. 0.76/1.04 19 (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]. 0.76/1.04 20 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 21 (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]. 0.76/1.04 22 (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]. 0.76/1.04 23 (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]. 0.76/1.04 24 (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]. 0.76/1.04 25 (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_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]. 0.76/1.04 26 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 27 (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,V3r_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)))) & 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,V4s_2E0))),s(A_27a,V4s_2E0)))))))) # label(thm_2Equotient_2EQUOTIENT__REL) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 28 (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]. 0.76/1.04 29 (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]. 0.76/1.04 30 (all A_27a all A_27b all V0f_2E0 all 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))) = 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)))) # label(thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 31 (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]. 0.76/1.04 32 (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_2Ecombin_2EW_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_2Equotient_2Erespects_2E0)) # label(thm_2Equotient_2Erespects__def) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 33 (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]. 0.76/1.04 34 (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)),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))) = 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)))) # 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]. 0.76/1.04 35 (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]. 0.76/1.04 36 (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]. 0.76/1.04 37 (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]. 0.76/1.04 38 (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]. 0.76/1.04 39 (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,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_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,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 0.76/1.04 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_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))) & 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_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)))))))))) # label(thm_2Equotient_2EFUN__REL__EQ__REL) # label(negated_conjecture) # label(non_clause). [assumption]. 0.76/1.04 0.76/1.04 ============================== end of process non-clausal formulas === 0.76/1.04 0.76/1.04 ============================== PROCESS INITIAL CLAUSES =============== 4.48/4.76 4.48/4.76 ============================== PREDICATE ELIMINATION ================= 4.48/4.76 4.48/4.76 ============================== end predicate elimination ============= 4.48/4.76 4.48/4.76 Auto_denials: (non-Horn, no changes). 4.48/4.76 4.48/4.76 Term ordering decisions: 4.48/4.76 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. f1=1. f2=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. f3=1. 4.48/4.76 4.48/4.76 ============================== end of process initial clauses ======== 4.48/4.76 4.48/4.76 ============================== CLAUSES FOR SEARCH ==================== 4.48/4.76 4.48/4.76 ============================== end of clauses for search ============= 4.48/4.76 4.48/4.76 ============================== SEARCH ================================ 4.48/4.76 4.48/4.76 % Starting search at 0.04 seconds. 4.48/4.76 4.48/4.76 Low Water (keep): wt=157.000, iters=3343 4.48/4.76 4.48/4.76 Low Water (keep): wt=149.000, iters=3353 4.48/4.76 4.48/4.76 Low Water (keep): wt=132.000, iters=3405 4.48/4.76 4.48/4.76 Low Water (keep): wt=131.000, iters=3403 4.48/4.76 4.48/4.76 Low Water (keep): wt=121.000, iters=3340 4.48/4.76 4.48/4.76 Low Water (keep): wt=118.000, iters=3480 4.48/4.76 4.48/4.76 Low Water (keep): wt=112.000, iters=3404 4.48/4.76 4.48/4.76 Low Water (keep): wt=107.000, iters=3334 4.48/4.76 4.48/4.76 Low Water (keep): wt=105.000, iters=3508 4.48/4.76 4.48/4.76 Low Water (keep): wt=102.000, iters=3421 4.48/4.76 4.48/4.76 Low Water (keep): wt=100.000, iters=3376 4.48/4.76 4.48/4.76 Low Water (keep): wt=97.000, iters=3357 4.48/4.76 4.48/4.76 Low Water (keep): wt=96.000, iters=3381 4.48/4.76 4.48/4.76 Low Water (keep): wt=94.000, iters=3409 4.48/4.76 4.48/4.76 Low Water (keep): wt=92.000, iters=3360 4.48/4.76 4.48/4.76 Low Water (keep): wt=90.000, iters=3606 4.48/4.76 4.48/4.76 Low Water (keep): wt=89.000, iters=3542 4.48/4.76 4.48/4.76 Low Water (keep): wt=88.000, iters=3495 4.48/4.76 4.48/4.76 Low Water (keep): wt=87.000, iters=3420 4.48/4.76 4.48/4.76 Low Water (keep): wt=84.000, iters=3380 4.48/4.76 4.48/4.76 Low Water (keep): wt=83.000, iters=3499 4.48/4.76 4.48/4.76 Low Water (keep): wt=78.000, iters=3353 4.48/4.76 4.48/4.76 Low Water (keep): wt=75.000, iters=3364 4.48/4.76 4.48/4.76 Low Water (keep): wt=71.000, iters=3358 4.48/4.76 4.48/4.76 Low Water (keep): wt=70.000, iters=3479 4.48/4.76 4.48/4.76 Low Water (keep): wt=68.000, iters=3405 4.48/4.76 4.48/4.76 Low Water (keep): wt=67.000, iters=3364 4.48/4.76 4.48/4.76 Low Water (keep): wt=66.000, iters=3340 4.48/4.76 4.48/4.76 Low Water (keep): wt=65.000, iters=3426 4.48/4.76 4.48/4.76 Low Water (keep): wt=64.000, iters=3503 4.48/4.76 4.48/4.76 Low Water (keep): wt=62.000, iters=3514 4.48/4.76 4.48/4.76 Low Water (keep): wt=57.000, iters=3366 4.48/4.76 4.48/4.76 Low Water (keep): wt=56.000, iters=3393 4.48/4.76 4.48/4.76 Low Water (keep): wt=53.000, iters=3335 4.48/4.76 4.48/4.76 Low Water (keep): wt=52.000, iters=3366 4.48/4.76 4.48/4.76 Low Water (keep): wt=50.000, iters=3353 4.48/4.76 4.48/4.76 Low Water (keep): wt=49.000, iters=3344 4.48/4.76 4.48/4.76 Low Water (keep): wt=46.000, iters=3350 4.48/4.76 4.48/4.76 Low Water (keep): wt=44.000, iters=3412 4.48/4.76 4.48/4.76 Low Water (keep): wt=43.000, iters=3352 4.48/4.76 4.48/4.76 Low Water (keep): wt=41.000, iters=3350 4.48/4.76 4.48/4.76 Low Water (keep): wt=40.000, iters=3353 4.48/4.76 4.48/4.76 Low Water (displace): id=3650, wt=199.000 4.48/4.76 4.48/4.76 Low Water (displace): id=1553, wt=198.000 4.48/4.76 4.48/4.76 Low Water (keep): wt=39.000, iters=3349 4.48/4.76 4.48/4.76 Low Water (displace): id=8391, wt=197.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8369, wt=196.000 4.48/4.76 4.48/4.76 Low Water (displace): id=5854, wt=195.000 4.48/4.76 4.48/4.76 Low Water (displace): id=10478, wt=194.000 4.48/4.76 4.48/4.76 Low Water (displace): id=10468, wt=193.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8243, wt=192.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8271, wt=191.000 4.48/4.76 4.48/4.76 Low Water (keep): wt=38.000, iters=3342 4.48/4.76 4.48/4.76 Low Water (displace): id=8300, wt=190.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8239, wt=189.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8213, wt=188.000 4.48/4.76 4.48/4.76 Low Water (displace): id=4122, wt=187.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8345, wt=186.000 4.48/4.76 4.48/4.76 Low Water (displace): id=7014, wt=185.000 4.48/4.76 4.48/4.76 Low Water (displace): id=8285, wt=184.000 4.48/4.76 4.48/4.76 Low Water (displace): id=10746, wt=183.000 4.48/4.76 4.48/4.76 Low Water (displace): id=10744, wt=182.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10736, wt=181.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8155, wt=180.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10793, wt=179.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10426, wt=178.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10781, wt=177.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10600, wt=176.000 72.79/73.06 72.79/73.06 Low Water (displace): id=7417, wt=175.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10769, wt=174.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8669, wt=173.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10723, wt=172.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10722, wt=171.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10714, wt=170.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10715, wt=169.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8332, wt=168.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10706, wt=167.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10707, wt=166.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10512, wt=165.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8671, wt=164.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10608, wt=163.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10614, wt=162.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10605, wt=161.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10449, wt=160.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8287, wt=159.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10601, wt=158.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8637, wt=157.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10792, wt=156.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10424, wt=155.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10779, wt=154.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10751, wt=153.000 72.79/73.06 72.79/73.06 Low Water (displace): id=11538, wt=152.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=37.000, iters=3340 72.79/73.06 72.79/73.06 Low Water (keep): wt=36.000, iters=3342 72.79/73.06 72.79/73.06 Low Water (displace): id=10767, wt=151.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10615, wt=150.000 72.79/73.06 72.79/73.06 Low Water (displace): id=12228, wt=149.000 72.79/73.06 72.79/73.06 Low Water (displace): id=12693, wt=148.000 72.79/73.06 72.79/73.06 Low Water (displace): id=7967, wt=147.000 72.79/73.06 72.79/73.06 Low Water (displace): id=12237, wt=146.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=35.000, iters=3371 72.79/73.06 72.79/73.06 Low Water (displace): id=12788, wt=145.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10523, wt=144.000 72.79/73.06 72.79/73.06 Low Water (displace): id=12236, wt=143.000 72.79/73.06 72.79/73.06 Low Water (displace): id=10795, wt=142.000 72.79/73.06 72.79/73.06 Low Water (displace): id=8167, wt=141.000 72.79/73.06 72.79/73.06 Low Water (displace): id=13704, wt=140.000 72.79/73.06 72.79/73.06 Low Water (displace): id=13939, wt=33.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=34.000, iters=3393 72.79/73.06 72.79/73.06 Low Water (keep): wt=33.000, iters=3336 72.79/73.06 72.79/73.06 Low Water (displace): id=15218, wt=32.000 72.79/73.06 72.79/73.06 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 103 (0.00 of 7.31 sec). 72.79/73.06 72.79/73.06 Low Water (keep): wt=32.000, iters=3340 72.79/73.06 72.79/73.06 Low Water (displace): id=15857, wt=31.000 72.79/73.06 72.79/73.06 Low Water (displace): id=15997, wt=30.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=31.000, iters=3343 72.79/73.06 72.79/73.06 Low Water (displace): id=19593, wt=29.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=30.000, iters=3340 72.79/73.06 72.79/73.06 Low Water (displace): id=31403, wt=28.000 72.79/73.06 72.79/73.06 Low Water (displace): id=38324, wt=27.000 72.79/73.06 72.79/73.06 Low Water (keep): wt=29.000, iters=3333 72.79/73.06 72.79/73.06 ============================== STATISTICS ============================ 72.79/73.06 72.79/73.06 Given=1099. Generated=619347. Kept=116843. proofs=0. 72.79/73.06 Usable=848. Sos=9999. Demods=106. Limbo=344, Disabled=105726. Hints=0. 72.79/73.06 Kept_by_rule=0, Deleted_by_rule=114287. 72.79/73.06 Forward_subsumed=166166. Back_subsumed=152. 72.79/73.06 Sos_limit_deleted=222051. Sos_displaced=99781. Sos_removed=0. 72.79/73.06 New_demodulators=206 (0 lex), Back_demodulated=5718. Back_unit_deleted=1. 72.79/73.06 Demod_attempts=62059816. Demod_rewrites=248287. 72.79/73.06 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 72.79/73.06 Nonunit_fsub_feature_tests=453452. Nonunit_bsub_feature_tests=41752. 72.79/73.06 Megabytes=419.43. 72.79/73.06 User_CPU=71.55, System_CPU=0.48, Wall_clock=72. 72.79/73.06 72.79/73.06 Megs malloced by palloc(): 400. 72.79/73.06 type (bytes each) gets frees in use bytes 72.79/73.06 chunk ( 104) 3234 3234 0 0.0 K 72.79/73.06 string_buf ( 8) 2737 2737 0 0.0 K 72.79/73.06 token ( 20) 7141 7141 0 0.0 K 72.79/73.06 pterm ( 16) 4763 4763 0 0.0 K 72.79/73.06 hashtab ( 8) 40 40 0 0.0 K 72.79/73.06 hashnode ( 8) 138 138 0 0.0 K 72.79/73.06 term ( 20) 106362428 92419393 13943035 272324.9 K 72.79/73.06 term arg arrays: 59313.0 K 72.79/73.06 attribute ( 12) 370 10 360 4.2 K 72.79/73.06 ilist ( 8) 479513421 478743465 769956 6015.3 K 72.79/73.06 plist ( 8) 14097697 13967462 130235 1017.5 K 72.79/73.06 i2list ( 12) 7447359 7447359 0 0.0 K 72.79/73.06 just ( 12) 911822 781025 130797 1532.8 K 72.79/73.06 parajust ( 16) 429060 419373 9687 151.4 K 72.79/73.06 instancejust ( 8) 0 0 0 0.0 K 72.79/73.06 ivyjust ( 24) 0 0 0 0.0 K 72.79/73.06 formula ( 28) 2125 1495 630 17.2 K 72.79/73.06 formula arg arrays: 2.1 K 72.79/73.06 topform ( 52) 619462 502504 116958 5939.3 K 72.79/73.06 clist_pos ( 20) 340447 223424 117023 2285.6 K 72.79/73.06 clist ( 16) 8 1 7 0.1 K 72.79/73.06 context ( 808) 3767145 3767142 3 2.4 K 72.79/73.06 trail ( 12) 3360009 3360007 2 0.0 K 72.79/73.06 ac_match_pos (70044) 0 0 0 0.0 K 72.79/73.06 ac_match_free_vars_pos (20020) 72.79/73.06 0 0 0 0.0 K 72.79/73.06 btm_state ( 60) 0 0 0 0.0 K 72.79/73.06 btu_state ( 60) 0 0 0 0.0 K 72.79/73.06 ac_position (285432) 0 0 0 0.0 K 72.79/73.06 fpa_trie ( 20) 1622110 1370249 251861 4919.2 K 72.79/73.06 fpa_state ( 28) 2715497 2715482 15 0.4 K 72.79/73.06 fpa_index ( 12) 10 0 10 0.1 K 72.79/73.06 fpa_chunk ( 20) 3649570 3554678 94892 1853.4 K 72.79/73.06 fpa_list ( 16) 1417406 0 1417406 22147.0 K 72.79/73.06 fpa_list chunks: 11760.4 K 72.79/73.06 discrim ( 12) 5004712 4898190 106522 1248.3 K 72.79/73.06 discrim_pos ( 16) 351316 351316 0 0.0 K 72.79/73.06 flat2 ( 32) 28919647 28919647 0 0.0 K 72.79/73.06 flat ( 48) 0 0 0 0.0 K 72.79/73.06 flatterm ( 32) 90442607 90442607 0 0.0 K 72.79/73.06 mindex ( 28) 13 0 13 0.4 K 72.79/73.06 mindex_pos ( 56) 2282140 2282138 2 0.1 K 72.79/73.06 lindex ( 12) 5 0 5 0.1 K 72.79/73.06 clash ( 40) 31899 31896 3 0.1 K 72.79/73.06 di_tree ( 12) 1934792 1089746 845046 9902.9 K 72.79/73.06 avl_node ( 20) 232928 212930 19998 390.6 K 72.79/73.06 72.79/73.06 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 72.79/73.06 List 1, length 44, 0.2 K 72.79/73.06 List 2, length 203, 1.6 K 72.79/73.06 List 3, length 194556, 2280.0 K 72.79/73.06 List 8, length 11095, 346.7 K 72.79/73.06 List 9, length 6, 0.2 K 72.79/73.06 List 10, length 2, 0.1 K 72.79/73.06 List 14, length 1, 0.1 K 72.79/73.06 List 16, length 12089, 755.6 K 72.79/73.06 List 26, length 240, 24.4 K 72.79/73.06 List 32, length 6872, 859.0 K 72.79/73.06 List 64, length 7191, 1797.8 K 72.79/73.06 List 128, length 4831, 2415.5 K 72.79/73.06 List 202, length 2, 1.6 K 72.79/73.06 List 256, length 777, 777.0 K 72.79/73.06 72.79/73.06 ============================== SELECTOR REPORT ======================= 72.79/73.06 Sos_deleted=222051, Sos_displaced=99781, Sos_size=9999 72.79/73.06 SELECTOR PART PRIORITY ORDER SIZE SELECTED 72.79/73.06 I 2147483647 high age 0 70 72.79/73.06 H 1 high weight 0 0 72.79/73.06 A 1 low age 9999 115 72.79/73.06 F 4 low weight 2184 458 72.79/73.06 T 4 low weight 7815 456 72.79/73.06 ============================== end of selector report ================ 72.79/73.06 72.79/73.06 ============================== end of statistics ===================== 72.79/73.06 72.79/73.06 Exiting with failure. 72.79/73.06 72.79/73.06 Process 19745 exit (max_megs) Thu Jul 2 09:23:18 2020 72.79/73.06 Prover9 interrupted 72.79/73.07 EOF