TSTP Solution File: ANA028-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA028-2 : TPTP v8.1.0. Released v3.2.0.
% 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 19:21:46 EDT 2022
% Result : Unsatisfiable 0.75s 1.02s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA028-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.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 03:32:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 30600 was started by sandbox on n004.cluster.edu,
% 0.46/1.01 Fri Jul 8 03:32:23 2022
% 0.46/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30447_n004.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_30447_n004.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (13 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01
% 0.46/1.01 ============================== end of process non-clausal formulas ===
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.01
% 0.46/1.01 ============================== PREDICATE ELIMINATION =================
% 0.46/1.01 1 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 0.46/1.01 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.46/1.01 Derived: class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.46/1.01 3 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 0.46/1.01 Derived: class_OrderedGroup_Oab__group__add(t_b). [resolve(3,a,2,a)].
% 0.46/1.01 4 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_54) # label(axiom). [assumption].
% 0.46/1.01 Derived: class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(4,a,2,a)].
% 0.46/1.01 5 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.46/1.01 6 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.46/1.01 Derived: c_plus(c_0,A,t_b) = A. [resolve(5,a,6,a)].
% 0.46/1.01 7 class_OrderedGroup_Oab__group__add(t_b). [resolve(3,a,2,a)].
% 0.46/1.01 8 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 0.46/1.01 9 -class_OrderedGroup_Oab__group__add(A) | c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A) # label(cls_OrderedGroup_Ocompare__rls__2_0) # label(axiom). [assumption].
% 0.46/1.01 10 -class_OrderedGroup_Oab__group__add(A) | c_plus(c_minus(B,C,A),D,A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__3_0) # label(axiom). [assumption].
% 0.46/1.01 11 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__5_0) # label(axiom). [assumption].
% 0.75/1.02 Derived: c_minus(A,A,t_b) = c_0. [resolve(7,a,8,a)].
% 0.75/1.02 Derived: c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(7,a,9,a)].
% 0.75/1.02 Derived: c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(7,a,10,a)].
% 0.75/1.02 Derived: c_minus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(7,a,11,a)].
% 0.75/1.02 12 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(4,a,2,a)].
% 0.75/1.02 13 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_plus(C,D,A),A) | c_lessequals(c_minus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__8_1) # label(axiom). [assumption].
% 0.75/1.02 14 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),D,A) | c_lessequals(B,c_minus(D,C,A),A) # label(cls_OrderedGroup_Ocompare__rls__9_1) # label(axiom). [assumption].
% 0.75/1.02 Derived: -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(12,a,13,a)].
% 0.75/1.02 Derived: -c_lessequals(c_plus(A,B,t_b),C,t_b) | c_lessequals(A,c_minus(C,B,t_b),t_b). [resolve(12,a,14,a)].
% 0.75/1.02
% 0.75/1.02 ============================== end predicate elimination =============
% 0.75/1.02
% 0.75/1.02 Auto_denials:
% 0.75/1.02 % copying label cls_conjecture_3 to answer in negative clause
% 0.75/1.02
% 0.75/1.02 Term ordering decisions:
% 0.75/1.02 Function symbol KB weights: t_b=1. c_0=1. v_x=1. v_g=1. v_k=1. v_f=1. c_minus=1. c_plus=1.
% 0.75/1.02
% 0.75/1.02 ============================== end of process initial clauses ========
% 0.75/1.02
% 0.75/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.02
% 0.75/1.02 ============================== end of clauses for search =============
% 0.75/1.02
% 0.75/1.02 ============================== SEARCH ================================
% 0.75/1.02
% 0.75/1.02 % Starting search at 0.01 seconds.
% 0.75/1.02
% 0.75/1.02 ============================== PROOF =================================
% 0.75/1.02 % SZS status Unsatisfiable
% 0.75/1.02 % SZS output start Refutation
% 0.75/1.02
% 0.75/1.02 % Proof 1 at 0.02 (+ 0.00) seconds: cls_conjecture_3.
% 0.75/1.02 % Length of proof is 35.
% 0.75/1.02 % Level of proof is 10.
% 0.75/1.02 % Maximum clause weight is 15.000.
% 0.75/1.02 % Given clauses 28.
% 0.75/1.02
% 0.75/1.02 1 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 0.75/1.02 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.75/1.02 3 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 0.75/1.02 4 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_54) # label(axiom). [assumption].
% 0.75/1.02 5 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.75/1.02 6 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.75/1.02 7 class_OrderedGroup_Oab__group__add(t_b). [resolve(3,a,2,a)].
% 0.75/1.02 8 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 0.75/1.02 9 -class_OrderedGroup_Oab__group__add(A) | c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A) # label(cls_OrderedGroup_Ocompare__rls__2_0) # label(axiom). [assumption].
% 0.75/1.02 10 -class_OrderedGroup_Oab__group__add(A) | c_plus(c_minus(B,C,A),D,A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__3_0) # label(axiom). [assumption].
% 0.75/1.02 11 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__5_0) # label(axiom). [assumption].
% 0.75/1.02 12 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(4,a,2,a)].
% 0.75/1.02 13 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_plus(C,D,A),A) | c_lessequals(c_minus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__8_1) # label(axiom). [assumption].
% 0.75/1.02 14 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),D,A) | c_lessequals(B,c_minus(D,C,A),A) # label(cls_OrderedGroup_Ocompare__rls__9_1) # label(axiom). [assumption].
% 0.75/1.02 15 c_lessequals(v_g(A),v_k(A),t_b) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.75/1.02 16 -c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) # label(cls_conjecture_3) # label(negated_conjecture) # answer(cls_conjecture_3). [assumption].
% 0.75/1.02 17 c_plus(c_0,A,t_b) = A. [resolve(5,a,6,a)].
% 0.75/1.02 18 c_minus(A,A,t_b) = c_0. [resolve(7,a,8,a)].
% 0.75/1.02 19 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(7,a,9,a)].
% 0.75/1.02 20 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(7,a,10,a)].
% 0.75/1.02 21 c_minus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(7,a,11,a)].
% 0.75/1.02 22 c_minus(c_plus(A,B,t_b),C,t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [copy(21),flip(a)].
% 0.75/1.02 23 -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(12,a,13,a)].
% 0.75/1.02 24 -c_lessequals(c_plus(A,B,t_b),C,t_b) | c_lessequals(A,c_minus(C,B,t_b),t_b). [resolve(12,a,14,a)].
% 0.75/1.02 25 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_minus(B,C,t_b),t_b). [back_rewrite(20),rewrite([22(8)])].
% 0.75/1.02 26 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [back_rewrite(19),rewrite([22(8)])].
% 0.75/1.02 27 c_minus(c_0,c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b). [para(17(a,1),22(a,1,1)),flip(a)].
% 0.75/1.02 34 c_minus(A,c_minus(A,B,t_b),t_b) = B. [para(18(a,1),25(a,1,1)),rewrite([17(3)]),flip(a)].
% 0.75/1.02 47 c_minus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_plus(C,B,t_b),t_b). [para(22(a,1),27(a,1,2)),rewrite([27(7)])].
% 0.75/1.02 50 c_plus(A,B,t_b) = c_plus(B,A,t_b). [para(34(a,1),25(a,1,1)),rewrite([47(6),34(8)])].
% 0.75/1.02 57 -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,B,t_b),C,t_b). [para(50(a,1),23(a,2))].
% 0.75/1.02 58 -c_lessequals(c_plus(A,B,t_b),C,t_b) | c_lessequals(B,c_minus(C,A,t_b),t_b). [para(50(a,1),24(a,1))].
% 0.75/1.02 70 -c_lessequals(v_f(v_x),c_minus(v_k(v_x),c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b) # answer(cls_conjecture_3). [ur(57,b,16,a),rewrite([26(12)])].
% 0.75/1.02 80 -c_lessequals(v_g(v_x),v_k(v_x),t_b) # answer(cls_conjecture_3). [ur(58,b,70,a),rewrite([50(10),26(10),34(10)])].
% 0.75/1.02 81 $F # answer(cls_conjecture_3). [resolve(80,a,15,a)].
% 0.75/1.02
% 0.75/1.02 % SZS output end Refutation
% 0.75/1.02 ============================== end of proof ==========================
% 0.75/1.02
% 0.75/1.02 ============================== STATISTICS ============================
% 0.75/1.02
% 0.75/1.02 Given=28. Generated=229. Kept=65. proofs=1.
% 0.75/1.02 Usable=26. Sos=22. Demods=12. Limbo=0, Disabled=39. Hints=0.
% 0.75/1.02 Megabytes=0.10.
% 0.75/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.75/1.02
% 0.75/1.02 ============================== end of statistics =====================
% 0.75/1.02
% 0.75/1.02 ============================== end of search =========================
% 0.75/1.02
% 0.75/1.02 THEOREM PROVED
% 0.75/1.02 % SZS status Unsatisfiable
% 0.75/1.02
% 0.75/1.02 Exiting with 1 proof.
% 0.75/1.02
% 0.75/1.02 Process 30600 exit (max_proofs) Fri Jul 8 03:32:23 2022
% 0.75/1.02 Prover9 interrupted
%------------------------------------------------------------------------------