TSTP Solution File: ITP004+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ITP004+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 00:21:15 EDT 2022
% Result : Theorem 1.15s 1.43s
% Output : Refutation 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP004+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 3 00:05:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.77/1.02 ============================== Prover9 ===============================
% 0.77/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.02 Process 24876 was started by sandbox2 on n017.cluster.edu,
% 0.77/1.02 Fri Jun 3 00:05:29 2022
% 0.77/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24723_n017.cluster.edu".
% 0.77/1.02 ============================== end of head ===========================
% 0.77/1.02
% 0.77/1.02 ============================== INPUT =================================
% 0.77/1.02
% 0.77/1.02 % Reading from file /tmp/Prover9_24723_n017.cluster.edu
% 0.77/1.02
% 0.77/1.02 set(prolog_style_variables).
% 0.77/1.02 set(auto2).
% 0.77/1.02 % set(auto2) -> set(auto).
% 0.77/1.02 % set(auto) -> set(auto_inference).
% 0.77/1.02 % set(auto) -> set(auto_setup).
% 0.77/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.02 % set(auto) -> set(auto_limits).
% 0.77/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.02 % set(auto) -> set(auto_denials).
% 0.77/1.02 % set(auto) -> set(auto_process).
% 0.77/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.02 % set(auto2) -> assign(stats, some).
% 0.77/1.02 % set(auto2) -> clear(echo_input).
% 0.77/1.02 % set(auto2) -> set(quiet).
% 0.77/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.02 % set(auto2) -> clear(print_given).
% 0.77/1.02 assign(lrs_ticks,-1).
% 0.77/1.02 assign(sos_limit,10000).
% 0.77/1.02 assign(order,kbo).
% 0.77/1.02 set(lex_order_vars).
% 0.77/1.02 clear(print_given).
% 0.77/1.02
% 0.77/1.02 % formulas(sos). % not echoed (31 formulas)
% 0.77/1.02
% 0.77/1.02 ============================== end of input ==========================
% 0.77/1.02
% 0.77/1.02 % From the command line: assign(max_seconds, 300).
% 0.77/1.02
% 0.77/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.02
% 0.77/1.02 % Formulas that are not ordinary clauses:
% 0.77/1.02 1 (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].
% 0.77/1.02 2 (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].
% 0.77/1.02 3 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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].
% 0.77/1.02 4 (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].
% 0.77/1.02 5 (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].
% 0.77/1.02 6 (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_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))) = 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)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 7 (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].
% 0.77/1.02 8 (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].
% 0.77/1.02 9 (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].
% 0.77/1.02 10 (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].
% 0.77/1.02 11 (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,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 12 (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].
% 0.77/1.02 13 (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].
% 0.77/1.02 14 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 15 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_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].
% 0.77/1.02 16 (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].
% 0.77/1.02 17 (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].
% 0.77/1.02 18 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X0_2E0) = s(A_27a,X1_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 19 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 20 (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].
% 0.77/1.02 21 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 22 (all A_27a all X0_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 23 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 24 (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].
% 0.77/1.02 25 (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].
% 0.77/1.02 26 (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].
% 1.15/1.43 27 (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,V1x_2E0) != s(A_27a,V2y_2E0))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption].
% 1.15/1.43 28 (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].
% 1.15/1.43 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].
% 1.15/1.43
% 1.15/1.43 ============================== end of process non-clausal formulas ===
% 1.15/1.43
% 1.15/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.15/1.43
% 1.15/1.43 ============================== PREDICATE ELIMINATION =================
% 1.15/1.43
% 1.15/1.43 ============================== end predicate elimination =============
% 1.15/1.43
% 1.15/1.43 Auto_denials: (non-Horn, no changes).
% 1.15/1.43
% 1.15/1.43 Term ordering decisions:
% 1.15/1.43 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. f2=1. f3=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. f4=1. f1=1.
% 1.15/1.43
% 1.15/1.43 ============================== end of process initial clauses ========
% 1.15/1.43
% 1.15/1.43 ============================== CLAUSES FOR SEARCH ====================
% 1.15/1.43
% 1.15/1.43 ============================== end of clauses for search =============
% 1.15/1.43
% 1.15/1.43 ============================== SEARCH ================================
% 1.15/1.43
% 1.15/1.43 % Starting search at 0.02 seconds.
% 1.15/1.43
% 1.15/1.43 ============================== PROOF =================================
% 1.15/1.43 % SZS status Theorem
% 1.15/1.43 % SZS output start Refutation
% 1.15/1.43
% 1.15/1.43 % Proof 1 at 0.41 (+ 0.01) seconds.
% 1.15/1.43 % Length of proof is 18.
% 1.15/1.43 % Level of proof is 5.
% 1.15/1.43 % Maximum clause weight is 32.000.
% 1.15/1.43 % Given clauses 132.
% 1.15/1.43
% 1.15/1.43 2 (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].
% 1.15/1.43 26 (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].
% 1.15/1.43 27 (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,V1x_2E0) != s(A_27a,V2y_2E0))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption].
% 1.15/1.43 28 (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].
% 1.15/1.43 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].
% 1.15/1.43 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(2)].
% 1.15/1.43 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,f4(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),B)))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom). [clausify(26)].
% 1.15/1.43 47 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(28)].
% 1.15/1.43 58 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(reserved_2Eho_2Enotfalse) # label(axiom). [assumption].
% 1.15/1.43 61 -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)].
% 1.15/1.43 85 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,f4(A,B,C)),s(tyop_2Emin_2Efun(A,tyop_2Emin_2Ebool),C)))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom). [clausify(26)].
% 1.15/1.43 89 -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(27)].
% 1.15/1.43 203 p(s(tyop_2Emin_2Ebool,A)) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,A). [resolve(58,a,35,b)].
% 1.15/1.43 541 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f4(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(85,a,61,a)].
% 1.15/1.43 1780 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(203,a,61,a),flip(a)].
% 1.15/1.43 1864 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f4(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(89,b,541,a)].
% 1.15/1.43 2060 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(c1,f4(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(47(a,1),1864(a,1,2,2))].
% 1.15/1.43 2128 $F. [resolve(2060,a,46,b),rewrite([1780(18)]),unit_del(a,58)].
% 1.15/1.43
% 1.15/1.43 % SZS output end Refutation
% 1.15/1.43 ============================== end of proof ==========================
% 1.15/1.43
% 1.15/1.43 ============================== STATISTICS ============================
% 1.15/1.43
% 1.15/1.43 Given=132. Generated=8761. Kept=2089. proofs=1.
% 1.15/1.43 Usable=91. Sos=1163. Demods=53. Limbo=1, Disabled=888. Hints=0.
% 1.15/1.43 Megabytes=5.89.
% 1.15/1.43 User_CPU=0.42, System_CPU=0.01, Wall_clock=0.
% 1.15/1.43
% 1.15/1.43 ============================== end of statistics =====================
% 1.15/1.43
% 1.15/1.43 ============================== end of search =========================
% 1.15/1.43
% 1.15/1.43 THEOREM PROVED
% 1.15/1.43 % SZS status Theorem
% 1.15/1.43
% 1.15/1.43 Exiting with 1 proof.
% 1.15/1.43
% 1.15/1.43 Process 24876 exit (max_proofs) Fri Jun 3 00:05:29 2022
% 1.15/1.43 Prover9 interrupted
%------------------------------------------------------------------------------