TSTP Solution File: GRP144-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP144-1 : 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 11:17:43 EDT 2022
% Result : Unsatisfiable 2.66s 2.94s
% Output : Refutation 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP144-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.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 : Mon Jun 13 05:18:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.66/2.94 ============================== Prover9 ===============================
% 2.66/2.94 Prover9 (32) version 2009-11A, November 2009.
% 2.66/2.94 Process 31658 was started by sandbox on n010.cluster.edu,
% 2.66/2.94 Mon Jun 13 05:18:10 2022
% 2.66/2.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31298_n010.cluster.edu".
% 2.66/2.94 ============================== end of head ===========================
% 2.66/2.94
% 2.66/2.94 ============================== INPUT =================================
% 2.66/2.94
% 2.66/2.94 % Reading from file /tmp/Prover9_31298_n010.cluster.edu
% 2.66/2.94
% 2.66/2.94 set(prolog_style_variables).
% 2.66/2.94 set(auto2).
% 2.66/2.94 % set(auto2) -> set(auto).
% 2.66/2.94 % set(auto) -> set(auto_inference).
% 2.66/2.94 % set(auto) -> set(auto_setup).
% 2.66/2.94 % set(auto_setup) -> set(predicate_elim).
% 2.66/2.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.66/2.94 % set(auto) -> set(auto_limits).
% 2.66/2.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.66/2.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.66/2.94 % set(auto) -> set(auto_denials).
% 2.66/2.94 % set(auto) -> set(auto_process).
% 2.66/2.94 % set(auto2) -> assign(new_constants, 1).
% 2.66/2.94 % set(auto2) -> assign(fold_denial_max, 3).
% 2.66/2.94 % set(auto2) -> assign(max_weight, "200.000").
% 2.66/2.94 % set(auto2) -> assign(max_hours, 1).
% 2.66/2.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.66/2.94 % set(auto2) -> assign(max_seconds, 0).
% 2.66/2.94 % set(auto2) -> assign(max_minutes, 5).
% 2.66/2.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.66/2.94 % set(auto2) -> set(sort_initial_sos).
% 2.66/2.94 % set(auto2) -> assign(sos_limit, -1).
% 2.66/2.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.66/2.94 % set(auto2) -> assign(max_megs, 400).
% 2.66/2.94 % set(auto2) -> assign(stats, some).
% 2.66/2.94 % set(auto2) -> clear(echo_input).
% 2.66/2.94 % set(auto2) -> set(quiet).
% 2.66/2.94 % set(auto2) -> clear(print_initial_clauses).
% 2.66/2.94 % set(auto2) -> clear(print_given).
% 2.66/2.94 assign(lrs_ticks,-1).
% 2.66/2.94 assign(sos_limit,10000).
% 2.66/2.94 assign(order,kbo).
% 2.66/2.94 set(lex_order_vars).
% 2.66/2.94 clear(print_given).
% 2.66/2.94
% 2.66/2.94 % formulas(sos). % not echoed (16 formulas)
% 2.66/2.94
% 2.66/2.94 ============================== end of input ==========================
% 2.66/2.94
% 2.66/2.94 % From the command line: assign(max_seconds, 300).
% 2.66/2.94
% 2.66/2.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.66/2.94
% 2.66/2.94 % Formulas that are not ordinary clauses:
% 2.66/2.94
% 2.66/2.94 ============================== end of process non-clausal formulas ===
% 2.66/2.94
% 2.66/2.94 ============================== PROCESS INITIAL CLAUSES ===============
% 2.66/2.94
% 2.66/2.94 ============================== PREDICATE ELIMINATION =================
% 2.66/2.94
% 2.66/2.94 ============================== end predicate elimination =============
% 2.66/2.94
% 2.66/2.94 Auto_denials:
% 2.66/2.94 % copying label prove_ax_glb3a to answer in negative clause
% 2.66/2.94
% 2.66/2.94 Term ordering decisions:
% 2.66/2.94
% 2.66/2.94 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 2.66/2.94 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 2.66/2.94
% 2.66/2.94 ============================== end of process initial clauses ========
% 2.66/2.94
% 2.66/2.94 ============================== CLAUSES FOR SEARCH ====================
% 2.66/2.94
% 2.66/2.94 ============================== end of clauses for search =============
% 2.66/2.94
% 2.66/2.94 ============================== SEARCH ================================
% 2.66/2.94
% 2.66/2.94 % Starting search at 0.01 seconds.
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=37.000, iters=3366
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=36.000, iters=3360
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=35.000, iters=3385
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=32.000, iters=3422
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=31.000, iters=3394
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=30.000, iters=3334
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=29.000, iters=3483
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=28.000, iters=3393
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=27.000, iters=3365
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=26.000, iters=3338
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=25.000, iters=3360
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=24.000, iters=3336
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=23.000, iters=3350
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=22.000, iters=3337
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=21.000, iters=3333
% 2.66/2.94
% 2.66/2.94 Low Water (keep): wt=20.000, iters=3341
% 2.66/2.94
% 2.66/2.94 ============================== PROOF =================================
% 2.66/2.94 % SZS status Unsatisfiable
% 2.66/2.94 % SZS output start Refutation
% 2.66/2.94
% 2.66/2.94 % Proof 1 at 1.91 (+ 0.05) seconds: prove_ax_glb3a.
% 2.66/2.94 % Length of proof is 37.
% 2.66/2.94 % Level of proof is 9.
% 2.66/2.94 % Maximum clause weight is 15.000.
% 2.66/2.94 % Given clauses 486.
% 2.66/2.94
% 2.66/2.94 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.66/2.94 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.66/2.95 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 2.66/2.95 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 2.66/2.95 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 2.66/2.95 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 2.66/2.95 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.66/2.95 14 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 2.66/2.95 15 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(14),flip(a)].
% 2.66/2.95 16 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 2.66/2.95 17 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(16),flip(a)].
% 2.66/2.95 18 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 2.66/2.95 19 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(18),flip(a)].
% 2.66/2.95 20 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 2.66/2.95 21 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(20),flip(a)].
% 2.66/2.95 22 least_upper_bound(greatest_lower_bound(a,b),b) != b # label(prove_ax_glb3a) # label(negated_conjecture) # answer(prove_ax_glb3a). [assumption].
% 2.66/2.95 23 least_upper_bound(b,greatest_lower_bound(a,b)) != b # answer(prove_ax_glb3a). [copy(22),rewrite([6(5)])].
% 2.66/2.95 24 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 2.66/2.95 32 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(4(a,1),19(a,1,1)),rewrite([6(5)])].
% 2.66/2.95 36 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(4(a,1),21(a,1,1)),rewrite([5(5)])].
% 2.66/2.95 40 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),24(a,1,2))].
% 2.66/2.95 42 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(24(a,1),15(a,1,1)),rewrite([6(6)]),flip(a)].
% 2.66/2.95 43 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(24(a,1),17(a,1,1)),rewrite([5(6)]),flip(a)].
% 2.66/2.95 46 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(24(a,1),24(a,1,2))].
% 2.66/2.95 47 multiply(A,identity) = A. [back_rewrite(40),rewrite([46(4)])].
% 2.66/2.95 60 inverse(inverse(A)) = A. [para(46(a,1),47(a,1)),rewrite([47(2)]),flip(a)].
% 2.66/2.95 189 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(32(a,1),8(a,1,2))].
% 2.66/2.95 206 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(32(a,2),24(a,1,2))].
% 2.66/2.95 265 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(60(a,1),189(a,1,2,1,2))].
% 2.66/2.95 383 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(36(a,1),7(a,1,2))].
% 2.66/2.95 432 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(60(a,1),383(a,1,2,1,2))].
% 2.66/2.95 598 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(432(a,1),42(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 2.66/2.95 645 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(265(a,1),43(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 2.66/2.95 11216 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(432(a,1),206(a,1,2)),rewrite([60(3),6(2),47(5)])].
% 2.66/2.95 11244 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11216(a,1),645(a,1,2)),rewrite([5(4),11216(7)])].
% 2.66/2.95 11291 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11244(a,1),598(a,1,2,1)),rewrite([60(3),60(3),6(2),11244(6),60(4)])].
% 2.66/2.95 11292 $F # answer(prove_ax_glb3a). [resolve(11291,a,23,a)].
% 2.66/2.95
% 2.66/2.95 % SZS output end Refutation
% 2.66/2.95 ============================== end of proof ==========================
% 2.66/2.95
% 2.66/2.95 ============================== STATISTICS ============================
% 2.66/2.95
% 2.66/2.95 Given=486. Generated=95439. Kept=11284. proofs=1.
% 2.66/2.95 Usable=461. Sos=9169. Demods=8430. Limbo=4, Disabled=1665. Hints=0.
% 2.66/2.95 Megabytes=12.95.
% 2.66/2.95 User_CPU=1.91, System_CPU=0.05, Wall_clock=2.
% 2.66/2.95
% 2.66/2.95 ============================== end of statistics =====================
% 2.66/2.95
% 2.66/2.95 ============================== end of search =========================
% 2.66/2.95
% 2.66/2.95 THEOREM PROVED
% 2.66/2.95 % SZS status Unsatisfiable
% 2.66/2.95
% 2.66/2.95 Exiting with 1 proof.
% 2.66/2.95
% 2.66/2.95 Process 31658 exit (max_proofs) Mon Jun 13 05:18:12 2022
% 2.66/2.95 Prover9 interrupted
%------------------------------------------------------------------------------