TSTP Solution File: SWW469+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Thu Jul 21 01:17:04 EDT 2022
% Result : Theorem 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n018.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 : Sat Jun 4 21:05:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.47/1.07 ============================== Prover9 ===============================
% 0.47/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.07 Process 31909 was started by sandbox on n018.cluster.edu,
% 0.47/1.07 Sat Jun 4 21:05:33 2022
% 0.47/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31756_n018.cluster.edu".
% 0.47/1.07 ============================== end of head ===========================
% 0.47/1.07
% 0.47/1.07 ============================== INPUT =================================
% 0.47/1.07
% 0.47/1.07 % Reading from file /tmp/Prover9_31756_n018.cluster.edu
% 0.47/1.07
% 0.47/1.07 set(prolog_style_variables).
% 0.47/1.07 set(auto2).
% 0.47/1.07 % set(auto2) -> set(auto).
% 0.47/1.07 % set(auto) -> set(auto_inference).
% 0.47/1.07 % set(auto) -> set(auto_setup).
% 0.47/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.07 % set(auto) -> set(auto_limits).
% 0.47/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.07 % set(auto) -> set(auto_denials).
% 0.47/1.07 % set(auto) -> set(auto_process).
% 0.47/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.07 % set(auto2) -> assign(stats, some).
% 0.47/1.07 % set(auto2) -> clear(echo_input).
% 0.47/1.07 % set(auto2) -> set(quiet).
% 0.47/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.07 % set(auto2) -> clear(print_given).
% 0.47/1.07 assign(lrs_ticks,-1).
% 0.47/1.07 assign(sos_limit,10000).
% 0.47/1.07 assign(order,kbo).
% 0.47/1.07 set(lex_order_vars).
% 0.47/1.07 clear(print_given).
% 0.47/1.07
% 0.47/1.07 % formulas(sos). % not echoed (63 formulas)
% 0.47/1.07
% 0.47/1.07 ============================== end of input ==========================
% 0.47/1.07
% 0.47/1.07 % From the command line: assign(max_seconds, 300).
% 0.47/1.07
% 0.47/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.07
% 0.47/1.07 % Formulas that are not ordinary clauses:
% 0.47/1.07 1 (all X_a (cl_HOL_Oequal(X_a) -> ti(fun(X_a,fun(X_a,bool)),equal_equal(X_a)) = equal_equal(X_a))) # label(tsy_c_HOL_Oequal__class_Oequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 2 (all X_a ti(fun(X_a,fun(X_a,bool)),induct_equal(X_a)) = induct_equal(X_a)) # label(tsy_c_HOL_Oinduct__equal_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 3 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 4 (all X_a ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),hoare_244953527triple(X_a)) = hoare_244953527triple(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 5 (all X_a ti(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)) = hoare_2037801986triple(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 6 (all X_a ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),hoare_1580379338ep_set(X_a)) = hoare_1580379338ep_set(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 7 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 8 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool))),type_definition(X_a,X_b)) = type_definition(X_a,X_b)) # label(tsy_c_Typedef_Otype__definition_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 9 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 10 (all X_b all X_a all B_1 all B_2 hAPP(X_b,X_a,ti(fun(X_b,X_a),B_1),B_2) = hAPP(X_b,X_a,B_1,B_2)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 11 (all X_b all X_a all B_1 all B_2 hAPP(X_b,X_a,B_1,ti(X_b,B_2)) = hAPP(X_b,X_a,B_1,B_2)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 12 (all X_a all X_b all B_1 all B_2 ti(X_a,hAPP(X_b,X_a,B_1,B_2)) = hAPP(X_b,X_a,B_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 13 (all B_1 (hBOOL(ti(bool,B_1)) <-> hBOOL(B_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.47/1.07 14 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 15 hBOOL(hoare_1883395792gleton) <-> (exists S exists T ti(state,S) != ti(state,T)) # label(fact_0_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 16 (all X_a all X_1 all Y_1 (hBOOL(hAPP(hoare_509422987triple(X_a),bool,hAPP(hoare_509422987triple(X_a),fun(hoare_509422987triple(X_a),bool),equal_equal(hoare_509422987triple(X_a)),X_1),Y_1)) <-> X_1 = Y_1)) # label(fact_1_equal__triple__def) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 17 (all X_a all X_1 all Y_1 (hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1) = hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),Y_1) <-> X_1 = Y_1)) # label(fact_2_Rep__triple__inject) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 18 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_3_equal) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 19 (all X_a (cl_HOL_Oequal(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X),X))))) # label(fact_4_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 20 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_5_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 21 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_6_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 22 (all X_a all X_1 hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)) = X_1) # label(fact_7_Rep__triple__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 23 (all X_a all X_1 hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))) # label(fact_8_Rep__triple) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 24 (all X_a all P all Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> ((all X_2 hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2)))) -> hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,Y_1))))) # label(fact_9_Rep__triple__induct) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 25 (all X_a all Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> -(all X_2 Y_1 != hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2)))) # label(fact_10_Rep__triple__cases) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 26 (all X_a all Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)) = Y_1)) # label(fact_11_Abs__triple__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 27 (all X_a hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool)),type_definition(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)),hoare_244953527triple(X_a)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))) # label(fact_12_type__definition__triple) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 28 (all X_a all Y_1 all X_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),X_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> (hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),X_1) = hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_13_Abs__triple__inject) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 29 (all X_a all X_1 all P ((all Y_2 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))) -> hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2))))) -> hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,X_1)))) # label(fact_14_Abs__triple__induct) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 30 (all X_a all X_1 -(all Y_2 (X_1 = hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2) -> -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))))) # label(fact_15_Abs__triple__cases) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 31 (all X_b all X_a all Y_1 all X_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1)) -> (hAPP(X_b,X_a,Abs,X_1) = hAPP(X_b,X_a,Abs,Y_1) <-> ti(X_b,X_1) = ti(X_b,Y_1)))))) # label(fact_16_type__definition_OAbs__inject) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.07 32 (all X_b all X_a all Y_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1)) -> hAPP(X_a,X_b,Rep,hAPP(X_b,X_a,Abs,Y_1)) = ti(X_b,Y_1)))) # label(fact_17_type__definition_OAbs__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 33 (all X_b all X_a all X_1 all Y_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> (hAPP(X_a,X_b,Rep,X_1) = hAPP(X_a,X_b,Rep,Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1)))) # label(fact_18_type__definition_ORep__inject) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 34 (all X_b all X_a all X_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> hAPP(X_b,X_a,Abs,hAPP(X_a,X_b,Rep,X_1)) = ti(X_a,X_1))) # label(fact_19_type__definition_ORep__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 35 (all X_b all X_a all X_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Rep,X_1)),A_1)))) # label(fact_20_type__definition_ORep) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 36 (all X_b all X_a all Y_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1)) -> -(all X_2 ti(X_b,Y_1) != hAPP(X_a,X_b,Rep,X_2))))) # label(fact_22_type__definition_ORep__cases) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 37 (all X_b all X_a all X_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> -(all Y_2 (ti(X_a,X_1) = hAPP(X_b,X_a,Abs,Y_2) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1)))))) # label(fact_23_type__definition_OAbs__cases) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 38 (all X_b all X_a all X_1 all P all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> ((all Y_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1)) -> hBOOL(hAPP(X_a,bool,P,hAPP(X_b,X_a,Abs,Y_2))))) -> hBOOL(hAPP(X_a,bool,P,X_1))))) # label(fact_24_type__definition_OAbs__induct) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 39 (all X_b all X_a all P all Y_1 all Rep all Abs all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1)) -> ((all X_2 hBOOL(hAPP(X_b,bool,P,hAPP(X_a,X_b,Rep,X_2)))) -> hBOOL(hAPP(X_b,bool,P,Y_1)))))) # label(fact_25_type__definition_ORep__induct) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 40 (all X_a all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),induct_equal(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))) # label(fact_28_induct__equal__def) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 41 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_29_ext) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 42 (all X_a all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_1)))) # label(fact_30_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.08 43 (all X_a all P hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P) = ti(fun(X_a,bool),P)) # label(fact_31_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 44 (all T_2 all T_1_1 (enum(T_1_1) & enum(T_2) -> enum(sum_sum(T_2,T_1_1)))) # label(arity_sum___Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 45 (all T_2 all T_1_1 (enum(T_1_1) & enum(T_2) -> enum(fun(T_2,T_1_1)))) # label(arity_fun___Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 46 (all T_2 all T_1_1 (cl_HOL_Oequal(T_1_1) & enum(T_2) -> cl_HOL_Oequal(fun(T_2,T_1_1)))) # label(arity_fun___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 47 (all T_2 all T_1_1 cl_HOL_Oequal(sum_sum(T_2,T_1_1))) # label(arity_sum___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 48 (all T_1_1 cl_HOL_Oequal(hoare_509422987triple(T_1_1))) # label(arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.09 49 (all T_1 all A ti(T_1,ti(T_1,A)) = ti(T_1,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 50 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 51 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 52 -(all T -(all S ti(state,S) = ti(state,T))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials: (non-Horn, no changes).
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: bool=1. state=1. com=1. hoare_1883395792gleton=1. induct_true=1. induct_false=1. c1=1. c2=1. c3=1. fun=1. sum_sum=1. node=1. ti=1. type_definition=1. f2=1. f4=1. hoare_509422987triple=1. member=1. collect=1. hoare_1580379338ep_set=1. hoare_2037801986triple=1. hoare_244953527triple=1. equal_equal=1. fequal=1. induct_equal=1. undefined=1. f1=1. f3=1. hAPP=1. f9=1. f5=1. f6=1. f7=1. f8=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.04 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.82/1.09 % Length of proof is 17.
% 0.82/1.09 % Level of proof is 7.
% 0.82/1.09 % Maximum clause weight is 7.000.
% 0.82/1.09 % Given clauses 13.
% 0.82/1.09
% 0.82/1.09 3 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 15 hBOOL(hoare_1883395792gleton) <-> (exists S exists T ti(state,S) != ti(state,T)) # label(fact_0_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 52 -(all T -(all S ti(state,S) = ti(state,T))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09 58 hBOOL(hoare_1883395792gleton) # label(conj_0) # label(hypothesis). [assumption].
% 0.82/1.09 64 undefined(A) = ti(A,undefined(A)) # label(tsy_c_HOL_Oundefined_res) # label(axiom). [clausify(3)].
% 0.82/1.09 65 ti(A,undefined(A)) = undefined(A). [copy(64),flip(a)].
% 0.82/1.09 66 ti(state,c3) = ti(state,A) # label(conj_1) # label(negated_conjecture). [clausify(52)].
% 0.82/1.09 100 -hBOOL(hoare_1883395792gleton) | ti(state,c2) != ti(state,c1) # label(fact_0_state__not__singleton__def) # label(axiom). [clausify(15)].
% 0.82/1.09 101 ti(state,c2) != ti(state,c1). [copy(100),unit_del(a,58)].
% 0.82/1.09 147 ti(state,c2) = c_0. [new_symbol(101)].
% 0.82/1.09 150 ti(state,c1) != c_0. [back_rewrite(101),rewrite([147(3)]),flip(a)].
% 0.82/1.09 151 ti(state,c3) = undefined(state). [para(66(a,2),65(a,1))].
% 0.82/1.09 152 ti(state,A) = ti(state,B). [para(66(a,1),66(a,1))].
% 0.82/1.09 153 ti(state,A) = undefined(state). [para(66(a,1),66(a,2)),rewrite([151(3)]),flip(a)].
% 0.82/1.09 154 undefined(state) = c_1. [new_symbol(152),rewrite([153(2)])].
% 0.82/1.09 155 c_1 != c_0. [back_rewrite(150),rewrite([153(3),154(2)])].
% 0.82/1.09 156 $F. [back_rewrite(147),rewrite([153(3),154(2)]),unit_del(a,155)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=13. Generated=99. Kept=83. proofs=1.
% 0.82/1.09 Usable=12. Sos=62. Demods=21. Limbo=3, Disabled=83. Hints=0.
% 0.82/1.09 Megabytes=0.55.
% 0.82/1.09 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 31909 exit (max_proofs) Sat Jun 4 21:05:33 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------