TSTP Solution File: ANA019-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Thu Jul 14 19:21:35 EDT 2022
% Result : Unsatisfiable 1.51s 1.78s
% Output : Refutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 03:10:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.99 ============================== Prover9 ===============================
% 0.45/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.99 Process 7317 was started by sandbox on n027.cluster.edu,
% 0.45/0.99 Fri Jul 8 03:10:15 2022
% 0.45/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7163_n027.cluster.edu".
% 0.45/0.99 ============================== end of head ===========================
% 0.45/0.99
% 0.45/0.99 ============================== INPUT =================================
% 0.45/0.99
% 0.45/0.99 % Reading from file /tmp/Prover9_7163_n027.cluster.edu
% 0.45/0.99
% 0.45/0.99 set(prolog_style_variables).
% 0.45/0.99 set(auto2).
% 0.45/0.99 % set(auto2) -> set(auto).
% 0.45/0.99 % set(auto) -> set(auto_inference).
% 0.45/0.99 % set(auto) -> set(auto_setup).
% 0.45/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.99 % set(auto) -> set(auto_limits).
% 0.45/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.99 % set(auto) -> set(auto_denials).
% 0.45/0.99 % set(auto) -> set(auto_process).
% 0.45/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.99 % set(auto2) -> assign(stats, some).
% 0.45/0.99 % set(auto2) -> clear(echo_input).
% 0.45/0.99 % set(auto2) -> set(quiet).
% 0.45/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.99 % set(auto2) -> clear(print_given).
% 0.45/0.99 assign(lrs_ticks,-1).
% 0.45/0.99 assign(sos_limit,10000).
% 0.45/0.99 assign(order,kbo).
% 0.45/0.99 set(lex_order_vars).
% 0.45/0.99 clear(print_given).
% 0.45/0.99
% 0.45/0.99 % formulas(sos). % not echoed (15 formulas)
% 0.45/0.99
% 0.45/0.99 ============================== end of input ==========================
% 0.45/0.99
% 0.45/0.99 % From the command line: assign(max_seconds, 300).
% 0.45/0.99
% 0.45/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.99
% 0.45/0.99 % Formulas that are not ordinary clauses:
% 0.45/0.99
% 0.45/0.99 ============================== end of process non-clausal formulas ===
% 0.45/0.99
% 0.45/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/0.99
% 0.45/0.99 ============================== PREDICATE ELIMINATION =================
% 0.45/0.99 1 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 0.45/0.99 2 class_Ring__and__Field_Oordered__idom(t_a) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.45/0.99 Derived: class_LOrder_Ojoin__semilorder(t_a). [resolve(1,a,2,a)].
% 0.45/0.99 3 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_40) # label(axiom). [assumption].
% 0.45/0.99 Derived: class_Ring__and__Field_Opordered__cancel__semiring(t_a). [resolve(3,a,2,a)].
% 0.45/0.99 4 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom). [assumption].
% 0.45/0.99 Derived: class_OrderedGroup_Olordered__ab__group__abs(t_a). [resolve(4,a,2,a)].
% 0.45/0.99 5 class_LOrder_Ojoin__semilorder(t_a). [resolve(1,a,2,a)].
% 0.45/0.99 6 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 0.45/0.99 Derived: class_Orderings_Oorder(t_a). [resolve(5,a,6,a)].
% 0.45/0.99 7 class_OrderedGroup_Olordered__ab__group__abs(t_a). [resolve(4,a,2,a)].
% 0.45/0.99 8 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_0,A) = c_0 # label(cls_OrderedGroup_Oabs__eq__0_1) # label(axiom). [assumption].
% 0.45/0.99 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 0.45/0.99 Derived: c_HOL_Oabs(c_0,t_a) = c_0. [resolve(7,a,8,a)].
% 0.45/0.99 Derived: c_lessequals(c_0,c_HOL_Oabs(A,t_a),t_a). [resolve(7,a,9,a)].
% 0.45/0.99 10 class_Orderings_Oorder(t_a). [resolve(5,a,6,a)].
% 0.45/0.99 11 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_lessequals(B,C,A) # label(cls_Orderings_Oorder__less__imp__le_0) # label(axiom). [assumption].
% 1.51/1.78 Derived: -c_less(A,B,t_a) | c_lessequals(A,B,t_a). [resolve(10,a,11,a)].
% 1.51/1.78 12 class_Ring__and__Field_Opordered__cancel__semiring(t_a). [resolve(3,a,2,a)].
% 1.51/1.78 13 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_times(C,B,A),A) # label(cls_Ring__and__Field_Omult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.51/1.78 Derived: -c_lessequals(c_0,A,t_a) | -c_lessequals(c_0,B,t_a) | c_lessequals(c_0,c_times(B,A,t_a),t_a). [resolve(12,a,13,a)].
% 1.51/1.78
% 1.51/1.78 ============================== end predicate elimination =============
% 1.51/1.78
% 1.51/1.78 Auto_denials: (non-Horn, no changes).
% 1.51/1.78
% 1.51/1.78 Term ordering decisions:
% 1.51/1.78 Function symbol KB weights: t_a=1. c_0=1. tc_nat=1. v_x=1. c_1=1. c_HOL_Oabs=1. c_Suc=1. v_f=1. v_h=1. v_xa=1. c_times=1. c_minus=1.
% 1.51/1.78
% 1.51/1.78 ============================== end of process initial clauses ========
% 1.51/1.78
% 1.51/1.78 ============================== CLAUSES FOR SEARCH ====================
% 1.51/1.78
% 1.51/1.78 ============================== end of clauses for search =============
% 1.51/1.78
% 1.51/1.78 ============================== SEARCH ================================
% 1.51/1.78
% 1.51/1.78 % Starting search at 0.01 seconds.
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=29.000, iters=3373
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=28.000, iters=3421
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=27.000, iters=3410
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=25.000, iters=3379
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=24.000, iters=3343
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=23.000, iters=3335
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=22.000, iters=3340
% 1.51/1.78
% 1.51/1.78 Low Water (keep): wt=21.000, iters=3333
% 1.51/1.78
% 1.51/1.78 ============================== PROOF =================================
% 1.51/1.78 % SZS status Unsatisfiable
% 1.51/1.78 % SZS output start Refutation
% 1.51/1.78
% 1.51/1.78 % Proof 1 at 0.79 (+ 0.02) seconds.
% 1.51/1.78 % Length of proof is 34.
% 1.51/1.78 % Level of proof is 6.
% 1.51/1.78 % Maximum clause weight is 20.000.
% 1.51/1.78 % Given clauses 479.
% 1.51/1.78
% 1.51/1.78 1 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 1.51/1.78 2 class_Ring__and__Field_Oordered__idom(t_a) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 1.51/1.78 3 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_40) # label(axiom). [assumption].
% 1.51/1.78 4 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom). [assumption].
% 1.51/1.78 5 class_LOrder_Ojoin__semilorder(t_a). [resolve(1,a,2,a)].
% 1.51/1.78 6 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 1.51/1.78 7 class_OrderedGroup_Olordered__ab__group__abs(t_a). [resolve(4,a,2,a)].
% 1.51/1.78 8 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_0,A) = c_0 # label(cls_OrderedGroup_Oabs__eq__0_1) # label(axiom). [assumption].
% 1.51/1.78 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 1.51/1.78 10 class_Orderings_Oorder(t_a). [resolve(5,a,6,a)].
% 1.51/1.78 11 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_lessequals(B,C,A) # label(cls_Orderings_Oorder__less__imp__le_0) # label(axiom). [assumption].
% 1.51/1.79 12 class_Ring__and__Field_Opordered__cancel__semiring(t_a). [resolve(3,a,2,a)].
% 1.51/1.79 13 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_times(C,B,A),A) # label(cls_Ring__and__Field_Omult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.51/1.79 14 v_f(c_0) = c_0 # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.51/1.79 15 c_less(c_0,v_x,t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.51/1.79 16 c_less(c_0,A,tc_nat) | A = c_0 # label(cls_Nat_Onot__gr0_0) # label(axiom). [assumption].
% 1.51/1.79 17 c_less(c_0,A,tc_nat) | c_0 = A. [copy(16),flip(b)].
% 1.51/1.79 18 c_lessequals(c_HOL_Oabs(v_f(c_Suc(A)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(A)),t_a),t_a),t_a) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 1.51/1.79 19 -c_lessequals(c_HOL_Oabs(v_f(v_xa(A)),t_a),c_times(A,c_HOL_Oabs(v_h(v_xa(A)),t_a),t_a),t_a) | -c_less(c_0,A,t_a) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 1.51/1.79 20 -c_less(c_0,A,tc_nat) | A = c_Suc(c_minus(A,c_1,tc_nat)) # label(cls_NatBin_OSuc__pred_H_0) # label(axiom). [assumption].
% 1.51/1.79 21 -c_less(c_0,A,tc_nat) | c_Suc(c_minus(A,c_1,tc_nat)) = A. [copy(20),flip(b)].
% 1.51/1.79 22 c_HOL_Oabs(c_0,t_a) = c_0. [resolve(7,a,8,a)].
% 1.51/1.79 23 c_lessequals(c_0,c_HOL_Oabs(A,t_a),t_a). [resolve(7,a,9,a)].
% 1.51/1.79 24 -c_less(A,B,t_a) | c_lessequals(A,B,t_a). [resolve(10,a,11,a)].
% 1.51/1.79 25 -c_lessequals(c_0,A,t_a) | -c_lessequals(c_0,B,t_a) | c_lessequals(c_0,c_times(B,A,t_a),t_a). [resolve(12,a,13,a)].
% 1.51/1.79 27 -c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a). [resolve(19,b,15,a)].
% 1.51/1.79 28 c_Suc(c_minus(A,c_1,tc_nat)) = A | c_0 = A. [resolve(21,a,17,a)].
% 1.51/1.79 30 c_lessequals(c_0,v_x,t_a). [resolve(24,a,15,a)].
% 1.51/1.79 31 -c_lessequals(c_0,A,t_a) | c_lessequals(c_0,c_times(A,c_HOL_Oabs(B,t_a),t_a),t_a). [resolve(25,a,23,a)].
% 1.51/1.79 47 c_0 = A | c_lessequals(c_HOL_Oabs(v_f(A),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(A,c_1,tc_nat))),t_a),t_a),t_a). [para(28(a,1),18(a,1,1,1))].
% 1.51/1.79 70 c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(A,t_a),t_a),t_a). [resolve(31,a,30,a)].
% 1.51/1.79 699 c_0 = A | c_lessequals(c_HOL_Oabs(v_f(A),t_a),c_times(v_x,c_HOL_Oabs(v_h(A),t_a),t_a),t_a). [para(28(a,1),47(b,2,2,1,1)),merge(b)].
% 1.51/1.79 8376 v_xa(v_x) = c_0. [resolve(699,b,27,a),flip(a)].
% 1.51/1.79 8378 $F. [back_rewrite(27),rewrite([8376(2),14(2),22(3),8376(4)]),unit_del(a,70)].
% 1.51/1.79
% 1.51/1.79 % SZS output end Refutation
% 1.51/1.79 ============================== end of proof ==========================
% 1.51/1.79
% 1.51/1.79 ============================== STATISTICS ============================
% 1.51/1.79
% 1.51/1.79 Given=479. Generated=24762. Kept=8362. proofs=1.
% 1.51/1.79 Usable=472. Sos=7876. Demods=3. Limbo=2, Disabled=35. Hints=0.
% 1.51/1.79 Megabytes=8.20.
% 1.51/1.79 User_CPU=0.79, System_CPU=0.02, Wall_clock=1.
% 1.51/1.79
% 1.51/1.79 ============================== end of statistics =====================
% 1.51/1.79
% 1.51/1.79 ============================== end of search =========================
% 1.51/1.79
% 1.51/1.79 THEOREM PROVED
% 1.51/1.79 % SZS status Unsatisfiable
% 1.51/1.79
% 1.51/1.79 Exiting with 1 proof.
% 1.51/1.79
% 1.51/1.79 Process 7317 exit (max_proofs) Fri Jul 8 03:10:16 2022
% 1.51/1.79 Prover9 interrupted
%------------------------------------------------------------------------------