TSTP Solution File: SWV181+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 : Wed Jul 20 21:10:47 EDT 2022
% Result : Theorem 8.28s 8.57s
% Output : Refutation 8.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jun 15 08:15:19 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.79/1.10 ============================== Prover9 ===============================
% 0.79/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.10 Process 19355 was started by sandbox2 on n027.cluster.edu,
% 0.79/1.10 Wed Jun 15 08:15:20 2022
% 0.79/1.10 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19201_n027.cluster.edu".
% 0.79/1.10 ============================== end of head ===========================
% 0.79/1.10
% 0.79/1.10 ============================== INPUT =================================
% 0.79/1.10
% 0.79/1.10 % Reading from file /tmp/Prover9_19201_n027.cluster.edu
% 0.79/1.10
% 0.79/1.10 set(prolog_style_variables).
% 0.79/1.10 set(auto2).
% 0.79/1.10 % set(auto2) -> set(auto).
% 0.79/1.10 % set(auto) -> set(auto_inference).
% 0.79/1.10 % set(auto) -> set(auto_setup).
% 0.79/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.10 % set(auto) -> set(auto_limits).
% 0.79/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.10 % set(auto) -> set(auto_denials).
% 0.79/1.10 % set(auto) -> set(auto_process).
% 0.79/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.10 % set(auto2) -> assign(stats, some).
% 0.79/1.10 % set(auto2) -> clear(echo_input).
% 0.79/1.10 % set(auto2) -> set(quiet).
% 0.79/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.10 % set(auto2) -> clear(print_given).
% 0.79/1.10 assign(lrs_ticks,-1).
% 0.79/1.10 assign(sos_limit,10000).
% 0.79/1.10 assign(order,kbo).
% 0.79/1.10 set(lex_order_vars).
% 0.79/1.10 clear(print_given).
% 0.79/1.10
% 0.79/1.10 % formulas(sos). % not echoed (92 formulas)
% 0.79/1.10
% 0.79/1.10 ============================== end of input ==========================
% 0.79/1.10
% 0.79/1.10 % From the command line: assign(max_seconds, 300).
% 0.79/1.10
% 0.79/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.10
% 0.79/1.10 % Formulas that are not ordinary clauses:
% 0.79/1.10 1 (all X all Y (gt(X,Y) | gt(Y,X) | X = Y)) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 2 (all X all Y all Z (gt(X,Y) & gt(Y,Z) -> gt(X,Z))) # label(transitivity_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 4 (all X leq(X,X)) # label(reflexivity_leq) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 5 (all X all Y all Z (leq(X,Y) & leq(Y,Z) -> leq(X,Z))) # label(transitivity_leq) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 6 (all X all Y (lt(X,Y) <-> gt(Y,X))) # label(lt_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 7 (all X all Y (geq(X,Y) <-> leq(Y,X))) # label(leq_geq) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 8 (all X all Y (gt(Y,X) -> leq(X,Y))) # label(leq_gt1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 11 (all X gt(succ(X),X)) # label(gt_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 12 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 14 (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].
% 0.79/1.10 15 (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].
% 0.79/1.10 16 (all I all L all U all Val (leq(L,I) & leq(I,U) -> a_select2(tptp_const_array1(dim(L,U),Val),I) = Val)) # label(const_array1_select) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.10 17 (all I all L1 all U1 all J all L2 all U2 all Val (leq(L1,I) & leq(I,U1) & leq(L2,J) & leq(J,U2) -> a_select3(tptp_const_array2(dim(L1,U1),dim(L2,U2),Val),I,J) = Val)) # label(const_array2_select) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 18 (all A all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (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].
% 0.79/1.11 19 (all A all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(inv(A),I,J) = a_select3(inv(A),J,I))))) # label(matrix_symm_inv) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 20 (all A all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) -> (all I all J all K all VAL (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) & leq(n0,K) & leq(K,N) -> a_select3(tptp_update3(A,K,K,VAL),I,J) = a_select3(tptp_update3(A,K,K,VAL),J,I))))) # label(matrix_symm_update_diagonal) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 21 (all A all B all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) & (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(B,I,J) = a_select3(B,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(tptp_madd(A,B),I,J) = a_select3(tptp_madd(A,B),J,I))))) # label(matrix_symm_add) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 22 (all A all B all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) & (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(B,I,J) = a_select3(B,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,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].
% 0.79/1.11 23 (all A all B all N ((all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(B,I,J) = a_select3(B,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,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].
% 0.79/1.11 24 (all A all B all N all M ((all I all J (leq(n0,I) & leq(I,M) & leq(n0,J) & leq(J,M) -> a_select3(B,I,J) = a_select3(B,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,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_aba2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 25 (all A all B all C all D all E all F all N all M ((all I all J (leq(n0,I) & leq(I,M) & leq(n0,J) & leq(J,M) -> a_select3(D,I,J) = a_select3(D,J,I))) & (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(A,I,J) = a_select3(A,J,I))) & (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> a_select3(F,I,J) = a_select3(F,J,I))) -> (all I all J (leq(n0,I) & leq(I,N) & leq(n0,J) & leq(J,N) -> 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) = 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))))) # label(matrix_symm_joseph_update) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 26 (all Body sum(n0,tptp_minus_1,Body) = n0) # label(sum_plus_base) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 27 (all Body tptp_float_0_0 = sum(n0,tptp_minus_1,Body)) # label(sum_plus_base_float) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 28 (all X plus(X,n1) = succ(X)) # label(succ_plus_1_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 29 (all X plus(n1,X) = succ(X)) # label(succ_plus_1_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 32 (all X plus(X,n3) = succ(succ(succ(X)))) # label(succ_plus_3_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 33 (all X plus(n3,X) = succ(succ(succ(X)))) # label(succ_plus_3_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 34 (all X plus(X,n4) = succ(succ(succ(succ(X))))) # label(succ_plus_4_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 35 (all X plus(n4,X) = succ(succ(succ(succ(X))))) # label(succ_plus_4_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 36 (all X plus(X,n5) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 37 (all X plus(n5,X) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 38 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 40 (all X succ(pred(X)) = X) # label(succ_pred) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 42 (all X all Y (leq(succ(X),Y) -> gt(Y,X))) # label(leq_succ_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 43 (all X all Y (leq(minus(X,Y),X) -> leq(n0,Y))) # label(leq_minus) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 44 (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].
% 0.79/1.11 45 (all I all J all U all V all X all VAL all VAL2 (I != U & J = V & a_select3(X,U,V) = VAL -> a_select3(tptp_update3(X,I,J,VAL2),U,V) = VAL)) # label(sel3_update_2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 46 (all I all J all U all V all X all VAL ((all I0 all J0 (leq(n0,I0) & leq(n0,J0) & leq(I0,U) & leq(J0,V) -> a_select3(X,I0,J0) = VAL)) & leq(n0,I) & leq(I,U) & leq(n0,J) & leq(J,V) -> a_select3(tptp_update3(X,U,V,VAL),I,J) = VAL)) # label(sel3_update_3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 47 (all X all U all VAL a_select2(tptp_update2(X,U,VAL),U) = VAL) # label(sel2_update_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 48 (all I all U all X all VAL all VAL2 (I != U & a_select2(X,U) = VAL -> a_select2(tptp_update2(X,I,VAL2),U) = VAL)) # label(sel2_update_2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 49 (all I all U all X all VAL ((all I0 (leq(n0,I0) & leq(I0,U) -> a_select2(X,I0) = VAL)) & leq(n0,I) & leq(I,U) -> a_select2(tptp_update2(X,U,VAL),I) = VAL)) # label(sel2_update_3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 50 (all X (leq(n0,X) & leq(X,n4) -> X = n0 | X = n1 | X = n2 | X = n3 | X = n4)) # label(finite_domain_4) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 51 (all X (leq(n0,X) & leq(X,n5) -> X = n0 | X = n1 | X = n2 | X = n3 | X = n4 | X = n5)) # label(finite_domain_5) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 53 (all X (leq(n0,X) & leq(X,n1) -> X = n0 | X = n1)) # label(finite_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 54 (all X (leq(n0,X) & leq(X,n2) -> X = n0 | X = n1 | X = n2)) # label(finite_domain_2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 55 (all X (leq(n0,X) & leq(X,n3) -> X = n0 | X = n1 | X = n2 | X = n3)) # label(finite_domain_3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 56 -(leq(tptp_float_0_001,pv76) & leq(n1,loopcounter) & gt(n1,loopcounter) & (all A (leq(n0,A) & leq(A,n135299) -> (all B (leq(n0,B) & leq(B,n4) -> a_select3(q_init,A,B) = init)))) & (all C (leq(n0,C) & leq(C,n4) -> a_select3(center_init,C,n0) = init)) & (gt(loopcounter,n0) -> (all D (leq(n0,D) & leq(D,n4) -> a_select2(mu_init,D) = init))) & (gt(loopcounter,n0) -> (all E (leq(n0,E) & leq(E,n4) -> a_select2(rho_init,E) = init))) & (gt(loopcounter,n0) -> (all F (leq(n0,F) & leq(F,n4) -> a_select2(sigma_init,F) = init))) -> (all G (leq(n0,G) & leq(G,n4) -> a_select2(muold_init,G) = init))) # label(cl5_nebula_init_0081) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.28/8.56
% 8.28/8.56 ============================== end of process non-clausal formulas ===
% 8.28/8.56
% 8.28/8.56 ============================== PROCESS INITIAL CLAUSES ===============
% 8.28/8.56
% 8.28/8.56 ============================== PREDICATE ELIMINATION =================
% 8.28/8.56 57 lt(A,B) | -gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 8.28/8.56 58 -lt(A,B) | gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 8.28/8.56 59 geq(A,B) | -leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 8.28/8.56 60 -geq(A,B) | leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 8.28/8.56
% 8.28/8.56 ============================== end predicate elimination =============
% 8.28/8.56
% 8.28/8.56 Auto_denials: (non-Horn, no changes).
% 8.28/8.56
% 8.28/8.56 Term ordering decisions:
% 8.28/8.56 Function symbol KB weights: n0=1. n1=1. n4=1. n2=1. n3=1. n5=1. tptp_minus_1=1. n135299=1. init=1. loopcounter=1. center_init=1. mu_init=1. pv76=1. q_init=1. rho_init=1. sigma_init=1. tptp_float_0_0=1. tptp_float_0_001=1. def=1. muold_init=1. use=1. c1=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. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. trans=1. succ=1. inv=1. pred=1. a_select3=1. tptp_update2=1. sum=1. tptp_const_array2=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. tptp_update3=1. f17=1. f18=1. f27=1. f25=1. f26=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1.
% 8.28/8.57
% 8.28/8.57 ============================== end of process initial clauses ========
% 8.28/8.57
% 8.28/8.57 ============================== CLAUSES FOR SEARCH ====================
% 8.28/8.57
% 8.28/8.57 ============================== end of clauses for search =============
% 8.28/8.57
% 8.28/8.57 ============================== SEARCH ================================
% 8.28/8.57
% 8.28/8.57 % Starting search at 0.25 seconds.
% 8.28/8.57
% 8.28/8.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 579 (0.00 of 0.91 sec).
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=179.000, iters=3519
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=149.000, iters=3507
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=119.000, iters=3365
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=116.000, iters=3376
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=110.000, iters=3641
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=89.000, iters=3581
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=86.000, iters=3498
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=80.000, iters=3376
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% 8.28/8.57 Low Water (keep): wt=58.000, iters=3406
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=55.000, iters=3491
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=50.000, iters=3475
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=49.000, iters=3469
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=44.000, iters=3442
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% 8.28/8.57 Low Water (keep): wt=43.000, iters=3438
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=40.000, iters=3608
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=34.000, iters=3391
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=6292, wt=179.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=10925, wt=31.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=11051, wt=25.000
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% 8.28/8.57 Low Water (displace): id=11136, wt=22.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=11141, wt=19.000
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=32.000, iters=3348
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=31.000, iters=3370
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=28.000, iters=3333
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=14274, wt=18.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=14487, wt=17.000
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=27.000, iters=3385
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=26.000, iters=3567
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=25.000, iters=3531
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=16204, wt=16.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=16223, wt=13.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=17498, wt=11.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=17595, wt=10.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=18179, wt=7.000
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=24.000, iters=3408
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=23.000, iters=3411
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=22.000, iters=3347
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=20555, wt=6.000
% 8.28/8.57
% 8.28/8.57 Low Water (displace): id=22435, wt=5.000
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=21.000, iters=3333
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=20.000, iters=3338
% 8.28/8.57
% 8.28/8.57 Low Water (keep): wt=19.000, iters=3337
% 8.28/8.57
% 8.28/8.57 ============================== PROOF =================================
% 8.28/8.57 % SZS status Theorem
% 8.28/8.57 % SZS output start Refutation
% 8.28/8.57
% 8.28/8.57 % Proof 1 at 7.36 (+ 0.12) seconds.
% 8.28/8.57 % Length of proof is 40.
% 8.28/8.57 % Level of proof is 6.
% 8.28/8.57 % Maximum clause weight is 9.000.
% 8.28/8.57 % Given clauses 1354.
% 8.28/8.57
% 8.28/8.57 2 (all X all Y all Z (gt(X,Y) & gt(Y,Z) -> gt(X,Z))) # label(transitivity_gt) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 8.28/8.57 56 -(leq(tptp_float_0_001,pv76) & leq(n1,loopcounter) & gt(n1,loopcounter) & (all A (leq(n0,A) & leq(A,n135299) -> (all B (leq(n0,B) & leq(B,n4) -> a_select3(q_init,A,B) = init)))) & (all C (leq(n0,C) & leq(C,n4) -> a_select3(center_init,C,n0) = init)) & (gt(loopcounter,n0) -> (all D (leq(n0,D) & leq(D,n4) -> a_select2(mu_init,D) = init))) & (gt(loopcounter,n0) -> (all E (leq(n0,E) & leq(E,n4) -> a_select2(rho_init,E) = init))) & (gt(loopcounter,n0) -> (all F (leq(n0,F) & leq(F,n4) -> a_select2(sigma_init,F) = init))) -> (all G (leq(n0,G) & leq(G,n4) -> a_select2(muold_init,G) = init))) # label(cl5_nebula_init_0081) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.28/8.57 62 -gt(A,B) | -gt(B,C) | gt(A,C) # label(transitivity_gt) # label(axiom). [clausify(2)].
% 8.28/8.57 63 -gt(A,A) # label(irreflexivity_gt) # label(axiom). [clausify(3)].
% 8.28/8.57 69 leq(A,pred(B)) | -gt(B,A) # label(leq_gt_pred) # label(axiom). [clausify(10)].
% 8.28/8.57 72 -leq(A,B) | gt(succ(B),A) # label(leq_succ_gt_equiv) # label(axiom). [clausify(13)].
% 8.28/8.57 73 leq(A,B) | -gt(succ(B),A) # label(leq_succ_gt_equiv) # label(axiom). [clausify(13)].
% 8.28/8.57 284 plus(A,n2) = succ(succ(A)) # label(succ_plus_2_r) # label(axiom). [clausify(30)].
% 8.28/8.57 285 succ(succ(A)) = plus(A,n2). [copy(284),flip(a)].
% 8.28/8.57 286 plus(n2,A) = succ(succ(A)) # label(succ_plus_2_l) # label(axiom). [clausify(31)].
% 8.28/8.57 287 plus(n2,A) = plus(A,n2). [copy(286),rewrite([285(4)])].
% 8.28/8.57 301 pred(succ(A)) = A # label(pred_succ) # label(axiom). [clausify(39)].
% 8.28/8.57 304 leq(succ(A),succ(B)) | -leq(A,B) # label(leq_succ_succ) # label(axiom). [clausify(41)].
% 8.28/8.57 335 gt(n1,n0) # label(gt_1_0) # label(axiom). [assumption].
% 8.28/8.57 352 -leq(n0,A) | -leq(A,n0) | n0 = A # label(finite_domain_0) # label(axiom). [clausify(52)].
% 8.28/8.57 360 succ(n0) = n1 # label(successor_1) # label(axiom). [assumption].
% 8.28/8.57 361 succ(succ(n0)) = n2 # label(successor_2) # label(axiom). [assumption].
% 8.28/8.57 362 succ(n1) = n2. [copy(361),rewrite([360(2)])].
% 8.28/8.57 366 leq(n1,loopcounter) # label(cl5_nebula_init_0081) # label(negated_conjecture). [clausify(56)].
% 8.28/8.57 367 gt(n1,loopcounter) # label(cl5_nebula_init_0081) # label(negated_conjecture). [clausify(56)].
% 8.28/8.57 1700 -gt(A,n1) | gt(A,n0). [resolve(335,a,62,b)].
% 8.28/8.57 1765 plus(n0,n2) = n2. [para(360(a,1),285(a,1,1)),rewrite([362(2)]),flip(a)].
% 8.28/8.57 1766 pred(n1) = n0. [para(360(a,1),301(a,1,1))].
% 8.28/8.57 2094 leq(n2,succ(loopcounter)). [resolve(366,a,304,b),rewrite([362(2)])].
% 8.28/8.57 2306 gt(succ(loopcounter),n1). [resolve(366,a,72,a)].
% 8.28/8.57 2357 leq(loopcounter,n0). [resolve(367,a,69,b),rewrite([1766(3)])].
% 8.28/8.57 12579 -leq(n0,loopcounter) | loopcounter = n0. [resolve(2357,a,352,b),flip(b)].
% 8.28/8.57 14599 gt(plus(n2,loopcounter),n2). [resolve(2094,a,72,a),rewrite([285(3),287(3,R)])].
% 8.28/8.57 28989 gt(succ(loopcounter),n0). [resolve(1700,a,2306,a)].
% 8.28/8.57 29005 leq(n0,loopcounter). [resolve(28989,a,73,b)].
% 8.28/8.57 29143 loopcounter = n0. [back_unit_del(12579),unit_del(a,29005)].
% 8.28/8.57 29320 $F. [back_rewrite(14599),rewrite([29143(2),287(3),1765(3)]),unit_del(a,63)].
% 8.28/8.57
% 8.28/8.57 % SZS output end Refutation
% 8.28/8.57 ============================== end of proof ==========================
% 8.28/8.57
% 8.28/8.57 ============================== STATISTICS ============================
% 8.28/8.57
% 8.28/8.57 Given=1354. Generated=209109. Kept=29245. proofs=1.
% 8.28/8.57 Usable=1267. Sos=8757. Demods=694. Limbo=177, Disabled=19349. Hints=0.
% 8.28/8.57 Megabytes=35.07.
% 8.28/8.57 User_CPU=7.36, System_CPU=0.12, Wall_clock=7.
% 8.28/8.57
% 8.28/8.57 ============================== end of statistics =====================
% 8.28/8.57
% 8.28/8.57 ============================== end of search =========================
% 8.28/8.57
% 8.28/8.57 THEOREM PROVED
% 8.28/8.57 % SZS status Theorem
% 8.28/8.57
% 8.28/8.57 Exiting with 1 proof.
% 8.28/8.57
% 8.28/8.57 Process 19355 exit (max_proofs) Wed Jun 15 08:15:27 2022
% 8.28/8.57 Prover9 interrupted
%------------------------------------------------------------------------------