0.00/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.10	% Command    : tptp2X_and_run_prover9 %d %s
0.09/0.30	% Computer   : n009.cluster.edu
0.09/0.30	% Model      : x86_64 x86_64
0.09/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.30	% Memory     : 8042.1875MB
0.09/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.30	% CPULimit   : 960
0.09/0.30	% DateTime   : Thu Jul  2 07:54:36 EDT 2020
0.09/0.30	% CPUTime    : 
0.72/1.02	============================== Prover9 ===============================
0.72/1.02	Prover9 (32) version 2009-11A, November 2009.
0.72/1.02	Process 3331 was started by sandbox2 on n009.cluster.edu,
0.72/1.02	Thu Jul  2 07:54:37 2020
0.72/1.02	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_3177_n009.cluster.edu".
0.72/1.02	============================== end of head ===========================
0.72/1.02	
0.72/1.02	============================== INPUT =================================
0.72/1.02	
0.72/1.02	% Reading from file /tmp/Prover9_3177_n009.cluster.edu
0.72/1.02	
0.72/1.02	set(prolog_style_variables).
0.72/1.02	set(auto2).
0.72/1.02	    % set(auto2) -> set(auto).
0.72/1.02	    % set(auto) -> set(auto_inference).
0.72/1.02	    % set(auto) -> set(auto_setup).
0.72/1.02	    % set(auto_setup) -> set(predicate_elim).
0.72/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.72/1.02	    % set(auto) -> set(auto_limits).
0.72/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.72/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.72/1.02	    % set(auto) -> set(auto_denials).
0.72/1.02	    % set(auto) -> set(auto_process).
0.72/1.02	    % set(auto2) -> assign(new_constants, 1).
0.72/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.72/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.72/1.02	    % set(auto2) -> assign(max_hours, 1).
0.72/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.72/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.72/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.72/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.72/1.02	    % set(auto2) -> set(sort_initial_sos).
0.72/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.72/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.72/1.02	    % set(auto2) -> assign(max_megs, 400).
0.72/1.02	    % set(auto2) -> assign(stats, some).
0.72/1.02	    % set(auto2) -> clear(echo_input).
0.72/1.02	    % set(auto2) -> set(quiet).
0.72/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.72/1.02	    % set(auto2) -> clear(print_given).
0.72/1.02	assign(lrs_ticks,-1).
0.72/1.02	assign(sos_limit,10000).
0.72/1.02	assign(order,kbo).
0.72/1.02	set(lex_order_vars).
0.72/1.02	clear(print_given).
0.72/1.02	
0.72/1.02	% formulas(sos).  % not echoed (27 formulas)
0.72/1.02	
0.72/1.02	============================== end of input ==========================
0.72/1.02	
0.72/1.02	% From the command line: assign(max_seconds, 960).
0.72/1.02	
0.72/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.72/1.02	
0.72/1.02	% Formulas that are not ordinary clauses:
0.72/1.02	1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	2 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) <-> p(R)) -> R = Q))))) # label(boolext) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	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].
0.72/1.02	5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	6 (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].
0.72/1.02	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].
0.72/1.02	8 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	9 (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].
0.72/1.02	10 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2ESUBSET) # label(axiom) # label(non_clause).  [assumption].
0.72/1.02	11 (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].
0.72/1.02	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].
0.72/1.02	13 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	14 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (X = Y <-> p(ap(ap(c_2Emin_2E_3D(A),X),Y))))))))) # label(ax_eq_p) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	15 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x != V2y & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y)))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	16 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EREST) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	17 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDELETE(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EDELETE) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	18 (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].
1.78/2.08	19 (all Q (mem(Q,bool) -> (-p(Q) <-> p(ap(c_2Ebool_2E_7E,Q))))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	20 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) -> p(R)) <-> p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	21 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) = ap(c_2Epred__set_2EREST(A_27a),V0s))))) # label(ax_thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	22 -(all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)))))) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture) # label(non_clause).  [assumption].
1.78/2.08	
1.78/2.08	============================== end of process non-clausal formulas ===
1.78/2.08	
1.78/2.08	============================== PROCESS INITIAL CLAUSES ===============
1.78/2.08	
1.78/2.08	============================== PREDICATE ELIMINATION =================
1.78/2.08	
1.78/2.08	============================== end predicate elimination =============
1.78/2.08	
1.78/2.08	Auto_denials:  (non-Horn, no changes).
1.78/2.08	
1.78/2.08	Term ordering decisions:
1.78/2.08	Function symbol KB weights:  bool=1. c_2Ebool_2E_2F_5C=1. c_2Emin_2E_3D_3D_3E=1. c_2Ebool_2E_7E=1. ind=1. c1=1. c2=1. ap=1. arr=1. k=1. f3=1. c_2Ebool_2EIN=1. c_2Epred__set_2ESUBSET=1. c_2Ebool_2E_21=1. c_2Epred__set_2EDELETE=1. c_2Emin_2E_3D=1. c_2Epred__set_2ECHOICE=1. c_2Epred__set_2EREST=1. i=1. f2=1. f1=1.
1.78/2.08	
1.78/2.08	============================== end of process initial clauses ========
1.78/2.08	
1.78/2.08	============================== CLAUSES FOR SEARCH ====================
1.78/2.08	
1.78/2.08	============================== end of clauses for search =============
1.78/2.08	
1.78/2.08	============================== SEARCH ================================
1.78/2.08	
1.78/2.08	% Starting search at 0.01 seconds.
1.78/2.08	
1.78/2.08	Low Water (keep): wt=36.000, iters=3621
1.78/2.08	
1.78/2.08	Low Water (keep): wt=30.000, iters=3547
1.78/2.08	
1.78/2.08	Low Water (keep): wt=28.000, iters=3506
1.78/2.08	
1.78/2.08	Low Water (keep): wt=26.000, iters=3363
1.78/2.08	
1.78/2.08	Low Water (keep): wt=20.000, iters=3361
1.78/2.08	
1.78/2.08	Low Water (keep): wt=19.000, iters=3370
1.78/2.08	
1.78/2.08	Low Water (keep): wt=16.000, iters=3334
1.78/2.08	
1.78/2.08	Low Water (keep): wt=14.000, iters=3411
1.78/2.08	
1.78/2.08	Low Water (keep): wt=12.000, iters=3360
1.78/2.08	
1.78/2.08	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.60 sec).
1.78/2.08	
1.78/2.08	Low Water (keep): wt=10.000, iters=3426
1.78/2.08	
1.78/2.08	============================== PROOF =================================
1.78/2.08	% SZS status Theorem
1.78/2.08	% SZS output start Refutation
1.78/2.08	
1.78/2.08	% Proof 1 at 1.05 (+ 0.02) seconds.
1.78/2.08	% Length of proof is 33.
1.78/2.08	% Level of proof is 6.
1.78/2.08	% Maximum clause weight is 32.000.
1.78/2.08	% Given clauses 918.
1.78/2.08	
1.78/2.08	6 (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].
1.78/2.08	8 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	13 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	15 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x != V2y & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y)))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	16 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EREST) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	21 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) = ap(c_2Epred__set_2EREST(A_27a),V0s))))) # label(ax_thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause).  [assumption].
1.78/2.08	22 -(all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)))))) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture) # label(non_clause).  [assumption].
1.78/2.08	25 ne(c1) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture).  [clausify(22)].
1.78/2.08	27 mem(c2,arr(c1,bool)) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture).  [clausify(22)].
1.78/2.08	31 -p(ap(ap(c_2Epred__set_2ESUBSET(c1),ap(c_2Epred__set_2EREST(c1),c2)),c2)) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture).  [clausify(22)].
1.78/2.08	38 -ne(A) | mem(c_2Epred__set_2ECHOICE(A),arr(arr(A,bool),A)) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom).  [clausify(8)].
1.78/2.08	41 -ne(A) | mem(c_2Epred__set_2EREST(A),arr(arr(A,bool),arr(A,bool))) # label(mem_c_2Epred__set_2EREST) # label(axiom).  [clausify(16)].
1.78/2.08	44 -mem(A,arr(B,C)) | -mem(D,B) | mem(ap(A,D),C) # label(ap_tp) # label(axiom).  [clausify(6)].
1.78/2.08	59 -ne(A) | -mem(B,arr(A,bool)) | ap(c_2Epred__set_2EREST(A),B) = ap(ap(c_2Epred__set_2EDELETE(A),B),ap(c_2Epred__set_2ECHOICE(A),B)) # label(ax_thm_2Epred__set_2EREST__DEF) # label(axiom).  [clausify(21)].
1.78/2.08	60 -ne(A) | -mem(B,arr(A,bool)) | ap(ap(c_2Epred__set_2EDELETE(A),B),ap(c_2Epred__set_2ECHOICE(A),B)) = ap(c_2Epred__set_2EREST(A),B).  [copy(59),flip(c)].
1.78/2.08	61 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) | mem(f2(A,B,C),A) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(13)].
1.78/2.08	63 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) | p(ap(ap(c_2Ebool_2EIN(A),f2(A,B,C)),B)) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(13)].
1.78/2.08	64 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) | -p(ap(ap(c_2Ebool_2EIN(A),f2(A,B,C)),C)) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(13)].
1.78/2.08	65 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,A) | -mem(D,A) | p(ap(ap(c_2Ebool_2EIN(A),C),B)) | -p(ap(ap(c_2Ebool_2EIN(A),C),ap(ap(c_2Epred__set_2EDELETE(A),B),D))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom).  [clausify(15)].
1.78/2.08	107 mem(c_2Epred__set_2ECHOICE(c1),arr(arr(c1,bool),c1)).  [resolve(38,a,25,a)].
1.78/2.08	116 mem(c_2Epred__set_2EREST(c1),arr(arr(c1,bool),arr(c1,bool))).  [resolve(41,a,25,a)].
1.78/2.08	125 -mem(A,arr(arr(c1,bool),B)) | mem(ap(A,c2),B).  [resolve(44,b,27,a)].
1.78/2.08	167 ap(ap(c_2Epred__set_2EDELETE(c1),c2),ap(c_2Epred__set_2ECHOICE(c1),c2)) = ap(c_2Epred__set_2EREST(c1),c2).  [resolve(60,b,27,a),unit_del(a,25)].
1.78/2.08	171 -mem(A,arr(c1,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)) | mem(f2(c1,A,c2),c1).  [resolve(61,c,27,a),unit_del(a,25)].
1.78/2.08	183 -mem(A,arr(c1,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)) | p(ap(ap(c_2Ebool_2EIN(c1),f2(c1,A,c2)),A)).  [resolve(63,c,27,a),unit_del(a,25)].
1.78/2.08	187 -mem(A,arr(c1,bool)) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)) | -p(ap(ap(c_2Ebool_2EIN(c1),f2(c1,A,c2)),c2)).  [resolve(64,c,27,a),unit_del(a,25)].
1.78/2.08	189 -mem(A,c1) | -mem(B,c1) | p(ap(ap(c_2Ebool_2EIN(c1),A),c2)) | -p(ap(ap(c_2Ebool_2EIN(c1),A),ap(ap(c_2Epred__set_2EDELETE(c1),c2),B))).  [resolve(65,b,27,a),unit_del(a,25)].
1.78/2.08	3519 mem(ap(c_2Epred__set_2EREST(c1),c2),arr(c1,bool)).  [resolve(125,a,116,a)].
1.78/2.08	3521 mem(ap(c_2Epred__set_2ECHOICE(c1),c2),c1).  [resolve(125,a,107,a)].
1.78/2.08	8782 -p(ap(ap(c_2Ebool_2EIN(c1),f2(c1,ap(c_2Epred__set_2EREST(c1),c2),c2)),c2)).  [resolve(3519,a,187,a),unit_del(a,31)].
1.78/2.08	8783 mem(f2(c1,ap(c_2Epred__set_2EREST(c1),c2),c2),c1).  [resolve(3519,a,171,a),unit_del(a,31)].
1.78/2.08	8920 -p(ap(ap(c_2Ebool_2EIN(c1),f2(c1,ap(c_2Epred__set_2EREST(c1),c2),c2)),ap(c_2Epred__set_2EREST(c1),c2))).  [ur(189,a,8783,a,b,3521,a,c,8782,a),rewrite([167(19)])].
1.78/2.08	8922 $F.  [ur(183,b,31,a,c,8920,a),unit_del(a,3519)].
1.78/2.08	
1.78/2.08	% SZS output end Refutation
1.78/2.08	============================== end of proof ==========================
1.78/2.08	
1.78/2.08	============================== STATISTICS ============================
1.78/2.08	
1.78/2.08	Given=918. Generated=18727. Kept=8898. proofs=1.
1.78/2.08	Usable=917. Sos=7925. Demods=62. Limbo=0, Disabled=100. Hints=0.
1.78/2.08	Megabytes=7.59.
1.78/2.08	User_CPU=1.06, System_CPU=0.02, Wall_clock=1.
1.78/2.08	
1.78/2.08	============================== end of statistics =====================
1.78/2.08	
1.78/2.08	============================== end of search =========================
1.78/2.08	
1.78/2.08	THEOREM PROVED
1.78/2.08	% SZS status Theorem
1.78/2.08	
1.78/2.08	Exiting with 1 proof.
1.78/2.08	
1.78/2.08	Process 3331 exit (max_proofs) Thu Jul  2 07:54:38 2020
1.78/2.08	Prover9 interrupted
1.78/2.08	EOF