TSTP Solution File: GRP189-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP189-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 11:18:04 EDT 2022
% Result : Unsatisfiable 2.56s 2.91s
% Output : Refutation 2.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP189-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.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 : Tue Jun 14 09:09:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.56/2.91 ============================== Prover9 ===============================
% 2.56/2.91 Prover9 (32) version 2009-11A, November 2009.
% 2.56/2.91 Process 1619 was started by sandbox2 on n023.cluster.edu,
% 2.56/2.91 Tue Jun 14 09:09:06 2022
% 2.56/2.91 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1313_n023.cluster.edu".
% 2.56/2.91 ============================== end of head ===========================
% 2.56/2.91
% 2.56/2.91 ============================== INPUT =================================
% 2.56/2.91
% 2.56/2.91 % Reading from file /tmp/Prover9_1313_n023.cluster.edu
% 2.56/2.91
% 2.56/2.91 set(prolog_style_variables).
% 2.56/2.91 set(auto2).
% 2.56/2.91 % set(auto2) -> set(auto).
% 2.56/2.91 % set(auto) -> set(auto_inference).
% 2.56/2.91 % set(auto) -> set(auto_setup).
% 2.56/2.91 % set(auto_setup) -> set(predicate_elim).
% 2.56/2.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.56/2.91 % set(auto) -> set(auto_limits).
% 2.56/2.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.56/2.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.56/2.91 % set(auto) -> set(auto_denials).
% 2.56/2.91 % set(auto) -> set(auto_process).
% 2.56/2.91 % set(auto2) -> assign(new_constants, 1).
% 2.56/2.91 % set(auto2) -> assign(fold_denial_max, 3).
% 2.56/2.91 % set(auto2) -> assign(max_weight, "200.000").
% 2.56/2.91 % set(auto2) -> assign(max_hours, 1).
% 2.56/2.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.56/2.91 % set(auto2) -> assign(max_seconds, 0).
% 2.56/2.91 % set(auto2) -> assign(max_minutes, 5).
% 2.56/2.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.56/2.91 % set(auto2) -> set(sort_initial_sos).
% 2.56/2.91 % set(auto2) -> assign(sos_limit, -1).
% 2.56/2.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.56/2.91 % set(auto2) -> assign(max_megs, 400).
% 2.56/2.91 % set(auto2) -> assign(stats, some).
% 2.56/2.91 % set(auto2) -> clear(echo_input).
% 2.56/2.91 % set(auto2) -> set(quiet).
% 2.56/2.91 % set(auto2) -> clear(print_initial_clauses).
% 2.56/2.91 % set(auto2) -> clear(print_given).
% 2.56/2.91 assign(lrs_ticks,-1).
% 2.56/2.91 assign(sos_limit,10000).
% 2.56/2.91 assign(order,kbo).
% 2.56/2.91 set(lex_order_vars).
% 2.56/2.91 clear(print_given).
% 2.56/2.91
% 2.56/2.91 % formulas(sos). % not echoed (16 formulas)
% 2.56/2.91
% 2.56/2.91 ============================== end of input ==========================
% 2.56/2.91
% 2.56/2.91 % From the command line: assign(max_seconds, 300).
% 2.56/2.91
% 2.56/2.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.56/2.91
% 2.56/2.91 % Formulas that are not ordinary clauses:
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% 2.56/2.91 ============================== end of process non-clausal formulas ===
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% 2.56/2.91 ============================== PROCESS INITIAL CLAUSES ===============
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% 2.56/2.91 ============================== PREDICATE ELIMINATION =================
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% 2.56/2.91 ============================== end predicate elimination =============
% 2.56/2.91
% 2.56/2.91 Auto_denials:
% 2.56/2.91 % copying label prove_p38b to answer in negative clause
% 2.56/2.91
% 2.56/2.91 Term ordering decisions:
% 2.56/2.91
% 2.56/2.91 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 2.56/2.91 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 2.56/2.91
% 2.56/2.91 ============================== end of process initial clauses ========
% 2.56/2.91
% 2.56/2.91 ============================== CLAUSES FOR SEARCH ====================
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% 2.56/2.91 ============================== end of clauses for search =============
% 2.56/2.91
% 2.56/2.91 ============================== SEARCH ================================
% 2.56/2.91
% 2.56/2.91 % Starting search at 0.01 seconds.
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=37.000, iters=3366
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% 2.56/2.91 Low Water (keep): wt=36.000, iters=3360
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=35.000, iters=3385
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=32.000, iters=3422
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=31.000, iters=3394
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=30.000, iters=3334
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=29.000, iters=3483
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=28.000, iters=3393
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=27.000, iters=3365
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=26.000, iters=3338
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=25.000, iters=3360
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=24.000, iters=3336
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=23.000, iters=3350
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=22.000, iters=3337
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=21.000, iters=3333
% 2.56/2.91
% 2.56/2.91 Low Water (keep): wt=20.000, iters=3341
% 2.56/2.91
% 2.56/2.91 ============================== PROOF =================================
% 2.56/2.91 % SZS status Unsatisfiable
% 2.56/2.91 % SZS output start Refutation
% 2.56/2.91
% 2.56/2.91 % Proof 1 at 1.84 (+ 0.05) seconds: prove_p38b.
% 2.56/2.91 % Length of proof is 41.
% 2.56/2.91 % Level of proof is 11.
% 2.56/2.91 % Maximum clause weight is 15.000.
% 2.56/2.91 % Given clauses 484.
% 2.56/2.91
% 2.56/2.91 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.56/2.91 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.56/2.91 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 2.56/2.91 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 2.56/2.91 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 2.56/2.91 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 2.56/2.91 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.56/2.91 14 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 2.56/2.91 15 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(14),flip(a)].
% 2.56/2.91 16 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 2.56/2.91 17 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(16),flip(a)].
% 2.56/2.91 18 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 2.56/2.91 19 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(18),flip(a)].
% 2.56/2.91 20 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 2.56/2.91 21 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(20),flip(a)].
% 2.56/2.91 22 greatest_lower_bound(b,least_upper_bound(a,b)) != b # label(prove_p38b) # label(negated_conjecture) # answer(prove_p38b). [assumption].
% 2.56/2.91 23 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 2.56/2.91 28 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),15(a,1,1))].
% 2.56/2.91 31 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)])].
% 2.56/2.91 35 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)])].
% 2.56/2.91 39 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),23(a,1,2))].
% 2.56/2.91 42 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(23(a,1),17(a,1,1)),rewrite([5(6)]),flip(a)].
% 2.56/2.91 45 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(23(a,1),23(a,1,2))].
% 2.56/2.91 46 multiply(A,identity) = A. [back_rewrite(39),rewrite([45(4)])].
% 2.56/2.91 53 multiply(A,inverse(A)) = identity. [para(45(a,1),4(a,1))].
% 2.56/2.91 59 inverse(inverse(A)) = A. [para(45(a,1),46(a,1)),rewrite([46(2)]),flip(a)].
% 2.56/2.91 60 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(53(a,1),9(a,1)),flip(a)].
% 2.56/2.91 78 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(60(a,1),23(a,1,2)),rewrite([46(3)]),flip(a)].
% 2.56/2.91 86 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(78(a,1),23(a,1,2)),flip(a)].
% 2.56/2.91 111 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(28(a,1),8(a,1,2))].
% 2.56/2.91 188 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(31(a,1),8(a,1,2))].
% 2.56/2.91 205 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(31(a,2),23(a,1,2))].
% 2.56/2.91 264 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(59(a,1),188(a,1,2,1,2))].
% 2.56/2.91 382 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(35(a,1),7(a,1,2))].
% 2.56/2.91 431 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(59(a,1),382(a,1,2,1,2))].
% 2.56/2.91 457 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(111(a,1),431(a,1,2,1)),rewrite([86(6),59(6),1(6)])].
% 2.56/2.91 548 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(6(a,1),457(a,1,2,1,1))].
% 2.56/2.91 644 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(264(a,1),42(a,1,2)),rewrite([46(4),46(7)]),flip(a)].
% 2.56/2.91 11216 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(548(a,1),205(a,1,2)),rewrite([6(4),46(7)])].
% 2.56/2.91 11249 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(11216(a,1),644(a,1,2)),rewrite([59(3),5(2),11216(7)])].
% 2.56/2.91 11250 $F # answer(prove_p38b). [resolve(11249,a,22,a)].
% 2.56/2.91
% 2.56/2.91 % SZS output end Refutation
% 2.56/2.91 ============================== end of proof ==========================
% 2.56/2.91
% 2.56/2.91 ============================== STATISTICS ============================
% 2.56/2.91
% 2.56/2.91 Given=484. Generated=94545. Kept=11243. proofs=1.
% 2.56/2.91 Usable=465. Sos=9190. Demods=8453. Limbo=3, Disabled=1600. Hints=0.
% 2.56/2.91 Megabytes=12.94.
% 2.56/2.91 User_CPU=1.84, System_CPU=0.05, Wall_clock=2.
% 2.56/2.91
% 2.56/2.91 ============================== end of statistics =====================
% 2.56/2.91
% 2.56/2.91 ============================== end of search =========================
% 2.56/2.91
% 2.56/2.91 THEOREM PROVED
% 2.56/2.91 % SZS status Unsatisfiable
% 2.56/2.91
% 2.56/2.91 Exiting with 1 proof.
% 2.56/2.91
% 2.56/2.91 Process 1619 exit (max_proofs) Tue Jun 14 09:09:08 2022
% 2.56/2.91 Prover9 interrupted
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