TSTP Solution File: SWV142+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 21:10:39 EDT 2022
% Result : Theorem 5.83s 6.08s
% Output : Refutation 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 14:27:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.06 ============================== Prover9 ===============================
% 0.44/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.06 Process 17673 was started by sandbox2 on n018.cluster.edu,
% 0.44/1.06 Tue Jun 14 14:27:29 2022
% 0.44/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17520_n018.cluster.edu".
% 0.44/1.06 ============================== end of head ===========================
% 0.44/1.06
% 0.44/1.06 ============================== INPUT =================================
% 0.44/1.06
% 0.44/1.06 % Reading from file /tmp/Prover9_17520_n018.cluster.edu
% 0.44/1.06
% 0.44/1.06 set(prolog_style_variables).
% 0.44/1.06 set(auto2).
% 0.44/1.06 % set(auto2) -> set(auto).
% 0.44/1.06 % set(auto) -> set(auto_inference).
% 0.44/1.06 % set(auto) -> set(auto_setup).
% 0.44/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.06 % set(auto) -> set(auto_limits).
% 0.44/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.06 % set(auto) -> set(auto_denials).
% 0.44/1.06 % set(auto) -> set(auto_process).
% 0.44/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.06 % set(auto2) -> assign(stats, some).
% 0.44/1.06 % set(auto2) -> clear(echo_input).
% 0.44/1.06 % set(auto2) -> set(quiet).
% 0.44/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.06 % set(auto2) -> clear(print_given).
% 0.44/1.06 assign(lrs_ticks,-1).
% 0.44/1.06 assign(sos_limit,10000).
% 0.44/1.06 assign(order,kbo).
% 0.44/1.06 set(lex_order_vars).
% 0.44/1.06 clear(print_given).
% 0.44/1.06
% 0.44/1.06 % formulas(sos). % not echoed (85 formulas)
% 0.44/1.06
% 0.44/1.06 ============================== end of input ==========================
% 0.44/1.06
% 0.44/1.06 % From the command line: assign(max_seconds, 300).
% 0.44/1.06
% 0.44/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.06
% 0.44/1.06 % Formulas that are not ordinary clauses:
% 0.44/1.06 1 (all X all Y (gt(X,Y) | gt(Y,X) | X = Y)) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 4 (all X leq(X,X)) # label(reflexivity_leq) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 6 (all X all Y (lt(X,Y) <-> gt(Y,X))) # label(lt_gt) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 7 (all X all Y (geq(X,Y) <-> leq(Y,X))) # label(leq_geq) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 8 (all X all Y (gt(Y,X) -> leq(X,Y))) # label(leq_gt1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 10 (all X all Y (leq(X,pred(Y)) <-> gt(Y,X))) # label(leq_gt_pred) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 11 (all X gt(succ(X),X)) # label(gt_succ) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 12 (all X all Y (leq(X,Y) -> leq(X,succ(Y)))) # label(leq_succ) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 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].
% 0.44/1.06 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].
% 0.44/1.06 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 26 (all Body sum(n0,tptp_minus_1,Body) = n0) # label(sum_plus_base) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 27 (all Body tptp_float_0_0 = sum(n0,tptp_minus_1,Body)) # label(sum_plus_base_float) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 28 (all X plus(X,n1) = succ(X)) # label(succ_plus_1_r) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 29 (all X plus(n1,X) = succ(X)) # label(succ_plus_1_l) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 32 (all X plus(X,n3) = succ(succ(succ(X)))) # label(succ_plus_3_r) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 33 (all X plus(n3,X) = succ(succ(succ(X)))) # label(succ_plus_3_l) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 34 (all X plus(X,n4) = succ(succ(succ(succ(X))))) # label(succ_plus_4_r) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 35 (all X plus(n4,X) = succ(succ(succ(succ(X))))) # label(succ_plus_4_l) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 36 (all X plus(X,n5) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_r) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 37 (all X plus(n5,X) = succ(succ(succ(succ(succ(X)))))) # label(succ_plus_5_l) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 38 (all X minus(X,n1) = pred(X)) # label(pred_minus_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 39 (all X pred(succ(X)) = X) # label(pred_succ) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 40 (all X succ(pred(X)) = X) # label(succ_pred) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 42 (all X all Y (leq(succ(X),Y) -> gt(Y,X))) # label(leq_succ_gt) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 43 (all X all Y (leq(minus(X,Y),X) -> leq(n0,Y))) # label(leq_minus) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 52 (all X (leq(n0,X) & leq(X,n0) -> X = n0)) # label(finite_domain_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 53 (all X (leq(n0,X) & leq(X,n1) -> X = n0 | X = n1)) # label(finite_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 56 -(leq(tptp_float_0_001,pv1341) & leq(n1,loopcounter) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_best7)) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_sworst7)) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_worst7)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_best7,n3)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_sworst7,n3)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_worst7,n3)) & (gt(loopcounter,n0) -> leq(n0,s_best7)) & (gt(loopcounter,n0) -> leq(n0,s_sworst7)) & (gt(loopcounter,n0) -> leq(n0,s_worst7)) & (gt(loopcounter,n0) -> leq(s_best7,n3)) & (gt(loopcounter,n0) -> leq(s_sworst7,n3)) & (gt(loopcounter,n0) -> leq(s_worst7,n3)) -> leq(s_best7,n3)) # label(gauss_array_0012) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.83/6.08
% 5.83/6.08 ============================== end of process non-clausal formulas ===
% 5.83/6.08
% 5.83/6.08 ============================== PROCESS INITIAL CLAUSES ===============
% 5.83/6.08
% 5.83/6.08 ============================== PREDICATE ELIMINATION =================
% 5.83/6.08 57 lt(A,B) | -gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 5.83/6.08 58 -lt(A,B) | gt(B,A) # label(lt_gt) # label(axiom). [clausify(6)].
% 5.83/6.08 59 geq(A,B) | -leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 5.83/6.08 60 -geq(A,B) | leq(B,A) # label(leq_geq) # label(axiom). [clausify(7)].
% 5.83/6.08
% 5.83/6.08 ============================== end predicate elimination =============
% 5.83/6.08
% 5.83/6.08 Auto_denials: (non-Horn, no changes).
% 5.83/6.08
% 5.83/6.08 Term ordering decisions:
% 5.83/6.08 Function symbol KB weights: n0=1. n1=1. n3=1. n2=1. n4=1. n5=1. tptp_minus_1=1. loopcounter=1. s_best7=1. s_sworst7=1. s_worst7=1. pv1341=1. tptp_float_0_0=1. tptp_float_0_001=1. def=1. use=1. tptp_mmul=1. tptp_madd=1. tptp_msub=1. plus=1. a_select2=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.
% 5.83/6.08
% 5.83/6.08 ============================== end of process initial clauses ========
% 5.83/6.08
% 5.83/6.08 ============================== CLAUSES FOR SEARCH ====================
% 5.83/6.08
% 5.83/6.08 ============================== end of clauses for search =============
% 5.83/6.08
% 5.83/6.08 ============================== SEARCH ================================
% 5.83/6.08
% 5.83/6.08 % Starting search at 0.24 seconds.
% 5.83/6.08
% 5.83/6.08 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 226 (0.00 of 0.65 sec).
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=173.000, iters=3433
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=143.000, iters=3335
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=140.000, iters=3551
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=119.000, iters=3536
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=110.000, iters=3468
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=89.000, iters=3378
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=86.000, iters=3726
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=61.000, iters=3334
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=50.000, iters=3419
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=46.000, iters=3344
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=40.000, iters=3416
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=37.000, iters=3428
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=34.000, iters=3338
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=6402, wt=179.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=10922, wt=31.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=10923, wt=30.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=10927, wt=28.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=10930, wt=27.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=11161, wt=23.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=11777, wt=22.000
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=33.000, iters=3338
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=32.000, iters=3355
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=12019, wt=21.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=12165, wt=20.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=12298, wt=19.000
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=31.000, iters=3336
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=30.000, iters=3346
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=28.000, iters=3340
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=14403, wt=17.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=14527, wt=16.000
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=27.000, iters=3341
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=26.000, iters=3340
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=25.000, iters=3355
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=16563, wt=15.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=16646, wt=13.000
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=24.000, iters=3338
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=17452, wt=11.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=17818, wt=8.000
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=23.000, iters=3358
% 5.83/6.08
% 5.83/6.08 Low Water (keep): wt=22.000, iters=3353
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=20073, wt=7.000
% 5.83/6.08
% 5.83/6.08 Low Water (displace): id=20581, wt=6.000
% 5.83/6.08
% 5.83/6.08 ============================== PROOF =================================
% 5.83/6.08 % SZS status Theorem
% 5.83/6.08 % SZS output start Refutation
% 5.83/6.08
% 5.83/6.08 % Proof 1 at 4.95 (+ 0.09) seconds.
% 5.83/6.08 % Length of proof is 38.
% 5.83/6.08 % Level of proof is 6.
% 5.83/6.08 % Maximum clause weight is 9.000.
% 5.83/6.08 % Given clauses 1092.
% 5.83/6.08
% 5.83/6.08 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].
% 5.83/6.08 3 (all X -gt(X,X)) # label(irreflexivity_gt) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 9 (all X all Y (leq(X,Y) & X != Y -> gt(Y,X))) # label(leq_gt2) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 13 (all X all Y (leq(X,Y) <-> gt(succ(Y),X))) # label(leq_succ_gt_equiv) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 30 (all X plus(X,n2) = succ(succ(X))) # label(succ_plus_2_r) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 31 (all X plus(n2,X) = succ(succ(X))) # label(succ_plus_2_l) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 41 (all X all Y (leq(succ(X),succ(Y)) <-> leq(X,Y))) # label(leq_succ_succ) # label(axiom) # label(non_clause). [assumption].
% 5.83/6.08 56 -(leq(tptp_float_0_001,pv1341) & leq(n1,loopcounter) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_best7)) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_sworst7)) & (-leq(tptp_float_0_001,pv1341) -> leq(n0,s_worst7)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_best7,n3)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_sworst7,n3)) & (-leq(tptp_float_0_001,pv1341) -> leq(s_worst7,n3)) & (gt(loopcounter,n0) -> leq(n0,s_best7)) & (gt(loopcounter,n0) -> leq(n0,s_sworst7)) & (gt(loopcounter,n0) -> leq(n0,s_worst7)) & (gt(loopcounter,n0) -> leq(s_best7,n3)) & (gt(loopcounter,n0) -> leq(s_sworst7,n3)) & (gt(loopcounter,n0) -> leq(s_worst7,n3)) -> leq(s_best7,n3)) # label(gauss_array_0012) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.83/6.08 62 -gt(A,B) | -gt(B,C) | gt(A,C) # label(transitivity_gt) # label(axiom). [clausify(2)].
% 5.83/6.08 63 -gt(A,A) # label(irreflexivity_gt) # label(axiom). [clausify(3)].
% 5.83/6.08 67 -leq(A,B) | B = A | gt(B,A) # label(leq_gt2) # label(axiom). [clausify(9)].
% 5.83/6.08 72 -leq(A,B) | gt(succ(B),A) # label(leq_succ_gt_equiv) # label(axiom). [clausify(13)].
% 5.83/6.08 73 leq(A,B) | -gt(succ(B),A) # label(leq_succ_gt_equiv) # label(axiom). [clausify(13)].
% 5.83/6.08 284 plus(A,n2) = succ(succ(A)) # label(succ_plus_2_r) # label(axiom). [clausify(30)].
% 5.83/6.08 285 succ(succ(A)) = plus(A,n2). [copy(284),flip(a)].
% 5.83/6.08 286 plus(n2,A) = succ(succ(A)) # label(succ_plus_2_l) # label(axiom). [clausify(31)].
% 5.83/6.08 287 plus(n2,A) = plus(A,n2). [copy(286),rewrite([285(4)])].
% 5.83/6.08 304 leq(succ(A),succ(B)) | -leq(A,B) # label(leq_succ_succ) # label(axiom). [clausify(41)].
% 5.83/6.08 331 gt(n1,n0) # label(gt_1_0) # label(axiom). [assumption].
% 5.83/6.08 353 succ(n0) = n1 # label(successor_1) # label(axiom). [assumption].
% 5.83/6.08 354 succ(succ(n0)) = n2 # label(successor_2) # label(axiom). [assumption].
% 5.83/6.08 355 succ(n1) = n2. [copy(354),rewrite([353(2)])].
% 5.83/6.08 356 succ(succ(succ(n0))) = n3 # label(successor_3) # label(axiom). [assumption].
% 5.83/6.08 357 succ(n2) = n3. [copy(356),rewrite([353(2),355(2)])].
% 5.83/6.08 359 leq(n1,loopcounter) # label(gauss_array_0012) # label(negated_conjecture). [clausify(56)].
% 5.83/6.08 363 -gt(loopcounter,n0) | leq(s_best7,n3) # label(gauss_array_0012) # label(negated_conjecture). [clausify(56)].
% 5.83/6.08 366 -leq(s_best7,n3) # label(gauss_array_0012) # label(negated_conjecture). [clausify(56)].
% 5.83/6.08 829 -gt(loopcounter,n0). [back_unit_del(363),unit_del(b,366)].
% 5.83/6.08 1669 -gt(A,n1) | gt(A,n0). [resolve(331,a,62,b)].
% 5.83/6.08 1722 plus(n0,n2) = n2. [para(353(a,1),285(a,1,1)),rewrite([355(2)]),flip(a)].
% 5.83/6.08 2051 leq(n2,succ(loopcounter)). [resolve(359,a,304,b),rewrite([355(2)])].
% 5.83/6.08 2263 gt(succ(loopcounter),n1). [resolve(359,a,72,a)].
% 5.83/6.08 11731 leq(n3,plus(n2,loopcounter)). [resolve(2051,a,304,b),rewrite([357(2),285(4),287(4,R)])].
% 5.83/6.08 16225 gt(succ(plus(n2,loopcounter)),n3). [resolve(11731,a,72,a)].
% 5.83/6.08 21945 gt(succ(loopcounter),n0). [resolve(1669,a,2263,a)].
% 5.83/6.08 21950 leq(n0,loopcounter). [resolve(21945,a,73,b)].
% 5.83/6.08 22067 loopcounter = n0. [resolve(21950,a,67,a),unit_del(b,829)].
% 5.83/6.08 22146 $F. [back_rewrite(16225),rewrite([22067(2),287(3),1722(3),357(2)]),unit_del(a,63)].
% 5.83/6.08
% 5.83/6.08 % SZS output end Refutation
% 5.83/6.08 ============================== end of proof ==========================
% 5.83/6.08
% 5.83/6.08 ============================== STATISTICS ============================
% 5.83/6.08
% 5.83/6.08 Given=1092. Generated=120800. Kept=22071. proofs=1.
% 5.83/6.08 Usable=1061. Sos=9567. Demods=553. Limbo=79, Disabled=11660. Hints=0.
% 5.83/6.08 Megabytes=31.17.
% 5.83/6.08 User_CPU=4.95, System_CPU=0.09, Wall_clock=5.
% 5.83/6.08
% 5.83/6.08 ============================== end of statistics =====================
% 5.83/6.08
% 5.83/6.08 ============================== end of search =========================
% 5.83/6.08
% 5.83/6.08 THEOREM PROVED
% 5.83/6.08 % SZS status Theorem
% 5.83/6.08
% 5.83/6.08 Exiting with 1 proof.
% 5.83/6.08
% 5.83/6.08 Process 17673 exit (max_proofs) Tue Jun 14 14:27:34 2022
% 5.83/6.08 Prover9 interrupted
%------------------------------------------------------------------------------