TSTP Solution File: ITP001+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ITP001+5 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 00:21:12 EDT 2022
% Result : Theorem 0.67s 0.96s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP001+5 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sat Jun 4 01:51:47 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.67/0.95 ============================== Prover9 ===============================
% 0.67/0.95 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.95 Process 23132 was started by sandbox2 on n032.cluster.edu,
% 0.67/0.95 Sat Jun 4 01:51:47 2022
% 0.67/0.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22978_n032.cluster.edu".
% 0.67/0.95 ============================== end of head ===========================
% 0.67/0.95
% 0.67/0.95 ============================== INPUT =================================
% 0.67/0.95
% 0.67/0.95 % Reading from file /tmp/Prover9_22978_n032.cluster.edu
% 0.67/0.95
% 0.67/0.95 set(prolog_style_variables).
% 0.67/0.95 set(auto2).
% 0.67/0.95 % set(auto2) -> set(auto).
% 0.67/0.95 % set(auto) -> set(auto_inference).
% 0.67/0.95 % set(auto) -> set(auto_setup).
% 0.67/0.95 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.95 % set(auto) -> set(auto_limits).
% 0.67/0.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.95 % set(auto) -> set(auto_denials).
% 0.67/0.95 % set(auto) -> set(auto_process).
% 0.67/0.95 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.95 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.95 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.95 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.95 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.95 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.95 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.95 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.95 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.95 % set(auto2) -> assign(stats, some).
% 0.67/0.95 % set(auto2) -> clear(echo_input).
% 0.67/0.95 % set(auto2) -> set(quiet).
% 0.67/0.95 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.95 % set(auto2) -> clear(print_given).
% 0.67/0.95 assign(lrs_ticks,-1).
% 0.67/0.95 assign(sos_limit,10000).
% 0.67/0.95 assign(order,kbo).
% 0.67/0.95 set(lex_order_vars).
% 0.67/0.95 clear(print_given).
% 0.67/0.95
% 0.67/0.95 % formulas(sos). % not echoed (118 formulas)
% 0.67/0.95
% 0.67/0.95 ============================== end of input ==========================
% 0.67/0.95
% 0.67/0.95 % From the command line: assign(max_seconds, 300).
% 0.67/0.95
% 0.67/0.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.95
% 0.67/0.95 % Formulas that are not ordinary clauses:
% 0.67/0.95 1 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 2 (all A all B all F (mem(F,arr(A,B)) -> (all X (mem(X,A) -> mem(ap(F,X),B))))) # label(ap_tp) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 3 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) <-> p(R)) -> Q = R))))) # label(boolext) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 4 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(F,X) = ap(G,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 5 (all A all Y all X (mem(X,A) -> ap(k(A,Y),X) = Y)) # label(kbeta) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 6 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 7 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Emin_2E_3D) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 8 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> X = Y))))))) # label(ax_eq_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 9 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <-> (p(Q) -> p(R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 10 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Emin_2E_40) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 11 (all A0 (ne(A0) -> ne(ty_2Ebool_2Eitself(A0)))) # label(ne_ty_2Ebool_2Eitself) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 12 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_21) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 13 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_21(A),Q)) <-> (all X (mem(X,A) -> p(ap(Q,X))))))))) # label(ax_all_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 14 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <-> p(Q) & p(R)))))) # label(ax_and_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 15 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 16 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_3F(A),Q)) <-> (exists X (mem(X,A) & p(ap(Q,X))))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 17 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F_21) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 18 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EARB(A_27a),A_27a))) # label(mem_c_2Ebool_2EARB) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 19 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))))) # label(mem_c_2Ebool_2ECOND) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 20 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)))) # label(mem_c_2Ebool_2EDATATYPE) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 21 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2EIN) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 22 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2ELET) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 23 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONE__ONE) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONTO) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 25 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))))))) # label(mem_c_2Ebool_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 26 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 27 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 28 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 29 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))))) # label(mem_c_2Ebool_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 30 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))))))) # label(mem_c_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 31 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(Q) | p(R)))))) # label(ax_or_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 32 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))))))) # label(mem_c_2Ebool_2Eitself__case) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 33 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2Eliteral__case) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 34 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)))) # label(mem_c_2Ebool_2Ethe__value) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 35 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 36 $T <-> i(bool) = i(bool) # label(ax_thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 37 (all A_27a all V0P ap(f1(A_27a),V0P) = ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET))) # label(lameq_f1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 38 (all A_27a (ne(A_27a) -> c_2Ebool_2E_21(A_27a) = f1(A_27a))) # label(ax_thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 39 (all A_27a all V0P ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) # label(lameq_f2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 40 (all A_27a (ne(A_27a) -> c_2Ebool_2E_3F(A_27a) = f2(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 41 (all V1t2 (mem(V1t2,bool) -> (all V0t1 (mem(V0t1,bool) -> (all V2t ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t)))))) # label(lameq_f3) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 42 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1))))) # label(lameq_f4) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 43 (all V0t1 ap(f5,V0t1) = f4(V0t1)) # label(lameq_f5) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 44 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t ap(f6(V0t1,V1t2),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t))))))) # label(lameq_f6) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 45 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2))))) # label(lameq_f7) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 46 (all V0t1 ap(f8,V0t1) = f7(V0t1)) # label(lameq_f8) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 47 $F <-> (all V0t (mem(V0t,bool) -> p(V0t))) # label(ax_thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 48 (all V0t ap(f9,V0t) = ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF)) # label(lameq_f9) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 49 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y))))))) # label(lameq_f10) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 50 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(f11(A_27a,V0P),V1x) = ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x))))) # label(lameq_f11) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 51 (all A_27a all V0P ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P)))) # label(lameq_f12) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 52 (all A_27a (ne(A_27a) -> c_2Ebool_2E_3F_21(A_27a) = f12(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 53 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x)))) # label(lameq_f13) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 54 (all A_27b all A_27a all V0f ap(f14(A_27b,A_27a),V0f) = f13(A_27b,A_27a,V0f)) # label(lameq_f14) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 55 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a))))) # label(ax_thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 56 (all A_27a all V1t1 (mem(V1t1,A_27a) -> (all V2t2 (mem(V2t2,A_27a) -> (all V0t (mem(V0t,bool) -> (all V3x ap(f15(A_27a,V1t1,V2t2,V0t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2)))))))))) # label(lameq_f15) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 57 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,A_27a) -> (all V2t2 ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t))))))) # label(lameq_f16) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 58 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1)))) # label(lameq_f17) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 59 (all A_27a all V0t ap(f18(A_27a),V0t) = f17(A_27a,V0t)) # label(lameq_f18) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 60 (all A_27a (ne(A_27a) -> c_2Ebool_2ECOND(A_27a) = f18(A_27a))) # label(ax_thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 61 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 ap(f19(A_27b,A_27a,V0f,V1x1),V2x2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2))))))) # label(lameq_f19) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 62 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1))))) # label(lameq_f20) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 63 (all A_27b all A_27a all V0f ap(f21(A_27b,A_27a),V0f) = ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f))) # label(lameq_f21) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 64 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2EONE__ONE(A_27a,A_27b) = f21(A_27b,A_27a))))) # label(ax_thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 65 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27b) -> (all V2x ap(f22(A_27b,A_27a,V0f,V1y),V2x) = ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x))))))) # label(lameq_f22) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 66 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y))))) # label(lameq_f23) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 67 (all A_27a all A_27b all V0f ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f))) # label(lameq_f24) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 68 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2EONTO(A_27a,A_27b) = f24(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 69 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 (mem(V2x_27,A_27b) -> (all V3x_27_27 ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27))))))) # label(lameq_f25) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 70 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27))))) # label(lameq_f26) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 71 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x (mem(V4x,A_27a) -> (all V5x_27 ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27))))))) # label(lameq_f27) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 72 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x ap(f28(A_27b,A_27a,V0P,V1rep),V4x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x)))))))) # label(lameq_f28) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 73 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep ap(f29(A_27b,A_27a,V0P),V1rep) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep)))))) # label(lameq_f29) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 74 (all A_27b all A_27a all V0P ap(f30(A_27b,A_27a),V0P) = f29(A_27b,A_27a,V0P)) # label(lameq_f30) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 75 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a))))) # label(ax_thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 76 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $T) | (p(V0t) <-> $F))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 77 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,A_27b)) -> (all V1x ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x)))) # label(lameq_f31) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 78 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,A_27b)) -> f31(A_27b,A_27a,V0t) = V0t)))))) # label(ax_thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 79 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(V0P,V1x)) -> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(ax_thm_2Ebool_2ESELECT__AX) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 80 (exists V0f (mem(V0f,arr(ind,ind)) & p(ap(c_2Ebool_2EONE__ONE(ind,ind),V0f)) & -p(ap(c_2Ebool_2EONTO(ind,ind),V0f)))) # label(ax_thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 81 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2Eliteral__case(A_27a,A_27b) = f14(A_27b,A_27a))))) # label(ax_thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 82 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1f ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x)))) # label(lameq_f32) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 83 (all A_27a all V0x ap(f33(A_27a),V0x) = f32(A_27a,V0x)) # label(lameq_f33) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 84 (all A_27a (ne(A_27a) -> c_2Ebool_2EIN(A_27a) = f33(A_27a))) # label(ax_thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 85 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f34) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 86 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f35(A_27a,V0p),V1m) = ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m))))) # label(lameq_f35) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 87 (all A_27a all V0p ap(f36(A_27a),V0p) = f35(A_27a,V0p)) # label(lameq_f36) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 88 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a))) # label(ax_thm_2Ebool_2ERES__FORALL__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 89 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f37) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 90 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f38(A_27a,V0p),V1m) = ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m))))) # label(lameq_f38) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 91 (all A_27a all V0p ap(f39(A_27a),V0p) = f38(A_27a,V0p)) # label(lameq_f39) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 92 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__EXISTS(A_27a) = f39(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 93 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f40(A_27a,V1m),V2x) = ap(V1m,V2x)))) # label(lameq_f40) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 94 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(f41(A_27a,V1m,V3x),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y))))))) # label(lameq_f41) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.95 95 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V3x ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x))))))) # label(lameq_f42) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 96 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p)))))) # label(lameq_f43) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 97 (all A_27a all V0p ap(f44(A_27a),V0p) = f43(A_27a,V0p)) # label(lameq_f44) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 98 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a) = f44(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 99 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m))))) # label(lameq_f45) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 100 (all A_27a all V0p ap(f46(A_27a),V0p) = f45(A_27a,V0p)) # label(lameq_f46) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 101 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a))) # label(ax_thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 102 (all A_27a (ne(A_27a) -> c_2Ebool_2EDATATYPE(A_27a) = k(A_27a,c_2Ebool_2ET))) # label(ax_thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 103 -$T # label(conj_thm_2Ebool_2ETRUTH) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.96
% 0.67/0.96 ============================== end of process non-clausal formulas ===
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.96
% 0.67/0.96 ============================== PREDICATE ELIMINATION =================
% 0.67/0.96
% 0.67/0.96 ============================== end predicate elimination =============
% 0.67/0.96
% 0.67/0.96 Auto_denials: (non-Horn, no changes).
% 0.67/0.96
% 0.67/0.96 Term ordering decisions:
% 0.67/0.96 Function symbol KB weights: bool=1. c_2Emin_2E_3D_3D_3E=1. c_2Ebool_2E_2F_5C=1. c_2Ebool_2ET=1. c_2Ebool_2E_5C_2F=1. ind=1. c_2Ebool_2EF=1. c_2Ebool_2E_7E=1. c_2Ebool_2EBOUNDED=1. f5=1. f8=1. f9=1. c1=1. c2=1. ap=1. arr=1. k=1. c_2Ebool_2EONE__ONE=1. f14=1. c_2Ebool_2ELET=1. c_2Ebool_2EONTO=1. c_2Ebool_2ETYPE__DEFINITION=1. c_2Ebool_2Eliteral__case=1. f11=1. f17=1. f21=1. f24=1. f3=1. f30=1. f32=1. f35=1. f38=1. f40=1. f43=1. f45=1. f6=1. c_2Ebool_2ERES__ABSTRACT=1. c_2Ebool_2Eitself__case=1. f2=1. f4=1. c_2Emin_2E_3D=1. c_2Ebool_2E_21=1. c_2Ebool_2E_3F=1. c_2Emin_2E_40=1. c_2Ebool_2EIN=1. c_2Ebool_2ERES__FORALL=1. c_2Ebool_2ERES__EXISTS=1. i=1. ty_2Ebool_2Eitself=1. c_2Ebool_2ECOND=1. c_2Ebool_2EDATATYPE=1. c_2Ebool_2ERES__EXISTS__UNIQUE=1. c_2Ebool_2ERES__SELECT=1. c_2Ebool_2E_3F_21=1. f1=1. f12=1. f18=1. f2=1. f33=1. f36=1. f39=1. f4=1. f44=1. f46=1. f7=1. c_2Ebool_2EARB=1. c_2Ebool_2Ethe__value=1. f37=1. f10=1. f13=1. f16=1. f20=1. f23=1. f26=1. f29=1. f31=1. f34=1. f41=1. f42=1. f15=1. f19=1. f22=1. f25=1. f27=1. f28=1. f1=1.
% 0.67/0.96
% 0.67/0.96 ============================== PROOF =================================
% 0.67/0.96 % SZS status Theorem
% 0.67/0.96 % SZS output start Refutation
% 0.67/0.96
% 0.67/0.96 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.67/0.96 % Length of proof is 2.
% 0.67/0.96 % Level of proof is 1.
% 0.67/0.96 % Maximum clause weight is 0.000.
% 0.67/0.96 % Given clauses 0.
% 0.67/0.96
% 0.67/0.96 103 -$T # label(conj_thm_2Ebool_2ETRUTH) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.96 273 $F # label(conj_thm_2Ebool_2ETRUTH) # label(negated_conjecture). [clausify(103)].
% 0.67/0.96
% 0.67/0.96 % SZS output end Refutation
% 0.67/0.96 ============================== end of proof ==========================
% 0.67/0.96
% 0.67/0.96 ============================== STATISTICS ============================
% 0.67/0.96
% 0.67/0.96 Given=0. Generated=134. Kept=132. proofs=1.
% 0.67/0.96 Usable=0. Sos=0. Demods=20. Limbo=132, Disabled=134. Hints=0.
% 0.67/0.96 Megabytes=0.65.
% 0.67/0.96 User_CPU=0.03, System_CPU=0.00, Wall_clock=1.
% 0.67/0.96
% 0.67/0.96 ============================== end of statistics =====================
% 0.67/0.96
% 0.67/0.96 ============================== end of search =========================
% 0.67/0.96
% 0.67/0.96 THEOREM PROVED
% 0.67/0.96 % SZS status Theorem
% 0.67/0.96
% 0.67/0.96 Exiting with 1 proof.
% 0.67/0.96
% 0.67/0.96 Process 23132 exit (max_proofs) Sat Jun 4 01:51:48 2022
% 0.67/0.96 Prover9 interrupted
%------------------------------------------------------------------------------