TSTP Solution File: SWV092+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV092+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 21:10:30 EDT 2022
% Result : Theorem 1.71s 2.03s
% Output : Refutation 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SWV092+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Tue Jun 14 20:40:43 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.59/0.87 ============================== Prover9 ===============================
% 0.59/0.87 Prover9 (32) version 2009-11A, November 2009.
% 0.59/0.87 Process 18130 was started by sandbox on n032.cluster.edu,
% 0.59/0.87 Tue Jun 14 20:40:43 2022
% 0.59/0.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17976_n032.cluster.edu".
% 0.59/0.87 ============================== end of head ===========================
% 0.59/0.87
% 0.59/0.87 ============================== INPUT =================================
% 0.59/0.87
% 0.59/0.87 % Reading from file /tmp/Prover9_17976_n032.cluster.edu
% 0.59/0.87
% 0.59/0.87 set(prolog_style_variables).
% 0.59/0.87 set(auto2).
% 0.59/0.87 % set(auto2) -> set(auto).
% 0.59/0.87 % set(auto) -> set(auto_inference).
% 0.59/0.87 % set(auto) -> set(auto_setup).
% 0.59/0.87 % set(auto_setup) -> set(predicate_elim).
% 0.59/0.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.59/0.87 % set(auto) -> set(auto_limits).
% 0.59/0.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.59/0.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.59/0.87 % set(auto) -> set(auto_denials).
% 0.59/0.87 % set(auto) -> set(auto_process).
% 0.59/0.87 % set(auto2) -> assign(new_constants, 1).
% 0.59/0.87 % set(auto2) -> assign(fold_denial_max, 3).
% 0.59/0.87 % set(auto2) -> assign(max_weight, "200.000").
% 0.59/0.87 % set(auto2) -> assign(max_hours, 1).
% 0.59/0.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.59/0.87 % set(auto2) -> assign(max_seconds, 0).
% 0.59/0.87 % set(auto2) -> assign(max_minutes, 5).
% 0.59/0.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.59/0.87 % set(auto2) -> set(sort_initial_sos).
% 0.59/0.87 % set(auto2) -> assign(sos_limit, -1).
% 0.59/0.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.59/0.87 % set(auto2) -> assign(max_megs, 400).
% 0.59/0.87 % set(auto2) -> assign(stats, some).
% 0.59/0.87 % set(auto2) -> clear(echo_input).
% 0.59/0.87 % set(auto2) -> set(quiet).
% 0.59/0.87 % set(auto2) -> clear(print_initial_clauses).
% 0.59/0.87 % set(auto2) -> clear(print_given).
% 0.59/0.87 assign(lrs_ticks,-1).
% 0.59/0.87 assign(sos_limit,10000).
% 0.59/0.87 assign(order,kbo).
% 0.59/0.87 set(lex_order_vars).
% 0.59/0.87 clear(print_given).
% 0.59/0.87
% 0.59/0.87 % formulas(sos). % not echoed (85 formulas)
% 0.59/0.87
% 0.59/0.87 ============================== end of input ==========================
% 0.59/0.87
% 0.59/0.87 % From the command line: assign(max_seconds, 300).
% 0.59/0.87
% 0.59/0.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.59/0.87
% 0.59/0.87 % Formulas that are not ordinary clauses:
% 0.59/0.87 1 (all X all Y (gt(X,Y) | gt(Y,X) | X = Y)) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 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].
% 0.59/0.87 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 4 (all X leq(X,X)) # label(reflexivity_leq) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 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].
% 0.59/0.87 6 (all X all Y (lt(X,Y) <-> gt(Y,X))) # label(lt_gt) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 7 (all X all Y (geq(X,Y) <-> leq(Y,X))) # label(leq_geq) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 8 (all X all Y (gt(Y,X) -> leq(X,Y))) # label(leq_gt1) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 11 (all X gt(succ(X),X)) # label(gt_succ) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 12 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 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].
% 0.59/0.87 26 (all Body sum(n0,tptp_minus_1,Body) = n0) # label(sum_plus_base) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 27 (all Body tptp_float_0_0 = sum(n0,tptp_minus_1,Body)) # label(sum_plus_base_float) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 28 (all X plus(X,n1) = succ(X)) # label(succ_plus_1_r) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 29 (all X plus(n1,X) = succ(X)) # label(succ_plus_1_l) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.87 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 32 (all X plus(X,n3) = succ(succ(succ(X)))) # label(succ_plus_3_r) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 33 (all X plus(n3,X) = succ(succ(succ(X)))) # label(succ_plus_3_l) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 34 (all X plus(X,n4) = succ(succ(succ(succ(X))))) # label(succ_plus_4_r) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 35 (all X plus(n4,X) = succ(succ(succ(succ(X))))) # label(succ_plus_4_l) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 36 (all X plus(X,n5) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_r) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 37 (all X plus(n5,X) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_l) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 38 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 40 (all X succ(pred(X)) = X) # label(succ_pred) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 42 (all X all Y (leq(succ(X),Y) -> gt(Y,X))) # label(leq_succ_gt) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 43 (all X all Y (leq(minus(X,Y),X) -> leq(n0,Y))) # label(leq_minus) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 53 (all X (leq(n0,X) & leq(X,n1) -> X = n0 | X = n1)) # label(finite_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.59/0.88 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].
% 0.59/0.88 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].
% 0.59/0.88 56 -(a_select2(rho_defuse,n0) = use & a_select2(rho_defuse,n1) = use & a_select2(rho_defuse,n2) = use & a_select2(sigma_defuse,n0) = use & a_select2(sigma_defuse,n1) = use & a_select2(sigma_defuse,n2) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n4) = use & a_select2(sigma_defuse,n5) = use & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & a_select3(u_defuse,n2,n0) = use & a_select2(xinit_defuse,n3) = use & a_select2(xinit_defuse,n4) = use & a_select2(xinit_defuse,n5) = use & a_select2(xinit_mean_defuse,n0) = use & a_select2(xinit_mean_defuse,n1) = use & a_select2(xinit_mean_defuse,n2) = use & a_select2(xinit_mean_defuse,n3) = use & a_select2(xinit_mean_defuse,n4) = use & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & a_select2(xinit_noise_defuse,n1) = use & a_select2(xinit_noise_defuse,n2) = use & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n4) = use & a_select2(xinit_noise_defuse,n5) = use -> a_select2(rho_defuse,n0) = use & a_select2(rho_defuse,n1) = use & a_select2(rho_defuse,n2) = use & a_select2(sigma_defuse,n0) = use & a_select2(sigma_defuse,n1) = use & a_select2(sigma_defuse,n2) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n4) = use & a_select2(sigma_defuse,n5) = use & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & a_select3(u_defuse,n2,n0) = use & a_select2(xinit_defuse,n3) = use & a_select2(xinit_defuse,n4) = use & a_select2(xinit_defuse,n5) = use & a_select2(xinit_mean_defuse,n0) = use & a_select2(xinit_mean_defuse,n1) = use & a_select2(xinit_mean_defuse,n2) = use & a_select2(xinit_mean_defuse,n3) = use & a_select2(xinit_mean_defuse,n4) = use & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & a_select2(xinit_noise_defuse,n1) = use & a_select2(xinit_noise_defuse,n2) = use & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n4) = use & a_select2(xinit_noise_defuse,n5) = use & (all A all B (leq(n0,A) & leq(n0,B) & leq(A,n2) & leq(B,minus(n0,n1)) -> a_select3(u_defuse,A,B) = use & a_select3(z_defuse,A,B) = use))) # label(quaternion_ds1_inuse_0004) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.71/2.02
% 1.71/2.02 ============================== end of process non-clausal formulas ===
% 1.71/2.02
% 1.71/2.02 ============================== PROCESS INITIAL CLAUSES ===============
% 1.71/2.02
% 1.71/2.02 ============================== PREDICATE ELIMINATION =================
% 1.71/2.02 57 lt(A,B) | -gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 1.71/2.02 58 -lt(A,B) | gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 1.71/2.02 59 geq(A,B) | -leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 1.71/2.02 60 -geq(A,B) | leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 1.71/2.02
% 1.71/2.02 ============================== end predicate elimination =============
% 1.71/2.02
% 1.71/2.02 Auto_denials: (non-Horn, no changes).
% 1.71/2.02
% 1.71/2.02 Term ordering decisions:
% 1.71/2.02 Function symbol KB weights: n0=1. use=1. n1=1. n2=1. n3=1. n4=1. n5=1. sigma_defuse=1. xinit_mean_defuse=1. xinit_noise_defuse=1. rho_defuse=1. u_defuse=1. xinit_defuse=1. tptp_minus_1=1. tptp_float_0_0=1. def=1. z_defuse=1. c1=1. c2=1. tptp_mmul=1. tptp_madd=1. a_select2=1. tptp_msub=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.
% 1.71/2.03
% 1.71/2.03 ============================== end of process initial clauses ========
% 1.71/2.03
% 1.71/2.03 ============================== CLAUSES FOR SEARCH ====================
% 1.71/2.03
% 1.71/2.03 ============================== end of clauses for search =============
% 1.71/2.03
% 1.71/2.03 ============================== SEARCH ================================
% 1.71/2.03
% 1.71/2.03 % Starting search at 0.21 seconds.
% 1.71/2.03
% 1.71/2.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 623 (0.00 of 0.90 sec).
% 1.71/2.03
% 1.71/2.03 ============================== PROOF =================================
% 1.71/2.03 % SZS status Theorem
% 1.71/2.03 % SZS output start Refutation
% 1.71/2.03
% 1.71/2.03 % Proof 1 at 1.16 (+ 0.02) seconds.
% 1.71/2.03 % Length of proof is 52.
% 1.71/2.03 % Level of proof is 6.
% 1.71/2.03 % Maximum clause weight is 9.000.
% 1.71/2.03 % Given clauses 811.
% 1.71/2.03
% 1.71/2.03 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 12 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 38 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 1.71/2.03 56 -(a_select2(rho_defuse,n0) = use & a_select2(rho_defuse,n1) = use & a_select2(rho_defuse,n2) = use & a_select2(sigma_defuse,n0) = use & a_select2(sigma_defuse,n1) = use & a_select2(sigma_defuse,n2) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n4) = use & a_select2(sigma_defuse,n5) = use & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & a_select3(u_defuse,n2,n0) = use & a_select2(xinit_defuse,n3) = use & a_select2(xinit_defuse,n4) = use & a_select2(xinit_defuse,n5) = use & a_select2(xinit_mean_defuse,n0) = use & a_select2(xinit_mean_defuse,n1) = use & a_select2(xinit_mean_defuse,n2) = use & a_select2(xinit_mean_defuse,n3) = use & a_select2(xinit_mean_defuse,n4) = use & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & a_select2(xinit_noise_defuse,n1) = use & a_select2(xinit_noise_defuse,n2) = use & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n4) = use & a_select2(xinit_noise_defuse,n5) = use -> a_select2(rho_defuse,n0) = use & a_select2(rho_defuse,n1) = use & a_select2(rho_defuse,n2) = use & a_select2(sigma_defuse,n0) = use & a_select2(sigma_defuse,n1) = use & a_select2(sigma_defuse,n2) = use & a_select2(sigma_defuse,n3) = use & a_select2(sigma_defuse,n4) = use & a_select2(sigma_defuse,n5) = use & a_select3(u_defuse,n0,n0) = use & a_select3(u_defuse,n1,n0) = use & a_select3(u_defuse,n2,n0) = use & a_select2(xinit_defuse,n3) = use & a_select2(xinit_defuse,n4) = use & a_select2(xinit_defuse,n5) = use & a_select2(xinit_mean_defuse,n0) = use & a_select2(xinit_mean_defuse,n1) = use & a_select2(xinit_mean_defuse,n2) = use & a_select2(xinit_mean_defuse,n3) = use & a_select2(xinit_mean_defuse,n4) = use & a_select2(xinit_mean_defuse,n5) = use & a_select2(xinit_noise_defuse,n0) = use & a_select2(xinit_noise_defuse,n1) = use & a_select2(xinit_noise_defuse,n2) = use & a_select2(xinit_noise_defuse,n3) = use & a_select2(xinit_noise_defuse,n4) = use & a_select2(xinit_noise_defuse,n5) = use & (all A all B (leq(n0,A) & leq(n0,B) & leq(A,n2) & leq(B,minus(n0,n1)) -> a_select3(u_defuse,A,B) = use & a_select3(z_defuse,A,B) = use))) # label(quaternion_ds1_inuse_0004) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.71/2.03 63 -gt(A,A) # label(irreflexivity_gt) # label(axiom). [clausify(3)].
% 1.71/2.03 71 -leq(A,B) | leq(A,succ(B)) # label(leq_succ) # label(axiom). [clausify(12)].
% 1.71/2.03 72 -leq(A,B) | gt(succ(B),A) # label(leq_succ_gt_equiv) # label(axiom). [clausify(13)].
% 1.71/2.03 281 succ(tptp_minus_1) = n0 # label(succ_tptp_minus_1) # label(axiom). [assumption].
% 1.71/2.03 300 minus(A,n1) = pred(A) # label(pred_minus_1) # label(axiom). [clausify(38)].
% 1.71/2.03 301 pred(succ(A)) = A # label(pred_succ) # label(axiom). [clausify(39)].
% 1.71/2.03 344 -leq(n0,A) | -leq(A,n0) | n0 = A # label(finite_domain_0) # label(axiom). [clausify(52)].
% 1.71/2.03 357 a_select2(rho_defuse,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 358 a_select2(rho_defuse,n1) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 359 a_select2(rho_defuse,n2) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 360 a_select2(sigma_defuse,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 361 a_select2(sigma_defuse,n1) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 362 a_select2(sigma_defuse,n2) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 363 a_select2(sigma_defuse,n3) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 364 a_select2(sigma_defuse,n4) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 365 a_select2(sigma_defuse,n5) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 366 a_select3(u_defuse,n0,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 367 a_select3(u_defuse,n1,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 368 a_select3(u_defuse,n2,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 369 a_select2(xinit_defuse,n3) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 370 a_select2(xinit_defuse,n4) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 371 a_select2(xinit_defuse,n5) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 372 a_select2(xinit_mean_defuse,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 373 a_select2(xinit_mean_defuse,n1) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 374 a_select2(xinit_mean_defuse,n2) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 375 a_select2(xinit_mean_defuse,n3) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 376 a_select2(xinit_mean_defuse,n4) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 377 a_select2(xinit_mean_defuse,n5) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 378 a_select2(xinit_noise_defuse,n0) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 379 a_select2(xinit_noise_defuse,n1) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 380 a_select2(xinit_noise_defuse,n2) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 381 a_select2(xinit_noise_defuse,n3) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 382 a_select2(xinit_noise_defuse,n4) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 383 a_select2(xinit_noise_defuse,n5) = use # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 386 a_select2(rho_defuse,n0) != use | a_select2(rho_defuse,n1) != use | a_select2(rho_defuse,n2) != use | a_select2(sigma_defuse,n0) != use | a_select2(sigma_defuse,n1) != use | a_select2(sigma_defuse,n2) != use | a_select2(sigma_defuse,n3) != use | a_select2(sigma_defuse,n4) != use | a_select2(sigma_defuse,n5) != use | a_select3(u_defuse,n0,n0) != use | a_select3(u_defuse,n1,n0) != use | a_select3(u_defuse,n2,n0) != use | a_select2(xinit_defuse,n3) != use | a_select2(xinit_defuse,n4) != use | a_select2(xinit_defuse,n5) != use | a_select2(xinit_mean_defuse,n0) != use | a_select2(xinit_mean_defuse,n1) != use | a_select2(xinit_mean_defuse,n2) != use | a_select2(xinit_mean_defuse,n3) != use | a_select2(xinit_mean_defuse,n4) != use | a_select2(xinit_mean_defuse,n5) != use | a_select2(xinit_noise_defuse,n0) != use | a_select2(xinit_noise_defuse,n1) != use | a_select2(xinit_noise_defuse,n2) != use | a_select2(xinit_noise_defuse,n3) != use | a_select2(xinit_noise_defuse,n4) != use | a_select2(xinit_noise_defuse,n5) != use | leq(n0,c2) # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 387 leq(n0,c2). [copy(386),rewrite([357(3),358(6),359(9),360(12),361(15),362(18),363(21),364(24),365(27),366(31),367(34),368(37),369(39),370(42),371(45),372(48),373(51),374(54),375(57),376(60),377(63),378(66),379(69),380(72),381(75),382(78),383(81)]),xx(a),xx(b),xx(c),xx(d),xx(e),xx(f),xx(g),xx(h),xx(i),xx(j),xx(k),xx(l),xx(m),xx(n),xx(o),xx(p),xx(q),xx(r),xx(s),xx(t),xx(u),xx(v),xx(w),xx(x),xx(y),xx(z),xx(A)].
% 1.71/2.03 390 a_select2(rho_defuse,n0) != use | a_select2(rho_defuse,n1) != use | a_select2(rho_defuse,n2) != use | a_select2(sigma_defuse,n0) != use | a_select2(sigma_defuse,n1) != use | a_select2(sigma_defuse,n2) != use | a_select2(sigma_defuse,n3) != use | a_select2(sigma_defuse,n4) != use | a_select2(sigma_defuse,n5) != use | a_select3(u_defuse,n0,n0) != use | a_select3(u_defuse,n1,n0) != use | a_select3(u_defuse,n2,n0) != use | a_select2(xinit_defuse,n3) != use | a_select2(xinit_defuse,n4) != use | a_select2(xinit_defuse,n5) != use | a_select2(xinit_mean_defuse,n0) != use | a_select2(xinit_mean_defuse,n1) != use | a_select2(xinit_mean_defuse,n2) != use | a_select2(xinit_mean_defuse,n3) != use | a_select2(xinit_mean_defuse,n4) != use | a_select2(xinit_mean_defuse,n5) != use | a_select2(xinit_noise_defuse,n0) != use | a_select2(xinit_noise_defuse,n1) != use | a_select2(xinit_noise_defuse,n2) != use | a_select2(xinit_noise_defuse,n3) != use | a_select2(xinit_noise_defuse,n4) != use | a_select2(xinit_noise_defuse,n5) != use | leq(c2,minus(n0,n1)) # label(quaternion_ds1_inuse_0004) # label(negated_conjecture). [clausify(56)].
% 1.71/2.03 391 leq(c2,pred(n0)). [copy(390),rewrite([357(3),358(6),359(9),360(12),361(15),362(18),363(21),364(24),365(27),366(31),367(34),368(37),369(39),370(42),371(45),372(48),373(51),374(54),375(57),376(60),377(63),378(66),379(69),380(72),381(75),382(78),383(81),300(85)]),xx(a),xx(b),xx(c),xx(d),xx(e),xx(f),xx(g),xx(h),xx(i),xx(j),xx(k),xx(l),xx(m),xx(n),xx(o),xx(p),xx(q),xx(r),xx(s),xx(t),xx(u),xx(v),xx(w),xx(x),xx(y),xx(z),xx(A)].
% 1.71/2.03 1581 pred(n0) = tptp_minus_1. [para(281(a,1),301(a,1,1))].
% 1.71/2.03 1586 leq(c2,tptp_minus_1). [back_rewrite(391),rewrite([1581(3)])].
% 1.71/2.03 2575 -leq(c2,n0) | c2 = n0. [resolve(387,a,344,a),flip(b)].
% 1.71/2.03 4499 gt(n0,c2). [resolve(1586,a,72,a),rewrite([281(2)])].
% 1.71/2.03 4500 leq(c2,n0). [resolve(1586,a,71,a),rewrite([281(3)])].
% 1.71/2.03 4730 c2 = n0. [back_unit_del(2575),unit_del(a,4500)].
% 1.71/2.03 4738 $F. [back_rewrite(4499),rewrite([4730(2)]),unit_del(a,63)].
% 1.71/2.03
% 1.71/2.03 % SZS output end Refutation
% 1.71/2.03 ============================== end of proof ==========================
% 1.71/2.03
% 1.71/2.03 ============================== STATISTICS ============================
% 1.71/2.03
% 1.71/2.03 Given=811. Generated=12245. Kept=4659. proofs=1.
% 1.71/2.03 Usable=811. Sos=3362. Demods=95. Limbo=8, Disabled=797. Hints=0.
% 1.71/2.03 Megabytes=13.19.
% 1.71/2.03 User_CPU=1.16, System_CPU=0.02, Wall_clock=2.
% 1.71/2.03
% 1.71/2.03 ============================== end of statistics =====================
% 1.71/2.03
% 1.71/2.03 ============================== end of search =========================
% 1.71/2.03
% 1.71/2.03 THEOREM PROVED
% 1.71/2.03 % SZS status Theorem
% 1.71/2.03
% 1.71/2.03 Exiting with 1 proof.
% 1.71/2.03
% 1.71/2.03 Process 18130 exit (max_proofs) Tue Jun 14 20:40:45 2022
% 1.71/2.03 Prover9 interrupted
%------------------------------------------------------------------------------