TSTP Solution File: GRP140-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP140-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 11:17:42 EDT 2022
% Result : Unsatisfiable 2.35s 2.66s
% Output : Refutation 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP140-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 : Mon Jun 13 10:18:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.35/2.66 ============================== Prover9 ===============================
% 2.35/2.66 Prover9 (32) version 2009-11A, November 2009.
% 2.35/2.66 Process 30853 was started by sandbox on n029.cluster.edu,
% 2.35/2.66 Mon Jun 13 10:18:25 2022
% 2.35/2.66 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30700_n029.cluster.edu".
% 2.35/2.66 ============================== end of head ===========================
% 2.35/2.66
% 2.35/2.66 ============================== INPUT =================================
% 2.35/2.66
% 2.35/2.66 % Reading from file /tmp/Prover9_30700_n029.cluster.edu
% 2.35/2.66
% 2.35/2.66 set(prolog_style_variables).
% 2.35/2.66 set(auto2).
% 2.35/2.66 % set(auto2) -> set(auto).
% 2.35/2.66 % set(auto) -> set(auto_inference).
% 2.35/2.66 % set(auto) -> set(auto_setup).
% 2.35/2.66 % set(auto_setup) -> set(predicate_elim).
% 2.35/2.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.35/2.66 % set(auto) -> set(auto_limits).
% 2.35/2.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.35/2.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.35/2.66 % set(auto) -> set(auto_denials).
% 2.35/2.66 % set(auto) -> set(auto_process).
% 2.35/2.66 % set(auto2) -> assign(new_constants, 1).
% 2.35/2.66 % set(auto2) -> assign(fold_denial_max, 3).
% 2.35/2.66 % set(auto2) -> assign(max_weight, "200.000").
% 2.35/2.66 % set(auto2) -> assign(max_hours, 1).
% 2.35/2.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.35/2.66 % set(auto2) -> assign(max_seconds, 0).
% 2.35/2.66 % set(auto2) -> assign(max_minutes, 5).
% 2.35/2.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.35/2.66 % set(auto2) -> set(sort_initial_sos).
% 2.35/2.66 % set(auto2) -> assign(sos_limit, -1).
% 2.35/2.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.35/2.66 % set(auto2) -> assign(max_megs, 400).
% 2.35/2.66 % set(auto2) -> assign(stats, some).
% 2.35/2.66 % set(auto2) -> clear(echo_input).
% 2.35/2.66 % set(auto2) -> set(quiet).
% 2.35/2.66 % set(auto2) -> clear(print_initial_clauses).
% 2.35/2.66 % set(auto2) -> clear(print_given).
% 2.35/2.66 assign(lrs_ticks,-1).
% 2.35/2.66 assign(sos_limit,10000).
% 2.35/2.66 assign(order,kbo).
% 2.35/2.66 set(lex_order_vars).
% 2.35/2.66 clear(print_given).
% 2.35/2.66
% 2.35/2.66 % formulas(sos). % not echoed (18 formulas)
% 2.35/2.66
% 2.35/2.66 ============================== end of input ==========================
% 2.35/2.66
% 2.35/2.66 % From the command line: assign(max_seconds, 300).
% 2.35/2.66
% 2.35/2.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.35/2.66
% 2.35/2.66 % Formulas that are not ordinary clauses:
% 2.35/2.66
% 2.35/2.66 ============================== end of process non-clausal formulas ===
% 2.35/2.66
% 2.35/2.66 ============================== PROCESS INITIAL CLAUSES ===============
% 2.35/2.66
% 2.35/2.66 ============================== PREDICATE ELIMINATION =================
% 2.35/2.66
% 2.35/2.66 ============================== end predicate elimination =============
% 2.35/2.66
% 2.35/2.66 Auto_denials:
% 2.35/2.66 % copying label prove_ax_glb1c to answer in negative clause
% 2.35/2.66
% 2.35/2.66 Term ordering decisions:
% 2.35/2.66
% 2.35/2.66 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 2.35/2.66 Function symbol KB weights: c=1. identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 2.35/2.66
% 2.35/2.66 ============================== end of process initial clauses ========
% 2.35/2.66
% 2.35/2.66 ============================== CLAUSES FOR SEARCH ====================
% 2.35/2.66
% 2.35/2.66 ============================== end of clauses for search =============
% 2.35/2.66
% 2.35/2.66 ============================== SEARCH ================================
% 2.35/2.66
% 2.35/2.66 % Starting search at 0.01 seconds.
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=39.000, iters=3373
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=35.000, iters=3336
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=33.000, iters=3433
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=32.000, iters=3366
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=31.000, iters=3378
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=29.000, iters=3341
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=28.000, iters=3350
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=27.000, iters=3350
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=26.000, iters=3363
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=25.000, iters=3405
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=24.000, iters=3335
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=23.000, iters=3413
% 2.35/2.66
% 2.35/2.66 Low Water (keep): wt=22.000, iters=3350
% 2.35/2.66
% 2.35/2.66 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.59 sec).
% 2.35/2.66
% 2.35/2.66 ============================== PROOF =================================
% 2.35/2.66 % SZS status Unsatisfiable
% 2.35/2.66 % SZS output start Refutation
% 2.35/2.66
% 2.35/2.66 % Proof 1 at 1.66 (+ 0.05) seconds: prove_ax_glb1c.
% 2.35/2.66 % Length of proof is 50.
% 2.35/2.66 % Level of proof is 10.
% 2.35/2.66 % Maximum clause weight is 15.000.
% 2.35/2.66 % Given clauses 520.
% 2.35/2.66
% 2.35/2.66 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.35/2.66 4 greatest_lower_bound(a,c) = c # label(ax_glb1c_1) # label(hypothesis). [assumption].
% 2.35/2.66 5 greatest_lower_bound(b,c) = c # label(ax_glb1c_2) # label(hypothesis). [assumption].
% 2.35/2.66 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.35/2.66 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 2.35/2.66 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 2.35/2.66 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 2.35/2.66 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 2.35/2.66 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.35/2.66 12 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C) # label(associativity_of_glb) # label(axiom). [assumption].
% 2.35/2.66 13 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(12),rewrite([7(4)])].
% 2.35/2.66 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 2.35/2.66 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 2.35/2.66 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 2.35/2.66 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 2.35/2.66 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 2.35/2.66 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 2.35/2.66 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 2.35/2.66 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 2.35/2.66 24 least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b) # label(prove_ax_glb1c) # label(negated_conjecture) # answer(prove_ax_glb1c). [assumption].
% 2.35/2.66 25 least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b) # answer(prove_ax_glb1c). [copy(24),rewrite([8(5)])].
% 2.35/2.66 26 greatest_lower_bound(c,b) = c. [back_rewrite(5),rewrite([7(3)])].
% 2.35/2.66 27 greatest_lower_bound(c,a) = c. [back_rewrite(4),rewrite([7(3)])].
% 2.35/2.66 28 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 2.35/2.66 34 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),19(a,1,1))].
% 2.35/2.66 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)])].
% 2.35/2.66 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)])].
% 2.35/2.66 44 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),28(a,1,2))].
% 2.35/2.66 46 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(28(a,1),17(a,1,1)),rewrite([8(6)]),flip(a)].
% 2.35/2.66 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)].
% 2.35/2.66 50 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 2.35/2.66 51 multiply(A,identity) = A. [back_rewrite(44),rewrite([50(4)])].
% 2.35/2.66 65 multiply(A,multiply(inverse(A),B)) = B. [para(50(a,1),28(a,1))].
% 2.35/2.66 66 inverse(inverse(A)) = A. [para(50(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 2.35/2.66 144 greatest_lower_bound(identity,multiply(inverse(c),b)) = identity. [para(26(a,1),34(a,2,2)),rewrite([6(10)])].
% 2.35/2.66 154 greatest_lower_bound(A,multiply(A,multiply(inverse(c),b))) = A. [para(144(a,1),19(a,2,2)),rewrite([51(2),51(8)])].
% 2.35/2.66 205 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),10(a,1,2))].
% 2.35/2.66 222 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),28(a,1,2))].
% 2.35/2.66 241 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,multiply(inverse(c),b)))) = greatest_lower_bound(A,B). [para(154(a,1),13(a,2,2)),rewrite([7(6),7(8)])].
% 2.35/2.66 357 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(40(a,1),9(a,1,2))].
% 2.35/2.66 546 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(66(a,1),205(a,1,2,1,2))].
% 2.35/2.66 705 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(66(a,1),357(a,1,2,1,2))].
% 2.35/2.66 947 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(546(a,1),47(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 2.35/2.66 986 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(705(a,1),46(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 2.35/2.66 10393 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(705(a,1),222(a,1,2)),rewrite([66(3),8(2),51(5)])].
% 2.35/2.66 10433 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(10393(a,1),947(a,1,2)),rewrite([7(4),10393(7)])].
% 2.35/2.66 10529 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(10433(a,1),986(a,1,2,1)),rewrite([66(3),66(3),8(2),10433(6),66(4)])].
% 2.35/2.66 11038 greatest_lower_bound(c,greatest_lower_bound(a,b)) = c. [para(27(a,1),241(a,2)),rewrite([65(8)])].
% 2.35/2.66 11171 least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b). [para(11038(a,1),10529(a,1,2)),rewrite([8(5)])].
% 2.35/2.66 11172 $F # answer(prove_ax_glb1c). [resolve(11171,a,25,a)].
% 2.35/2.66
% 2.35/2.66 % SZS output end Refutation
% 2.35/2.66 ============================== end of proof ==========================
% 2.35/2.66
% 2.35/2.66 ============================== STATISTICS ============================
% 2.35/2.66
% 2.35/2.66 Given=520. Generated=71204. Kept=11164. proofs=1.
% 2.35/2.66 Usable=464. Sos=8687. Demods=7384. Limbo=14, Disabled=2016. Hints=0.
% 2.35/2.66 Megabytes=13.03.
% 2.35/2.66 User_CPU=1.66, System_CPU=0.05, Wall_clock=2.
% 2.35/2.66
% 2.35/2.66 ============================== end of statistics =====================
% 2.35/2.66
% 2.35/2.66 ============================== end of search =========================
% 2.35/2.66
% 2.35/2.66 THEOREM PROVED
% 2.35/2.66 % SZS status Unsatisfiable
% 2.35/2.66
% 2.35/2.66 Exiting with 1 proof.
% 2.35/2.66
% 2.35/2.66 Process 30853 exit (max_proofs) Mon Jun 13 10:18:27 2022
% 2.35/2.66 Prover9 interrupted
%------------------------------------------------------------------------------