0.00/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.33	% Computer   : n025.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1200
0.13/0.33	% DateTime   : Wed Jul 14 14:08:13 EDT 2021
0.13/0.33	% CPUTime    : 
0.42/1.05	============================== Prover9 ===============================
0.42/1.05	Prover9 (32) version 2009-11A, November 2009.
0.42/1.05	Process 27582 was started by sandbox on n025.cluster.edu,
0.42/1.05	Wed Jul 14 14:08:13 2021
0.42/1.05	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_27429_n025.cluster.edu".
0.42/1.05	============================== end of head ===========================
0.42/1.05	
0.42/1.05	============================== INPUT =================================
0.42/1.05	
0.42/1.05	% Reading from file /tmp/Prover9_27429_n025.cluster.edu
0.42/1.05	
0.42/1.05	set(prolog_style_variables).
0.42/1.05	set(auto2).
0.42/1.05	    % set(auto2) -> set(auto).
0.42/1.05	    % set(auto) -> set(auto_inference).
0.42/1.05	    % set(auto) -> set(auto_setup).
0.42/1.05	    % set(auto_setup) -> set(predicate_elim).
0.42/1.05	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.05	    % set(auto) -> set(auto_limits).
0.42/1.05	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.05	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.05	    % set(auto) -> set(auto_denials).
0.42/1.05	    % set(auto) -> set(auto_process).
0.42/1.05	    % set(auto2) -> assign(new_constants, 1).
0.42/1.05	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.05	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.05	    % set(auto2) -> assign(max_hours, 1).
0.42/1.05	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.05	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.05	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.05	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.05	    % set(auto2) -> set(sort_initial_sos).
0.42/1.05	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.05	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.05	    % set(auto2) -> assign(max_megs, 400).
0.42/1.05	    % set(auto2) -> assign(stats, some).
0.42/1.05	    % set(auto2) -> clear(echo_input).
0.42/1.05	    % set(auto2) -> set(quiet).
0.42/1.05	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.05	    % set(auto2) -> clear(print_given).
0.42/1.05	assign(lrs_ticks,-1).
0.42/1.05	assign(sos_limit,10000).
0.42/1.05	assign(order,kbo).
0.42/1.05	set(lex_order_vars).
0.42/1.05	clear(print_given).
0.42/1.05	
0.42/1.05	% formulas(sos).  % not echoed (92 formulas)
0.42/1.05	
0.42/1.05	============================== end of input ==========================
0.42/1.05	
0.42/1.05	% From the command line: assign(max_seconds, 1200).
0.42/1.05	
0.42/1.05	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.05	
0.42/1.05	% Formulas that are not ordinary clauses:
0.42/1.05	1 (all X all Y all Z (leq(Y,Z) & leq(X,Y) -> leq(X,Z))) # label(transitivity_leq) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	2 (all X all U all VAL VAL = a_select2(tptp_update2(X,U,VAL),U)) # label(sel2_update_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	3 (all X X = pred(succ(X))) # label(pred_succ) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	4 (all X plus(X,n4) = succ(succ(succ(succ(X))))) # label(succ_plus_4_r) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	5 (all X all Y (gt(X,Y) | gt(Y,X) | X = Y)) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	6 (all X all Y (leq(minus(X,Y),X) -> leq(n0,Y))) # label(leq_minus) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	7 (all A all B all N ((all I all J (leq(I,N) & leq(n0,J) & leq(J,N) & leq(n0,I) -> a_select3(B,J,I) = a_select3(B,I,J))) & (all I all J (leq(n0,I) & leq(n0,J) & leq(J,N) & leq(I,N) -> a_select3(A,J,I) = a_select3(A,I,J))) -> (all I all J (leq(n0,J) & leq(J,N) & leq(I,N) & leq(n0,I) -> a_select3(tptp_madd(A,B),J,I) = a_select3(tptp_madd(A,B),I,J))))) # label(matrix_symm_add) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	8 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	9 (all X all U all V all VAL a_select3(tptp_update3(X,U,V,VAL),U,V) = VAL) # label(sel3_update_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	10 (all X succ(X) = plus(X,n1)) # label(succ_plus_1_r) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	11 (all X plus(n1,X) = succ(X)) # label(succ_plus_1_l) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	12 (all I all U all X all VAL ((all I0 (leq(I0,U) & leq(n0,I0) -> a_select2(X,I0) = VAL)) & leq(I,U) & leq(n0,I) -> VAL = a_select2(tptp_update2(X,U,VAL),I))) # label(sel2_update_3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.05	13 (all I all J all U all V all X all VAL all VAL2 (V = J & a_select3(X,U,V) = VAL & I != U -> a_select3(tptp_update3(X,I,J,VAL2),U,V) = VAL)) # label(sel3_update_2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	14 (all X X = succ(pred(X))) # label(succ_pred) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	15 (all A all B all N ((all I all J (leq(n0,I) & leq(n0,J) & leq(J,N) & leq(I,N) -> a_select3(B,J,I) = a_select3(B,I,J))) -> (all I all J (leq(n0,I) & leq(J,N) & leq(n0,J) & leq(I,N) -> a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),I,J) = a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),J,I))))) # label(matrix_symm_aba1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	16 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	17 (all A all N ((all I all J (leq(n0,I) & leq(n0,J) & leq(J,N) & leq(I,N) -> a_select3(A,J,I) = a_select3(A,I,J))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(trans(A),I,J) = a_select3(trans(A),J,I))))) # label(matrix_symm_trans) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	18 (all X gt(succ(X),X)) # label(gt_succ) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	19 (all X all C (leq(n0,X) -> leq(n0,uniform_int_rnd(C,X)))) # label(uniform_int_rand_ranges_lo) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	20 (all X all Y (gt(Y,X) <-> leq(X,pred(Y)))) # label(leq_gt_pred) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	21 (all Body n0 = sum(n0,tptp_minus_1,Body)) # label(sum_plus_base) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	22 (all X plus(X,n3) = succ(succ(succ(X)))) # label(succ_plus_3_r) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	23 (all X all Y (leq(succ(X),Y) -> gt(Y,X))) # label(leq_succ_gt) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	24 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	25 (all Body sum(n0,tptp_minus_1,Body) = tptp_float_0_0) # label(sum_plus_base_float) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	26 (all X all Y all Z (gt(X,Y) & gt(Y,Z) -> gt(X,Z))) # label(transitivity_gt) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	27 (all X leq(X,X)) # label(reflexivity_leq) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	28 (all A all N ((all I all J (leq(n0,J) & leq(J,N) & leq(I,N) & leq(n0,I) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(J,N) & leq(n0,J) -> a_select3(inv(A),I,J) = a_select3(inv(A),J,I))))) # label(matrix_symm_inv) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	29 (all X all Y (geq(X,Y) <-> leq(Y,X))) # label(leq_geq) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	30 (all I all U all X all VAL all VAL2 (I != U & VAL = a_select2(X,U) -> a_select2(tptp_update2(X,I,VAL2),U) = VAL)) # label(sel2_update_2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	31 (all X all Y (gt(Y,X) <-> lt(X,Y))) # label(lt_gt) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	32 (all X succ(succ(succ(succ(X)))) = plus(n4,X)) # label(succ_plus_4_l) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	33 (all A all B all N ((all I all J (leq(n0,J) & leq(J,N) & leq(I,N) & leq(n0,I) -> a_select3(B,J,I) = a_select3(B,I,J))) & (all I all J (leq(n0,I) & leq(n0,J) & leq(J,N) & leq(I,N) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (all I all J (leq(n0,I) & leq(J,N) & leq(n0,J) & leq(I,N) -> a_select3(tptp_msub(A,B),I,J) = a_select3(tptp_msub(A,B),J,I))))) # label(matrix_symm_sub) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	34 (all A all B all C all D all E all F all N all M ((all I all J (leq(J,N) & leq(n0,J) & leq(I,N) & leq(n0,I) -> a_select3(A,I,J) = a_select3(A,J,I))) & (all I all J (leq(J,N) & leq(n0,J) & leq(I,N) & leq(n0,I) -> a_select3(F,I,J) = a_select3(F,J,I))) & (all I all J (leq(I,M) & leq(J,M) & leq(n0,J) & leq(n0,I) -> a_select3(D,J,I) = a_select3(D,I,J))) -> (all I all J (leq(n0,J) & leq(J,N) & leq(I,N) & leq(n0,I) -> a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),J,I) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),I,J))))) # label(matrix_symm_joseph_update) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	35 (all I all J all U all V all X all VAL (leq(n0,I) & leq(n0,J) & leq(J,V) & leq(I,U) & (all I0 all J0 (leq(n0,I0) & leq(I0,U) & leq(J0,V) & leq(n0,J0) -> a_select3(X,I0,J0) = VAL)) -> VAL = a_select3(tptp_update3(X,U,V,VAL),I,J))) # label(sel3_update_3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	36 (all X all C (leq(n0,X) -> leq(uniform_int_rnd(C,X),X))) # label(uniform_int_rand_ranges_hi) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	37 (all I all L all U all Val (leq(L,I) & leq(I,U) -> Val = a_select2(tptp_const_array1(dim(L,U),Val),I))) # label(const_array1_select) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	38 (all X all Y (Y != X & leq(X,Y) -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	39 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	40 (all X all Y (gt(Y,X) -> leq(X,Y))) # label(leq_gt1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	41 (all X succ(succ(succ(X))) = plus(n3,X)) # label(succ_plus_3_l) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	42 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	43 (all A all N ((all I all J (leq(n0,I) & leq(J,N) & leq(n0,J) & leq(I,N) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (all I all J all K all VAL (leq(n0,I) & leq(n0,J) & leq(K,N) & leq(n0,K) & leq(J,N) & leq(I,N) -> a_select3(tptp_update3(A,K,K,VAL),J,I) = a_select3(tptp_update3(A,K,K,VAL),I,J))))) # label(matrix_symm_update_diagonal) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	44 (all X succ(succ(succ(succ(succ(X))))) = plus(n5,X)) # label(succ_plus_5_l) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	45 (all I all L1 all U1 all J all L2 all U2 all Val (leq(L1,I) & leq(I,U1) & leq(J,U2) & leq(L2,J) -> Val = a_select3(tptp_const_array2(dim(L1,U1),dim(L2,U2),Val),I,J))) # label(const_array2_select) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	46 (all A all B all N all M ((all I all J (leq(I,M) & leq(n0,J) & leq(J,M) & leq(n0,I) -> a_select3(B,I,J) = a_select3(B,J,I))) -> (all I all J (leq(I,N) & leq(J,N) & leq(n0,J) & leq(n0,I) -> a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),I,J) = a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),J,I))))) # label(matrix_symm_aba2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	47 (all X succ(succ(succ(succ(succ(X))))) = plus(X,n5)) # label(succ_plus_5_r) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	48 (all X succ(succ(X)) = plus(n2,X)) # label(succ_plus_2_l) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	49 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	50 (all X (leq(X,n2) & leq(n0,X) -> n0 = X | n1 = X | X = n2)) # label(finite_domain_2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	51 (all X (leq(n0,X) & leq(X,n1) -> X = n0 | n1 = X)) # label(finite_domain_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	52 (all X (leq(X,n4) & leq(n0,X) -> X = n2 | X = n4 | X = n3 | n1 = X | X = n0)) # label(finite_domain_4) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	53 (all X (leq(X,n3) & leq(n0,X) -> X = n0 | X = n1 | X = n2 | n3 = X)) # label(finite_domain_3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	54 (all X (leq(X,n5) & leq(n0,X) -> n0 = X | X = n1 | n2 = X | X = n3 | n4 = X | n5 = X)) # label(finite_domain_5) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	55 (all X (leq(n0,X) & leq(X,n0) -> n0 = X)) # label(finite_domain_0) # label(axiom) # label(non_clause).  [assumption].
0.42/1.06	56 -(use = a_select2(rho_defuse,n1) & a_select2(rho_defuse,n2) = use & use = a_select2(sigma_defuse,n0) & use = a_select2(sigma_defuse,n1) & use = a_select2(sigma_defuse,n4) & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & use = a_select2(xinit_defuse,n3) & a_select2(xinit_defuse,n4) = use & use = a_select2(xinit_defuse,n5) & use = a_select2(xinit_mean_defuse,n1) & use = a_select2(xinit_mean_defuse,n4) & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & leq(pv5,n998) & (all C all D (leq(C,n2) & leq(D,pred(pv5)) & leq(n0,D) & leq(n0,C) -> use = a_select3(z_defuse,C,D))) & (all A all B (leq(A,n2) & leq(B,pred(pv5)) & leq(n0,B) & leq(n0,A) -> use = a_select3(u_defuse,A,B))) & leq(pv5,n0) & leq(n0,pv5) & a_select2(xinit_noise_defuse,n5) = use & use = a_select2(xinit_noise_defuse,n4) & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n2) = use & use = a_select2(xinit_noise_defuse,n1) & a_select2(xinit_mean_defuse,n3) = use & use = a_select2(xinit_mean_defuse,n2) & use = a_select2(xinit_mean_defuse,n0) & a_select3(u_defuse,n2,n0) = use & a_select2(sigma_defuse,n5) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n2) = use & a_select2(rho_defuse,n0) = use -> (all E all F (leq(n0,E) & leq(n0,F) & leq(F,pv5) & leq(E,n2) -> (-(n0 = E & F = pv5) & -(F = pv5 & n2 = E) & -(pv5 = F & E = n1) -> a_select3(z_defuse,E,F) = use)))) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture) # label(non_clause).  [assumption].
1.65/1.93	
1.65/1.93	============================== end of process non-clausal formulas ===
1.65/1.93	
1.65/1.93	============================== PROCESS INITIAL CLAUSES ===============
1.65/1.93	
1.65/1.93	============================== PREDICATE ELIMINATION =================
1.65/1.93	57 geq(A,B) | -leq(B,A) # label(leq_geq) # label(axiom).  [clausify(29)].
1.65/1.93	58 -geq(A,B) | leq(B,A) # label(leq_geq) # label(axiom).  [clausify(29)].
1.65/1.93	59 gt(A,B) | -lt(B,A) # label(lt_gt) # label(axiom).  [clausify(31)].
1.65/1.93	60 -gt(A,B) | lt(B,A) # label(lt_gt) # label(axiom).  [clausify(31)].
1.65/1.93	
1.65/1.93	============================== end predicate elimination =============
1.65/1.93	
1.65/1.93	Auto_denials:  (non-Horn, no changes).
1.65/1.93	
1.65/1.93	Term ordering decisions:
1.65/1.93	Function symbol KB weights:  n0=1. use=1. n2=1. n1=1. n3=1. n4=1. n5=1. tptp_minus_1=1. n998=1. pv5=1. sigma_defuse=1. xinit_mean_defuse=1. xinit_noise_defuse=1. u_defuse=1. rho_defuse=1. xinit_defuse=1. tptp_float_0_0=1. z_defuse=1. def=1. c1=1. c2=1. tptp_mmul=1. tptp_madd=1. tptp_msub=1. a_select2=1. plus=1. dim=1. minus=1. uniform_int_rnd=1. tptp_const_array1=1. f8=1. f9=1. f10=1. f11=1. f24=1. f25=1. trans=1. succ=1. inv=1. pred=1. a_select3=1. tptp_update2=1. sum=1. tptp_const_array2=1. f1=1. f2=1. f3=1. f4=1. f6=1. f7=1. f12=1. f13=1. f14=1. f15=1. tptp_update3=1. f5=1. f26=1. f27=1. f22=1. f23=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1.
1.65/1.93	
1.65/1.93	============================== end of process initial clauses ========
1.65/1.93	
1.65/1.93	============================== CLAUSES FOR SEARCH ====================
1.65/1.93	
1.65/1.93	============================== end of clauses for search =============
1.65/1.93	
1.65/1.93	============================== SEARCH ================================
1.65/1.93	
1.65/1.93	% Starting search at 0.27 seconds.
1.65/1.93	
1.65/1.93	============================== PROOF =================================
1.65/1.93	% SZS status Theorem
1.65/1.93	% SZS output start Refutation
1.65/1.93	
1.65/1.93	% Proof 1 at 0.90 (+ 0.01) seconds.
1.65/1.93	% Length of proof is 28.
1.65/1.93	% Level of proof is 6.
1.65/1.93	% Maximum clause weight is 15.000.
1.65/1.93	% Given clauses 317.
1.65/1.93	
1.65/1.93	50 (all X (leq(X,n2) & leq(n0,X) -> n0 = X | n1 = X | X = n2)) # label(finite_domain_2) # label(axiom) # label(non_clause).  [assumption].
1.65/1.93	55 (all X (leq(n0,X) & leq(X,n0) -> n0 = X)) # label(finite_domain_0) # label(axiom) # label(non_clause).  [assumption].
1.65/1.93	56 -(use = a_select2(rho_defuse,n1) & a_select2(rho_defuse,n2) = use & use = a_select2(sigma_defuse,n0) & use = a_select2(sigma_defuse,n1) & use = a_select2(sigma_defuse,n4) & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & use = a_select2(xinit_defuse,n3) & a_select2(xinit_defuse,n4) = use & use = a_select2(xinit_defuse,n5) & use = a_select2(xinit_mean_defuse,n1) & use = a_select2(xinit_mean_defuse,n4) & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & leq(pv5,n998) & (all C all D (leq(C,n2) & leq(D,pred(pv5)) & leq(n0,D) & leq(n0,C) -> use = a_select3(z_defuse,C,D))) & (all A all B (leq(A,n2) & leq(B,pred(pv5)) & leq(n0,B) & leq(n0,A) -> use = a_select3(u_defuse,A,B))) & leq(pv5,n0) & leq(n0,pv5) & a_select2(xinit_noise_defuse,n5) = use & use = a_select2(xinit_noise_defuse,n4) & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n2) = use & use = a_select2(xinit_noise_defuse,n1) & a_select2(xinit_mean_defuse,n3) = use & use = a_select2(xinit_mean_defuse,n2) & use = a_select2(xinit_mean_defuse,n0) & a_select3(u_defuse,n2,n0) = use & a_select2(sigma_defuse,n5) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n2) = use & a_select2(rho_defuse,n0) = use -> (all E all F (leq(n0,E) & leq(n0,F) & leq(F,pv5) & leq(E,n2) -> (-(n0 = E & F = pv5) & -(F = pv5 & n2 = E) & -(pv5 = F & E = n1) -> a_select3(z_defuse,E,F) = use)))) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture) # label(non_clause).  [assumption].
1.65/1.93	323 -leq(A,n2) | -leq(n0,A) | n0 = A | n1 = A | n2 = A # label(finite_domain_2) # label(axiom).  [clausify(50)].
1.65/1.93	358 -leq(n0,A) | -leq(A,n0) | n0 = A # label(finite_domain_0) # label(axiom).  [clausify(55)].
1.65/1.93	383 leq(pv5,n0) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	384 leq(n0,pv5) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	398 leq(n0,c1) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	399 leq(n0,c2) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	400 leq(c2,pv5) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	401 leq(c1,n2) # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	402 c1 != n0 | pv5 != c2 # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	403 c1 != n0 | c2 != pv5.  [copy(402),flip(b)].
1.65/1.93	404 pv5 != c2 | c1 != n2 # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	405 c2 != pv5 | c1 != n2.  [copy(404),flip(a)].
1.65/1.93	406 pv5 != c2 | c1 != n1 # label(quaternion_ds1_inuse_0010) # label(negated_conjecture).  [clausify(56)].
1.65/1.93	407 c2 != pv5 | c1 != n1.  [copy(406),flip(a)].
1.65/1.93	2093 pv5 = n0.  [resolve(383,a,358,b),flip(b),unit_del(a,384)].
1.65/1.93	2373 c2 != n0 | c1 != n1.  [back_rewrite(407),rewrite([2093(2)])].
1.65/1.93	2374 c2 != n0 | c1 != n2.  [back_rewrite(405),rewrite([2093(2)])].
1.65/1.93	2375 c1 != n0 | c2 != n0.  [back_rewrite(403),rewrite([2093(5)])].
1.65/1.93	2376 leq(c2,n0).  [back_rewrite(400),rewrite([2093(2)])].
1.65/1.93	2410 c1 = n0 | c1 = n1 | c1 = n2.  [resolve(398,a,323,b),flip(b),flip(c),flip(d),unit_del(a,401)].
1.65/1.93	3157 c2 = n0.  [resolve(399,a,358,a),flip(b),unit_del(a,2376)].
1.65/1.93	3158 c1 != n0.  [back_rewrite(2375),rewrite([3157(4)]),xx(b)].
1.65/1.93	3159 c1 != n2.  [back_rewrite(2374),rewrite([3157(1)]),xx(a)].
1.65/1.93	3160 c1 != n1.  [back_rewrite(2373),rewrite([3157(1)]),xx(a)].
1.65/1.93	3163 $F.  [back_unit_del(2410),unit_del(a,3158),unit_del(b,3160),unit_del(c,3159)].
1.65/1.93	
1.65/1.93	% SZS output end Refutation
1.65/1.93	============================== end of proof ==========================
1.65/1.93	
1.65/1.93	============================== STATISTICS ============================
1.65/1.93	
1.65/1.93	Given=317. Generated=9120. Kept=3084. proofs=1.
1.65/1.93	Usable=312. Sos=2438. Demods=71. Limbo=5, Disabled=663. Hints=0.
1.65/1.93	Megabytes=8.67.
1.65/1.93	User_CPU=0.90, System_CPU=0.01, Wall_clock=1.
1.65/1.93	
1.65/1.93	============================== end of statistics =====================
1.65/1.93	
1.65/1.93	============================== end of search =========================
1.65/1.93	
1.65/1.93	THEOREM PROVED
1.65/1.93	% SZS status Theorem
1.65/1.93	
1.65/1.93	Exiting with 1 proof.
1.65/1.93	
1.65/1.93	Process 27582 exit (max_proofs) Wed Jul 14 14:08:14 2021
1.65/1.93	Prover9 interrupted
1.65/1.94	EOF