TSTP Solution File: SWV157+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 21:10:42 EDT 2022
% Result : Theorem 5.11s 5.39s
% Output : Refutation 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 13:20:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.79/1.07 ============================== Prover9 ===============================
% 0.79/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.07 Process 4216 was started by sandbox on n025.cluster.edu,
% 0.79/1.07 Wed Jun 15 13:20:56 2022
% 0.79/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4062_n025.cluster.edu".
% 0.79/1.07 ============================== end of head ===========================
% 0.79/1.07
% 0.79/1.07 ============================== INPUT =================================
% 0.79/1.07
% 0.79/1.07 % Reading from file /tmp/Prover9_4062_n025.cluster.edu
% 0.79/1.07
% 0.79/1.07 set(prolog_style_variables).
% 0.79/1.07 set(auto2).
% 0.79/1.07 % set(auto2) -> set(auto).
% 0.79/1.07 % set(auto) -> set(auto_inference).
% 0.79/1.07 % set(auto) -> set(auto_setup).
% 0.79/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.07 % set(auto) -> set(auto_limits).
% 0.79/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.07 % set(auto) -> set(auto_denials).
% 0.79/1.07 % set(auto) -> set(auto_process).
% 0.79/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.07 % set(auto2) -> assign(stats, some).
% 0.79/1.07 % set(auto2) -> clear(echo_input).
% 0.79/1.07 % set(auto2) -> set(quiet).
% 0.79/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.07 % set(auto2) -> clear(print_given).
% 0.79/1.07 assign(lrs_ticks,-1).
% 0.79/1.07 assign(sos_limit,10000).
% 0.79/1.07 assign(order,kbo).
% 0.79/1.07 set(lex_order_vars).
% 0.79/1.07 clear(print_given).
% 0.79/1.07
% 0.79/1.07 % formulas(sos). % not echoed (100 formulas)
% 0.79/1.07
% 0.79/1.07 ============================== end of input ==========================
% 0.79/1.07
% 0.79/1.07 % From the command line: assign(max_seconds, 300).
% 0.79/1.07
% 0.79/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.07
% 0.79/1.07 % Formulas that are not ordinary clauses:
% 0.79/1.07 1 (all X all Y (gt(X,Y) | gt(Y,X) | X = Y)) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 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].
% 0.79/1.07 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 4 (all X leq(X,X)) # label(reflexivity_leq) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 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].
% 0.79/1.07 6 (all X all Y (lt(X,Y) <-> gt(Y,X))) # label(lt_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 7 (all X all Y (geq(X,Y) <-> leq(Y,X))) # label(leq_geq) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 8 (all X all Y (gt(Y,X) -> leq(X,Y))) # label(leq_gt1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 11 (all X gt(succ(X),X)) # label(gt_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 12 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 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].
% 0.79/1.07 26 (all Body sum(n0,tptp_minus_1,Body) = n0) # label(sum_plus_base) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 27 (all Body tptp_float_0_0 = sum(n0,tptp_minus_1,Body)) # label(sum_plus_base_float) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 28 (all X plus(X,n1) = succ(X)) # label(succ_plus_1_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 29 (all X plus(n1,X) = succ(X)) # label(succ_plus_1_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.07 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 32 (all X plus(X,n3) = succ(succ(succ(X)))) # label(succ_plus_3_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 33 (all X plus(n3,X) = succ(succ(succ(X)))) # label(succ_plus_3_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 34 (all X plus(X,n4) = succ(succ(succ(succ(X))))) # label(succ_plus_4_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 35 (all X plus(n4,X) = succ(succ(succ(succ(X))))) # label(succ_plus_4_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 36 (all X plus(X,n5) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_r) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 37 (all X plus(n5,X) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_l) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 38 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 40 (all X succ(pred(X)) = X) # label(succ_pred) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 42 (all X all Y (leq(succ(X),Y) -> gt(Y,X))) # label(leq_succ_gt) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 43 (all X all Y (leq(minus(X,Y),X) -> leq(n0,Y))) # label(leq_minus) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 53 (all X (leq(n0,X) & leq(X,n1) -> X = n0 | X = n1)) # label(finite_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.08 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].
% 0.79/1.08 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].
% 0.79/1.08 56 -(pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) & leq(n0,pv10) & leq(n0,pv47) & leq(pv10,n135299) & leq(pv47,n4) & (all A (leq(n0,A) & leq(A,pred(pv47)) -> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))) & (all B (leq(n0,B) & leq(B,pred(pv10)) -> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1)) -> (all C (leq(n0,C) & leq(C,pv47) -> (pv47 != C -> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))))) # label(cl5_nebula_norm_0007) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.31/3.58
% 3.31/3.58 ============================== end of process non-clausal formulas ===
% 3.31/3.58
% 3.31/3.58 ============================== PROCESS INITIAL CLAUSES ===============
% 3.31/3.58
% 3.31/3.58 ============================== PREDICATE ELIMINATION =================
% 3.31/3.58 57 lt(A,B) | -gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 3.31/3.58 58 -lt(A,B) | gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 3.31/3.58 59 geq(A,B) | -leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 3.31/3.58 60 -geq(A,B) | leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 3.31/3.58
% 3.31/3.58 ============================== end predicate elimination =============
% 3.31/3.58
% 3.31/3.58 Auto_denials: (non-Horn, no changes).
% 3.31/3.58
% 3.31/3.58 Term ordering decisions:
% 3.31/3.58 Function symbol KB weights: n0=1. n1=1. n2=1. n4=1. n3=1. n5=1. tptp_sum_index=1. tptp_minus_1=1. tptp_minus_2=1. pv10=1. n135299=1. sigma=1. mu=1. x=1. pv47=1. rho=1. tptp_pi=1. q=1. pv84=1. tptp_float_0_0=1. def=1. use=1. c1=1. tptp_mmul=1. tptp_madd=1. tptp_msub=1. a_select2=1. times=1. divide=1. plus=1. minus=1. dim=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. exp=1. sqrt=1. a_select3=1. sum=1. tptp_update2=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.
% 3.31/3.58
% 3.31/3.58 ============================== end of process initial clauses ========
% 3.31/3.58
% 3.31/3.58 ============================== CLAUSES FOR SEARCH ====================
% 3.31/3.58
% 3.31/3.58 ============================== end of clauses for search =============
% 3.31/3.58
% 3.31/3.58 ============================== SEARCH ================================
% 3.31/3.58
% 3.31/3.58 % Starting search at 0.26 seconds.
% 3.31/3.58
% 3.31/3.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 863 (0.00 of 1.20 sec).
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=176.000, iters=3471
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=146.000, iters=3417
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=119.000, iters=3498
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=113.000, iters=3518
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=89.000, iters=3338
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=83.000, iters=3659
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=58.000, iters=3346
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=53.000, iters=3337
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=49.000, iters=3484
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=43.000, iters=3368
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=40.000, iters=3383
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=34.000, iters=3335
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=3909, wt=179.000
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=10936, wt=31.000
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=10982, wt=28.000
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=11035, wt=25.000
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=11071, wt=22.000
% 3.31/3.58
% 3.31/3.58 Low Water (displace): id=11118, wt=19.000
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=32.000, iters=3337
% 3.31/3.58
% 3.31/3.58 Low Water (keep): wt=31.000, iters=3353
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=28.000, iters=3358
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=14182, wt=18.000
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=14424, wt=17.000
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=14517, wt=16.000
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=27.000, iters=3352
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=26.000, iters=3435
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=25.000, iters=3406
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=16909, wt=13.000
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=18353, wt=10.000
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=18970, wt=7.000
% 5.11/5.39
% 5.11/5.39 Low Water (displace): id=19154, wt=6.000
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=24.000, iters=3358
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=23.000, iters=3355
% 5.11/5.39
% 5.11/5.39 Low Water (keep): wt=22.000, iters=3430
% 5.11/5.39
% 5.11/5.39 ============================== PROOF =================================
% 5.11/5.39 % SZS status Theorem
% 5.11/5.39 % SZS output start Refutation
% 5.11/5.39
% 5.11/5.39 % Proof 1 at 4.27 (+ 0.07) seconds.
% 5.11/5.39 % Length of proof is 17.
% 5.11/5.39 % Level of proof is 5.
% 5.11/5.39 % Maximum clause weight is 53.000.
% 5.11/5.39 % Given clauses 958.
% 5.11/5.39
% 5.11/5.39 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 5.11/5.39 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 5.11/5.39 56 -(pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) & leq(n0,pv10) & leq(n0,pv47) & leq(pv10,n135299) & leq(pv47,n4) & (all A (leq(n0,A) & leq(A,pred(pv47)) -> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))) & (all B (leq(n0,B) & leq(B,pred(pv10)) -> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1)) -> (all C (leq(n0,C) & leq(C,pv47) -> (pv47 != C -> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))))) # label(cl5_nebula_norm_0007) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.11/5.39 67 -leq(A,B) | B = A | gt(B,A) # label(leq_gt2) # label(axiom). [clausify(9)].
% 5.11/5.39 69 leq(A,pred(B)) | -gt(B,A) # label(leq_gt_pred) # label(axiom). [clausify(10)].
% 5.11/5.39 373 sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) = pv84 # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 378 -leq(n0,A) | -leq(A,pred(pv47)) | divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) = a_select3(q,pv10,A) # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 379 -leq(n0,A) | -leq(A,pred(pv47)) | divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),pv84) = a_select3(q,pv10,A). [copy(378),rewrite([373(80)])].
% 5.11/5.39 381 leq(n0,c1) # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 382 leq(c1,pv47) # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 383 pv47 != c1 # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 384 c1 != pv47. [copy(383),flip(a)].
% 5.11/5.39 385 divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,c1)),minus(a_select2(x,pv10),a_select2(mu,c1))),tptp_minus_2),times(a_select2(sigma,c1),a_select2(sigma,c1)))),a_select2(rho,c1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,c1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) != a_select3(q,pv10,c1) # label(cl5_nebula_norm_0007) # label(negated_conjecture). [clausify(56)].
% 5.11/5.39 386 divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,c1)),minus(a_select2(x,pv10),a_select2(mu,c1))),tptp_minus_2),times(a_select2(sigma,c1),a_select2(sigma,c1)))),a_select2(rho,c1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,c1))),pv84) != a_select3(q,pv10,c1). [copy(385),rewrite([373(81)])].
% 5.11/5.39 4854 gt(pv47,c1). [resolve(382,a,67,a),flip(a),unit_del(a,384)].
% 5.11/5.39 13661 leq(c1,pred(pv47)). [resolve(4854,a,69,b)].
% 5.11/5.39 21312 $F. [resolve(13661,a,379,b),unit_del(a,381),unit_del(b,386)].
% 5.11/5.39
% 5.11/5.39 % SZS output end Refutation
% 5.11/5.39 ============================== end of proof ==========================
% 5.11/5.39
% 5.11/5.39 ============================== STATISTICS ============================
% 5.11/5.39
% 5.11/5.39 Given=958. Generated=88102. Kept=21234. proofs=1.
% 5.11/5.39 Usable=957. Sos=9999. Demods=548. Limbo=57, Disabled=10534. Hints=0.
% 5.11/5.39 Megabytes=31.93.
% 5.11/5.39 User_CPU=4.27, System_CPU=0.07, Wall_clock=4.
% 5.11/5.39
% 5.11/5.39 ============================== end of statistics =====================
% 5.11/5.39
% 5.11/5.39 ============================== end of search =========================
% 5.11/5.39
% 5.11/5.39 THEOREM PROVED
% 5.11/5.39 % SZS status Theorem
% 5.11/5.39
% 5.11/5.39 Exiting with 1 proof.
% 5.11/5.39
% 5.11/5.39 Process 4216 exit (max_proofs) Wed Jun 15 13:21:00 2022
% 5.11/5.39 Prover9 interrupted
%------------------------------------------------------------------------------