TSTP Solution File: GRP148-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 : Sat Jul 16 11:17:44 EDT 2022
% Result : Unsatisfiable 3.57s 3.81s
% Output : Refutation 3.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n010.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 : Mon Jun 13 05:49:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.57/3.81 ============================== Prover9 ===============================
% 3.57/3.81 Prover9 (32) version 2009-11A, November 2009.
% 3.57/3.81 Process 29076 was started by sandbox2 on n010.cluster.edu,
% 3.57/3.81 Mon Jun 13 05:49:25 2022
% 3.57/3.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28923_n010.cluster.edu".
% 3.57/3.81 ============================== end of head ===========================
% 3.57/3.81
% 3.57/3.81 ============================== INPUT =================================
% 3.57/3.81
% 3.57/3.81 % Reading from file /tmp/Prover9_28923_n010.cluster.edu
% 3.57/3.81
% 3.57/3.81 set(prolog_style_variables).
% 3.57/3.81 set(auto2).
% 3.57/3.81 % set(auto2) -> set(auto).
% 3.57/3.81 % set(auto) -> set(auto_inference).
% 3.57/3.81 % set(auto) -> set(auto_setup).
% 3.57/3.81 % set(auto_setup) -> set(predicate_elim).
% 3.57/3.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.57/3.81 % set(auto) -> set(auto_limits).
% 3.57/3.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.57/3.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.57/3.81 % set(auto) -> set(auto_denials).
% 3.57/3.81 % set(auto) -> set(auto_process).
% 3.57/3.81 % set(auto2) -> assign(new_constants, 1).
% 3.57/3.81 % set(auto2) -> assign(fold_denial_max, 3).
% 3.57/3.81 % set(auto2) -> assign(max_weight, "200.000").
% 3.57/3.81 % set(auto2) -> assign(max_hours, 1).
% 3.57/3.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.57/3.81 % set(auto2) -> assign(max_seconds, 0).
% 3.57/3.81 % set(auto2) -> assign(max_minutes, 5).
% 3.57/3.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.57/3.81 % set(auto2) -> set(sort_initial_sos).
% 3.57/3.81 % set(auto2) -> assign(sos_limit, -1).
% 3.57/3.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.57/3.81 % set(auto2) -> assign(max_megs, 400).
% 3.57/3.81 % set(auto2) -> assign(stats, some).
% 3.57/3.81 % set(auto2) -> clear(echo_input).
% 3.57/3.81 % set(auto2) -> set(quiet).
% 3.57/3.81 % set(auto2) -> clear(print_initial_clauses).
% 3.57/3.81 % set(auto2) -> clear(print_given).
% 3.57/3.81 assign(lrs_ticks,-1).
% 3.57/3.81 assign(sos_limit,10000).
% 3.57/3.81 assign(order,kbo).
% 3.57/3.81 set(lex_order_vars).
% 3.57/3.81 clear(print_given).
% 3.57/3.81
% 3.57/3.81 % formulas(sos). % not echoed (18 formulas)
% 3.57/3.81
% 3.57/3.81 ============================== end of input ==========================
% 3.57/3.81
% 3.57/3.81 % From the command line: assign(max_seconds, 300).
% 3.57/3.81
% 3.57/3.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.57/3.81
% 3.57/3.81 % Formulas that are not ordinary clauses:
% 3.57/3.81
% 3.57/3.81 ============================== end of process non-clausal formulas ===
% 3.57/3.81
% 3.57/3.81 ============================== PROCESS INITIAL CLAUSES ===============
% 3.57/3.81
% 3.57/3.81 ============================== PREDICATE ELIMINATION =================
% 3.57/3.81
% 3.57/3.81 ============================== end predicate elimination =============
% 3.57/3.81
% 3.57/3.81 Auto_denials:
% 3.57/3.81 % copying label prove_ax_lub1c to answer in negative clause
% 3.57/3.81
% 3.57/3.81 Term ordering decisions:
% 3.57/3.81
% 3.57/3.81 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.57/3.81 Function symbol KB weights: c=1. identity=1. a=1. b=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 3.57/3.81
% 3.57/3.81 ============================== end of process initial clauses ========
% 3.57/3.81
% 3.57/3.81 ============================== CLAUSES FOR SEARCH ====================
% 3.57/3.81
% 3.57/3.81 ============================== end of clauses for search =============
% 3.57/3.81
% 3.57/3.81 ============================== SEARCH ================================
% 3.57/3.81
% 3.57/3.81 % Starting search at 0.01 seconds.
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=33.000, iters=3342
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=32.000, iters=3410
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=31.000, iters=3364
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=29.000, iters=3359
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=28.000, iters=3356
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=27.000, iters=3337
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=26.000, iters=3385
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=25.000, iters=3348
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=24.000, iters=3372
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=23.000, iters=3356
% 3.57/3.81
% 3.57/3.81 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 1.64 sec).
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=22.000, iters=3333
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=21.000, iters=3345
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=20.000, iters=3341
% 3.57/3.81
% 3.57/3.81 Low Water (keep): wt=19.000, iters=3345
% 3.57/3.81
% 3.57/3.81 ============================== PROOF =================================
% 3.57/3.81 % SZS status Unsatisfiable
% 3.57/3.81 % SZS output start Refutation
% 3.57/3.81
% 3.57/3.81 % Proof 1 at 2.78 (+ 0.05) seconds: prove_ax_lub1c.
% 3.57/3.81 % Length of proof is 54.
% 3.57/3.81 % Level of proof is 12.
% 3.57/3.81 % Maximum clause weight is 15.000.
% 3.57/3.81 % Given clauses 665.
% 3.57/3.81
% 3.57/3.81 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.57/3.81 4 least_upper_bound(a,c) = c # label(ax_lub1c_1) # label(hypothesis). [assumption].
% 3.57/3.81 5 least_upper_bound(b,c) = c # label(ax_lub1c_2) # label(hypothesis). [assumption].
% 3.57/3.81 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.57/3.81 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 3.57/3.81 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 3.57/3.81 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 3.57/3.81 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 3.57/3.81 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 3.57/3.81 14 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C) # label(associativity_of_lub) # label(axiom). [assumption].
% 3.57/3.81 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 3.57/3.81 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 3.57/3.81 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 3.57/3.81 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 3.57/3.81 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 3.57/3.81 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 3.57/3.81 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 3.57/3.81 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 3.57/3.81 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 3.57/3.81 24 greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b) # label(prove_ax_lub1c) # label(negated_conjecture) # answer(prove_ax_lub1c). [assumption].
% 3.57/3.81 25 greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b) # answer(prove_ax_lub1c). [copy(24),rewrite([7(5)])].
% 3.57/3.81 26 least_upper_bound(c,b) = c. [back_rewrite(5),rewrite([8(3)])].
% 3.57/3.81 27 least_upper_bound(c,a) = c. [back_rewrite(4),rewrite([8(3)])].
% 3.57/3.81 28 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.57/3.81 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 3.57/3.81 36 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 3.57/3.81 40 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),23(a,1,1)),rewrite([7(5)])].
% 3.57/3.81 44 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),28(a,1,2))].
% 3.57/3.81 47 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(28(a,1),19(a,1,1)),rewrite([7(6)]),flip(a)].
% 3.57/3.81 50 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 3.57/3.81 51 multiply(A,identity) = A. [back_rewrite(44),rewrite([50(4)])].
% 3.57/3.81 58 multiply(A,inverse(A)) = identity. [para(50(a,1),6(a,1))].
% 3.57/3.81 63 multiply(A,multiply(inverse(A),B)) = B. [para(50(a,1),28(a,1))].
% 3.57/3.81 64 inverse(inverse(A)) = A. [para(50(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 3.57/3.81 65 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(58(a,1),11(a,1)),flip(a)].
% 3.57/3.81 89 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(65(a,1),28(a,1,2)),rewrite([51(3)]),flip(a)].
% 3.57/3.81 91 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(33(a,1),10(a,1,2))].
% 3.57/3.81 106 least_upper_bound(identity,multiply(inverse(c),b)) = identity. [para(26(a,1),33(a,2,2)),rewrite([6(10)])].
% 3.57/3.81 115 least_upper_bound(A,multiply(A,multiply(inverse(c),b))) = A. [para(106(a,1),17(a,2,2)),rewrite([51(2),51(8)])].
% 3.57/3.81 128 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(89(a,1),28(a,1,2)),flip(a)].
% 3.57/3.81 205 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),10(a,1,2))].
% 3.57/3.81 222 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),28(a,1,2))].
% 3.57/3.81 310 least_upper_bound(A,least_upper_bound(B,multiply(A,multiply(inverse(c),b)))) = least_upper_bound(A,B). [para(115(a,1),15(a,2,2)),rewrite([8(6),8(8)])].
% 3.57/3.81 362 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(40(a,1),9(a,1,2))].
% 3.57/3.81 598 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(64(a,1),205(a,1,2,1,2))].
% 3.57/3.81 717 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(64(a,1),362(a,1,2,1,2))].
% 3.57/3.81 980 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(598(a,1),47(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 3.57/3.81 1063 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(91(a,1),717(a,1,2,1)),rewrite([128(6),64(6),1(6)])].
% 3.57/3.81 1376 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(8(a,1),1063(a,1,2,1,1))].
% 3.57/3.81 9940 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(1376(a,1),222(a,1,2)),rewrite([8(4),51(7)])].
% 3.57/3.81 10142 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(9940(a,1),980(a,1,2)),rewrite([64(3),7(2),9940(7)])].
% 3.57/3.81 12844 least_upper_bound(c,least_upper_bound(a,b)) = c. [para(27(a,1),310(a,2)),rewrite([63(8)])].
% 3.57/3.81 12984 greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b). [para(12844(a,1),10142(a,1,2)),rewrite([7(5)])].
% 3.57/3.81 12985 $F # answer(prove_ax_lub1c). [resolve(12984,a,25,a)].
% 3.57/3.81
% 3.57/3.81 % SZS output end Refutation
% 3.57/3.81 ============================== end of proof ==========================
% 3.57/3.81
% 3.57/3.81 ============================== STATISTICS ============================
% 3.57/3.81
% 3.57/3.81 Given=665. Generated=116396. Kept=12977. proofs=1.
% 3.57/3.81 Usable=599. Sos=9993. Demods=8519. Limbo=13, Disabled=2389. Hints=0.
% 3.57/3.81 Megabytes=14.64.
% 3.57/3.81 User_CPU=2.78, System_CPU=0.05, Wall_clock=3.
% 3.57/3.81
% 3.57/3.81 ============================== end of statistics =====================
% 3.57/3.81
% 3.57/3.81 ============================== end of search =========================
% 3.57/3.81
% 3.57/3.81 THEOREM PROVED
% 3.57/3.81 % SZS status Unsatisfiable
% 3.57/3.81
% 3.57/3.81 Exiting with 1 proof.
% 3.57/3.81
% 3.57/3.81 Process 29076 exit (max_proofs) Mon Jun 13 05:49:28 2022
% 3.57/3.81 Prover9 interrupted
%------------------------------------------------------------------------------