TSTP Solution File: ANA023-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 19:21:39 EDT 2022
% Result : Unsatisfiable 0.67s 0.96s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.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 : Fri Jul 8 05:33:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.67/0.96 ============================== Prover9 ===============================
% 0.67/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.96 Process 15655 was started by sandbox2 on n004.cluster.edu,
% 0.67/0.96 Fri Jul 8 05:33:38 2022
% 0.67/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15501_n004.cluster.edu".
% 0.67/0.96 ============================== end of head ===========================
% 0.67/0.96
% 0.67/0.96 ============================== INPUT =================================
% 0.67/0.96
% 0.67/0.96 % Reading from file /tmp/Prover9_15501_n004.cluster.edu
% 0.67/0.96
% 0.67/0.96 set(prolog_style_variables).
% 0.67/0.96 set(auto2).
% 0.67/0.96 % set(auto2) -> set(auto).
% 0.67/0.96 % set(auto) -> set(auto_inference).
% 0.67/0.96 % set(auto) -> set(auto_setup).
% 0.67/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.96 % set(auto) -> set(auto_limits).
% 0.67/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.96 % set(auto) -> set(auto_denials).
% 0.67/0.96 % set(auto) -> set(auto_process).
% 0.67/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.96 % set(auto2) -> assign(stats, some).
% 0.67/0.96 % set(auto2) -> clear(echo_input).
% 0.67/0.96 % set(auto2) -> set(quiet).
% 0.67/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.96 % set(auto2) -> clear(print_given).
% 0.67/0.96 assign(lrs_ticks,-1).
% 0.67/0.96 assign(sos_limit,10000).
% 0.67/0.96 assign(order,kbo).
% 0.67/0.96 set(lex_order_vars).
% 0.67/0.96 clear(print_given).
% 0.67/0.96
% 0.67/0.96 % formulas(sos). % not echoed (14 formulas)
% 0.67/0.96
% 0.67/0.96 ============================== end of input ==========================
% 0.67/0.96
% 0.67/0.96 % From the command line: assign(max_seconds, 300).
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.96
% 0.67/0.96 % Formulas that are not ordinary clauses:
% 0.67/0.96
% 0.67/0.96 ============================== end of process non-clausal formulas ===
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.96
% 0.67/0.96 ============================== PREDICATE ELIMINATION =================
% 0.67/0.96
% 0.67/0.96 ============================== end predicate elimination =============
% 0.67/0.96
% 0.67/0.96 Auto_denials:
% 0.67/0.96 % copying label cls_conjecture_3 to answer in negative clause
% 0.67/0.96
% 0.67/0.96 Term ordering decisions:
% 0.67/0.96 Function symbol KB weights: true=1. t_b=1. v_x=1. c_0=1. class_Ring__and__Field_Oordered__idom=1. class_OrderedGroup_Opordered__ab__group__add=1. class_OrderedGroup_Ocomm__monoid__add=1. class_Orderings_Olinorder=1. class_Orderings_Oorder=1. v_k=1. v_f=1. v_g=1. c_lessequals=1. c_minus=1. c_plus=1. ifeq=1. ifeq2=1.
% 0.67/0.96
% 0.67/0.96 ============================== end of process initial clauses ========
% 0.67/0.96
% 0.67/0.96 ============================== CLAUSES FOR SEARCH ====================
% 0.67/0.96
% 0.67/0.96 ============================== end of clauses for search =============
% 0.67/0.96
% 0.67/0.96 ============================== SEARCH ================================
% 0.67/0.96
% 0.67/0.96 % Starting search at 0.01 seconds.
% 0.67/0.96
% 0.67/0.96 ============================== PROOF =================================
% 0.67/0.96 % SZS status Unsatisfiable
% 0.67/0.96 % SZS output start Refutation
% 0.67/0.96
% 0.67/0.96 % Proof 1 at 0.02 (+ 0.00) seconds: cls_conjecture_3.
% 0.67/0.96 % Length of proof is 39.
% 0.67/0.96 % Level of proof is 8.
% 0.67/0.96 % Maximum clause weight is 32.000.
% 0.67/0.96 % Given clauses 38.
% 0.67/0.96
% 0.67/0.96 1 class_Ring__and__Field_Oordered__idom(t_b) = true # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.67/0.96 2 true = class_Ring__and__Field_Oordered__idom(t_b). [copy(1),flip(a)].
% 0.67/0.96 3 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 0.67/0.96 4 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 0.67/0.96 5 c_lessequals(v_k(v_x),v_f(v_x),t_b) = true # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 0.67/0.96 6 c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [copy(5),rewrite([2(7)])].
% 0.67/0.96 7 ifeq(class_Orderings_Olinorder(A),true,class_Orderings_Oorder(A),true) = true # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 0.67/0.96 8 ifeq(class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(7),rewrite([2(2),2(5),2(8)])].
% 0.67/0.96 9 ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_OrderedGroup_Ocomm__monoid__add(A),true) = true # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 0.67/0.96 10 ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(9),rewrite([2(2),2(5),2(8)])].
% 0.67/0.96 11 ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_Orderings_Olinorder(A),true) = true # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 0.67/0.96 12 ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(11),rewrite([2(2),2(5),2(8)])].
% 0.67/0.96 13 ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_OrderedGroup_Opordered__ab__group__add(A),true) = true # label(clsrel_Ring__and__Field_Oordered__idom_54) # label(axiom). [assumption].
% 0.67/0.96 14 ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(13),rewrite([2(2),2(5),2(8)])].
% 0.67/0.96 15 ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),true,c_plus(c_0,B,A),B) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.67/0.96 16 ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,B,A),B) = B. [copy(15),rewrite([2(2)])].
% 0.67/0.96 17 c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.67/0.96 18 c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [copy(17),rewrite([2(10)])].
% 0.67/0.96 19 ifeq(class_OrderedGroup_Opordered__ab__group__add(A),true,ifeq(c_lessequals(B,c_minus(C,D,A),A),true,c_lessequals(c_plus(B,D,A),C,A),true),true) = true # label(cls_OrderedGroup_Ocompare__rls__9_0) # label(axiom). [assumption].
% 0.67/0.96 20 ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(19),rewrite([2(2),2(6),2(10),2(13),2(16)])].
% 0.67/0.96 21 ifeq(class_OrderedGroup_Opordered__ab__group__add(A),true,ifeq(c_lessequals(c_plus(B,C,A),D,A),true,c_lessequals(B,c_minus(D,C,A),A),true),true) = true # label(cls_OrderedGroup_Ocompare__rls__9_1) # label(axiom). [assumption].
% 0.67/0.96 22 ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(21),rewrite([2(2),2(6),2(10),2(13),2(16)])].
% 0.67/0.96 23 ifeq(class_Orderings_Oorder(A),true,ifeq(c_lessequals(B,C,A),true,ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 0.67/0.96 24 ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [copy(23),rewrite([2(2),2(5),2(8),2(11),2(14),2(17),2(20)])].
% 0.67/0.97 25 c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true # label(cls_conjecture_3) # label(negated_conjecture) # answer(cls_conjecture_3). [assumption].
% 0.67/0.97 26 c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != class_Ring__and__Field_Oordered__idom(t_b) # answer(cls_conjecture_3). [copy(25),rewrite([2(10)])].
% 0.67/0.97 27 class_OrderedGroup_Ocomm__monoid__add(t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(10(a,1),4(a,1)),flip(a)].
% 0.67/0.97 28 class_Orderings_Olinorder(t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(12(a,1),4(a,1)),flip(a)].
% 0.67/0.97 29 class_OrderedGroup_Opordered__ab__group__add(t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(14(a,1),4(a,1)),flip(a)].
% 0.67/0.97 30 c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(18(a,1),20(a,1,3,1)),rewrite([29(2),4(20),4(16)])].
% 0.67/0.97 32 ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,v_k(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,v_f(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [para(6(a,1),24(a,1,3,3,1)),rewrite([4(21)])].
% 0.67/0.97 37 c_plus(c_0,A,t_b) = A. [para(27(a,1),16(a,1,1)),rewrite([3(8)])].
% 0.67/0.97 38 c_lessequals(v_g(v_x),v_k(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [back_rewrite(30),rewrite([37(5)])].
% 0.67/0.97 39 class_Orderings_Oorder(t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(28(a,1),8(a,1,1)),rewrite([4(9)])].
% 0.67/0.97 44 ifeq(c_lessequals(A,v_k(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,v_f(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [back_rewrite(32),rewrite([39(2),4(20)])].
% 0.67/0.97 50 ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_minus(B,A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b). [para(37(a,1),22(a,1,3,1,1)),rewrite([29(2),4(19)])].
% 0.67/0.97 55 c_lessequals(v_g(v_x),v_f(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(38(a,1),44(a,1,1)),rewrite([4(13)])].
% 0.67/0.97 70 c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b). [para(55(a,1),50(a,1,1)),rewrite([4(16)])].
% 0.67/0.97 71 $F # answer(cls_conjecture_3). [resolve(70,a,26,a)].
% 0.67/0.97
% 0.67/0.97 % SZS output end Refutation
% 0.67/0.97 ============================== end of proof ==========================
% 0.67/0.97
% 0.67/0.97 ============================== STATISTICS ============================
% 0.67/0.97
% 0.67/0.97 Given=38. Generated=116. Kept=58. proofs=1.
% 0.67/0.97 Usable=38. Sos=10. Demods=49. Limbo=2, Disabled=21. Hints=0.
% 0.67/0.97 Megabytes=0.12.
% 0.67/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.67/0.97
% 0.67/0.97 ============================== end of statistics =====================
% 0.67/0.97
% 0.67/0.97 ============================== end of search =========================
% 0.67/0.97
% 0.67/0.97 THEOREM PROVED
% 0.67/0.97 % SZS status Unsatisfiable
% 0.67/0.97
% 0.67/0.97 Exiting with 1 proof.
% 0.67/0.97
% 0.67/0.97 Process 15655 exit (max_proofs) Fri Jul 8 05:33:38 2022
% 0.67/0.97 Prover9 interrupted
%------------------------------------------------------------------------------