0.00/0.10	% 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   : n029.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   : 1200
0.09/0.30	% DateTime   : Tue Jul 13 15:36:25 EDT 2021
0.09/0.31	% CPUTime    : 
0.75/1.07	============================== Prover9 ===============================
0.75/1.07	Prover9 (32) version 2009-11A, November 2009.
0.75/1.07	Process 19474 was started by sandbox on n029.cluster.edu,
0.75/1.07	Tue Jul 13 15:36:25 2021
0.75/1.07	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_19321_n029.cluster.edu".
0.75/1.07	============================== end of head ===========================
0.75/1.07	
0.75/1.07	============================== INPUT =================================
0.75/1.07	
0.75/1.07	% Reading from file /tmp/Prover9_19321_n029.cluster.edu
0.75/1.07	
0.75/1.07	set(prolog_style_variables).
0.75/1.07	set(auto2).
0.75/1.07	    % set(auto2) -> set(auto).
0.75/1.07	    % set(auto) -> set(auto_inference).
0.75/1.07	    % set(auto) -> set(auto_setup).
0.75/1.07	    % set(auto_setup) -> set(predicate_elim).
0.75/1.07	    % set(auto_setup) -> assign(eq_defs, unfold).
0.75/1.07	    % set(auto) -> set(auto_limits).
0.75/1.07	    % set(auto_limits) -> assign(max_weight, "100.000").
0.75/1.07	    % set(auto_limits) -> assign(sos_limit, 20000).
0.75/1.07	    % set(auto) -> set(auto_denials).
0.75/1.07	    % set(auto) -> set(auto_process).
0.75/1.07	    % set(auto2) -> assign(new_constants, 1).
0.75/1.07	    % set(auto2) -> assign(fold_denial_max, 3).
0.75/1.07	    % set(auto2) -> assign(max_weight, "200.000").
0.75/1.07	    % set(auto2) -> assign(max_hours, 1).
0.75/1.07	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.75/1.07	    % set(auto2) -> assign(max_seconds, 0).
0.75/1.07	    % set(auto2) -> assign(max_minutes, 5).
0.75/1.07	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.75/1.07	    % set(auto2) -> set(sort_initial_sos).
0.75/1.07	    % set(auto2) -> assign(sos_limit, -1).
0.75/1.07	    % set(auto2) -> assign(lrs_ticks, 3000).
0.75/1.07	    % set(auto2) -> assign(max_megs, 400).
0.75/1.07	    % set(auto2) -> assign(stats, some).
0.75/1.07	    % set(auto2) -> clear(echo_input).
0.75/1.07	    % set(auto2) -> set(quiet).
0.75/1.07	    % set(auto2) -> clear(print_initial_clauses).
0.75/1.07	    % set(auto2) -> clear(print_given).
0.75/1.07	assign(lrs_ticks,-1).
0.75/1.07	assign(sos_limit,10000).
0.75/1.07	assign(order,kbo).
0.75/1.07	set(lex_order_vars).
0.75/1.07	clear(print_given).
0.75/1.07	
0.75/1.07	% formulas(sos).  % not echoed (27 formulas)
0.75/1.07	
0.75/1.07	============================== end of input ==========================
0.75/1.07	
0.75/1.07	% From the command line: assign(max_seconds, 1200).
0.75/1.07	
0.75/1.07	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.75/1.07	
0.75/1.07	% Formulas that are not ordinary clauses:
0.75/1.07	1 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(R) <-> p(Q)) -> Q = R))))) # label(boolext) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	2 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(G,X) = ap(F,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	4 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	5 (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].
0.75/1.07	6 (all A all Y all X (mem(X,A) -> ap(k(A,Y),X) = Y)) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	7 (all Q (mem(Q,bool) -> (-p(Q) <-> p(ap(c_2Ebool_2E_7E,Q))))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	8 (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].
0.75/1.07	9 (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) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & V2y != V1x))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	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].
0.75/1.07	11 (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].
0.75/1.07	12 (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].
1.84/2.17	13 (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].
1.84/2.17	14 (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].
1.84/2.17	15 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((all X (mem(X,A) -> p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_21(A),Q))))))) # label(ax_all_p) # label(axiom) # label(non_clause).  [assumption].
1.84/2.17	16 (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].
1.84/2.17	17 (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].
1.84/2.17	18 (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].
1.84/2.17	19 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((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))))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause).  [assumption].
1.84/2.17	20 (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].
1.84/2.17	21 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(Q) & p(R) <-> p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))))))) # label(ax_and_p) # label(axiom) # label(non_clause).  [assumption].
1.84/2.17	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].
1.84/2.17	
1.84/2.17	============================== end of process non-clausal formulas ===
1.84/2.17	
1.84/2.17	============================== PROCESS INITIAL CLAUSES ===============
1.84/2.17	
1.84/2.17	============================== PREDICATE ELIMINATION =================
1.84/2.17	
1.84/2.17	============================== end predicate elimination =============
1.84/2.17	
1.84/2.17	Auto_denials:  (non-Horn, no changes).
1.84/2.17	
1.84/2.17	Term ordering decisions:
1.84/2.17	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. f2=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. f3=1. f1=1.
1.84/2.17	
1.84/2.17	============================== end of process initial clauses ========
1.84/2.17	
1.84/2.17	============================== CLAUSES FOR SEARCH ====================
1.84/2.17	
1.84/2.17	============================== end of clauses for search =============
1.84/2.17	
1.84/2.17	============================== SEARCH ================================
1.84/2.17	
1.84/2.17	% Starting search at 0.01 seconds.
1.84/2.17	
1.84/2.17	Low Water (keep): wt=36.000, iters=3584
1.84/2.17	
1.84/2.17	Low Water (keep): wt=30.000, iters=3511
1.84/2.17	
1.84/2.17	Low Water (keep): wt=28.000, iters=3471
1.84/2.17	
1.84/2.17	Low Water (keep): wt=26.000, iters=3369
1.84/2.17	
1.84/2.17	Low Water (keep): wt=20.000, iters=3361
1.84/2.17	
1.84/2.17	Low Water (keep): wt=19.000, iters=3341
1.84/2.17	
1.84/2.17	Low Water (keep): wt=17.000, iters=3390
1.84/2.17	
1.84/2.17	Low Water (keep): wt=16.000, iters=3333
1.84/2.17	
1.84/2.17	Low Water (keep): wt=14.000, iters=3382
1.84/2.17	
1.84/2.17	Low Water (keep): wt=12.000, iters=3360
1.84/2.17	
1.84/2.17	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.59 sec).
1.84/2.17	
1.84/2.17	Low Water (keep): wt=10.000, iters=3421
1.84/2.17	
1.84/2.17	============================== PROOF =================================
1.84/2.17	% SZS status Theorem
1.84/2.17	% SZS output start Refutation
1.84/2.17	
1.84/2.17	% Proof 1 at 1.07 (+ 0.03) seconds.
1.84/2.17	% Length of proof is 33.
1.84/2.17	% Level of proof is 6.
1.84/2.17	% Maximum clause weight is 32.000.
1.84/2.17	% Given clauses 928.
1.84/2.17	
1.84/2.17	5 (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].
1.84/2.17	8 (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].
1.84/2.17	9 (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) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & V2y != V1x))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause).  [assumption].
1.84/2.17	13 (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].
1.84/2.17	16 (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].
1.84/2.17	19 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((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))))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause).  [assumption].
1.84/2.17	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].
1.84/2.17	25 ne(c1) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture).  [clausify(22)].
1.84/2.17	27 mem(c2,arr(c1,bool)) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture).  [clausify(22)].
1.84/2.17	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)].
1.84/2.17	38 -ne(A) | mem(c_2Epred__set_2ECHOICE(A),arr(arr(A,bool),A)) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom).  [clausify(13)].
1.84/2.17	40 -ne(A) | mem(c_2Epred__set_2EREST(A),arr(arr(A,bool),arr(A,bool))) # label(mem_c_2Epred__set_2EREST) # label(axiom).  [clausify(8)].
1.84/2.17	44 -mem(A,arr(B,C)) | -mem(D,B) | mem(ap(A,D),C) # label(ap_tp) # label(axiom).  [clausify(5)].
1.84/2.17	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(16)].
1.84/2.17	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)].
1.84/2.17	61 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | mem(f3(A,B,C),A) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(19)].
1.84/2.17	63 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | p(ap(ap(c_2Ebool_2EIN(A),f3(A,B,C)),B)) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(19)].
1.84/2.17	64 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,arr(A,bool)) | -p(ap(ap(c_2Ebool_2EIN(A),f3(A,B,C)),C)) | p(ap(ap(c_2Epred__set_2ESUBSET(A),B),C)) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom).  [clausify(19)].
1.84/2.17	65 -ne(A) | -mem(B,arr(A,bool)) | -mem(C,A) | -mem(D,A) | -p(ap(ap(c_2Ebool_2EIN(A),C),ap(ap(c_2Epred__set_2EDELETE(A),B),D))) | p(ap(ap(c_2Ebool_2EIN(A),C),B)) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom).  [clausify(9)].
1.84/2.17	107 mem(c_2Epred__set_2ECHOICE(c1),arr(arr(c1,bool),c1)).  [resolve(38,a,25,a)].
1.84/2.17	113 mem(c_2Epred__set_2EREST(c1),arr(arr(c1,bool),arr(c1,bool))).  [resolve(40,a,25,a)].
1.84/2.17	125 -mem(A,arr(arr(c1,bool),B)) | mem(ap(A,c2),B).  [resolve(44,b,27,a)].
1.84/2.17	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)].
1.84/2.17	171 -mem(A,arr(c1,bool)) | mem(f3(c1,A,c2),c1) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)).  [resolve(61,c,27,a),unit_del(a,25)].
1.84/2.17	183 -mem(A,arr(c1,bool)) | p(ap(ap(c_2Ebool_2EIN(c1),f3(c1,A,c2)),A)) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)).  [resolve(63,c,27,a),unit_del(a,25)].
1.84/2.17	187 -mem(A,arr(c1,bool)) | -p(ap(ap(c_2Ebool_2EIN(c1),f3(c1,A,c2)),c2)) | p(ap(ap(c_2Epred__set_2ESUBSET(c1),A),c2)).  [resolve(64,c,27,a),unit_del(a,25)].
1.84/2.17	189 -mem(A,c1) | -mem(B,c1) | -p(ap(ap(c_2Ebool_2EIN(c1),A),ap(ap(c_2Epred__set_2EDELETE(c1),c2),B))) | p(ap(ap(c_2Ebool_2EIN(c1),A),c2)).  [resolve(65,b,27,a),unit_del(a,25)].
1.84/2.17	3486 mem(ap(c_2Epred__set_2EREST(c1),c2),arr(c1,bool)).  [resolve(125,a,113,a)].
1.84/2.17	3488 mem(ap(c_2Epred__set_2ECHOICE(c1),c2),c1).  [resolve(125,a,107,a)].
1.84/2.17	8876 -p(ap(ap(c_2Ebool_2EIN(c1),f3(c1,ap(c_2Epred__set_2EREST(c1),c2),c2)),c2)).  [resolve(3486,a,187,a),unit_del(b,31)].
1.84/2.17	8877 mem(f3(c1,ap(c_2Epred__set_2EREST(c1),c2),c2),c1).  [resolve(3486,a,171,a),unit_del(b,31)].
1.84/2.17	9014 -p(ap(ap(c_2Ebool_2EIN(c1),f3(c1,ap(c_2Epred__set_2EREST(c1),c2),c2)),ap(c_2Epred__set_2EREST(c1),c2))).  [ur(189,a,8877,a,b,3488,a,d,8876,a),rewrite([167(19)])].
1.84/2.17	9016 $F.  [ur(183,b,9014,a,c,31,a),unit_del(a,3486)].
1.84/2.17	
1.84/2.17	% SZS output end Refutation
1.84/2.17	============================== end of proof ==========================
1.84/2.17	
1.84/2.17	============================== STATISTICS ============================
1.84/2.17	
1.84/2.17	Given=928. Generated=20161. Kept=8992. proofs=1.
1.84/2.17	Usable=923. Sos=8012. Demods=62. Limbo=0, Disabled=101. Hints=0.
1.84/2.17	Megabytes=7.64.
1.84/2.17	User_CPU=1.07, System_CPU=0.03, Wall_clock=1.
1.84/2.17	
1.84/2.17	============================== end of statistics =====================
1.84/2.17	
1.84/2.17	============================== end of search =========================
1.84/2.17	
1.84/2.17	THEOREM PROVED
1.84/2.17	% SZS status Theorem
1.84/2.17	
1.84/2.17	Exiting with 1 proof.
1.84/2.17	
1.84/2.17	Process 19474 exit (max_proofs) Tue Jul 13 15:36:26 2021
1.84/2.17	Prover9 interrupted
1.84/2.17	EOF