TSTP Solution File: GRP189-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 2.64s 2.92s
% Output : Refutation 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n005.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 06:13:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.64/2.92 ============================== Prover9 ===============================
% 2.64/2.92 Prover9 (32) version 2009-11A, November 2009.
% 2.64/2.92 Process 31368 was started by sandbox2 on n005.cluster.edu,
% 2.64/2.92 Tue Jun 14 06:13:09 2022
% 2.64/2.92 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31100_n005.cluster.edu".
% 2.64/2.92 ============================== end of head ===========================
% 2.64/2.92
% 2.64/2.92 ============================== INPUT =================================
% 2.64/2.92
% 2.64/2.92 % Reading from file /tmp/Prover9_31100_n005.cluster.edu
% 2.64/2.92
% 2.64/2.92 set(prolog_style_variables).
% 2.64/2.92 set(auto2).
% 2.64/2.92 % set(auto2) -> set(auto).
% 2.64/2.92 % set(auto) -> set(auto_inference).
% 2.64/2.92 % set(auto) -> set(auto_setup).
% 2.64/2.92 % set(auto_setup) -> set(predicate_elim).
% 2.64/2.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.64/2.92 % set(auto) -> set(auto_limits).
% 2.64/2.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.64/2.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.64/2.92 % set(auto) -> set(auto_denials).
% 2.64/2.92 % set(auto) -> set(auto_process).
% 2.64/2.92 % set(auto2) -> assign(new_constants, 1).
% 2.64/2.92 % set(auto2) -> assign(fold_denial_max, 3).
% 2.64/2.92 % set(auto2) -> assign(max_weight, "200.000").
% 2.64/2.92 % set(auto2) -> assign(max_hours, 1).
% 2.64/2.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.64/2.92 % set(auto2) -> assign(max_seconds, 0).
% 2.64/2.92 % set(auto2) -> assign(max_minutes, 5).
% 2.64/2.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.64/2.92 % set(auto2) -> set(sort_initial_sos).
% 2.64/2.92 % set(auto2) -> assign(sos_limit, -1).
% 2.64/2.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.64/2.92 % set(auto2) -> assign(max_megs, 400).
% 2.64/2.92 % set(auto2) -> assign(stats, some).
% 2.64/2.92 % set(auto2) -> clear(echo_input).
% 2.64/2.92 % set(auto2) -> set(quiet).
% 2.64/2.92 % set(auto2) -> clear(print_initial_clauses).
% 2.64/2.92 % set(auto2) -> clear(print_given).
% 2.64/2.92 assign(lrs_ticks,-1).
% 2.64/2.92 assign(sos_limit,10000).
% 2.64/2.92 assign(order,kbo).
% 2.64/2.92 set(lex_order_vars).
% 2.64/2.92 clear(print_given).
% 2.64/2.92
% 2.64/2.92 % formulas(sos). % not echoed (19 formulas)
% 2.64/2.92
% 2.64/2.92 ============================== end of input ==========================
% 2.64/2.92
% 2.64/2.92 % From the command line: assign(max_seconds, 300).
% 2.64/2.92
% 2.64/2.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.64/2.92
% 2.64/2.92 % Formulas that are not ordinary clauses:
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% 2.64/2.92 ============================== end of process non-clausal formulas ===
% 2.64/2.92
% 2.64/2.92 ============================== PROCESS INITIAL CLAUSES ===============
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% 2.64/2.92 ============================== PREDICATE ELIMINATION =================
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% 2.64/2.92 ============================== end predicate elimination =============
% 2.64/2.92
% 2.64/2.92 Auto_denials:
% 2.64/2.92 % copying label prove_p38b to answer in negative clause
% 2.64/2.92
% 2.64/2.92 Term ordering decisions:
% 2.64/2.92
% 2.64/2.92 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 2.64/2.92 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 2.64/2.92
% 2.64/2.92 ============================== end of process initial clauses ========
% 2.64/2.92
% 2.64/2.92 ============================== CLAUSES FOR SEARCH ====================
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% 2.64/2.92 ============================== end of clauses for search =============
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% 2.64/2.92 ============================== SEARCH ================================
% 2.64/2.92
% 2.64/2.92 % Starting search at 0.01 seconds.
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=37.000, iters=3387
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% 2.64/2.92 Low Water (keep): wt=33.000, iters=3354
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=31.000, iters=3378
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=30.000, iters=3446
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=29.000, iters=3404
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=27.000, iters=3340
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=26.000, iters=3380
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=25.000, iters=3403
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=24.000, iters=3335
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=23.000, iters=3379
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=22.000, iters=3360
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=21.000, iters=3360
% 2.64/2.92
% 2.64/2.92 Low Water (keep): wt=20.000, iters=3351
% 2.64/2.92
% 2.64/2.92 ============================== PROOF =================================
% 2.64/2.92 % SZS status Unsatisfiable
% 2.64/2.92 % SZS output start Refutation
% 2.64/2.92
% 2.64/2.92 % Proof 1 at 1.86 (+ 0.06) seconds: prove_p38b.
% 2.64/2.92 % Length of proof is 38.
% 2.64/2.92 % Level of proof is 9.
% 2.64/2.92 % Maximum clause weight is 15.000.
% 2.64/2.92 % Given clauses 487.
% 2.64/2.92
% 2.64/2.92 1 inverse(identity) = identity # label(p38b_1) # label(hypothesis). [assumption].
% 2.64/2.92 2 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.64/2.92 5 inverse(inverse(A)) = A # label(p38b_2) # label(hypothesis). [assumption].
% 2.64/2.92 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.64/2.92 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 2.64/2.92 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 2.64/2.92 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 2.64/2.92 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 2.64/2.92 11 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)) # label(p38b_3) # label(hypothesis). [assumption].
% 2.64/2.92 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.64/2.92 17 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 2.64/2.92 18 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(17),flip(a)].
% 2.64/2.92 19 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 2.64/2.92 20 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(19),flip(a)].
% 2.64/2.92 21 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 2.64/2.92 22 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(21),flip(a)].
% 2.64/2.92 23 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 2.64/2.92 24 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(23),flip(a)].
% 2.64/2.92 25 greatest_lower_bound(b,least_upper_bound(a,b)) != b # label(prove_p38b) # label(negated_conjecture) # answer(prove_p38b). [assumption].
% 2.64/2.92 27 multiply(inverse(A),identity) = inverse(A). [para(1(a,1),11(a,2,2)),rewrite([2(2)]),flip(a)].
% 2.64/2.92 29 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),12(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.64/2.92 34 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),18(a,1,1))].
% 2.64/2.92 37 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),22(a,1,1)),rewrite([8(5)])].
% 2.64/2.92 41 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),24(a,1,1)),rewrite([7(5)])].
% 2.64/2.92 50 multiply(A,identity) = A. [para(5(a,1),27(a,1,1)),rewrite([5(4)])].
% 2.64/2.92 56 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(29(a,1),20(a,1,1)),rewrite([7(6)]),flip(a)].
% 2.64/2.92 93 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(34(a,1),10(a,1,2))].
% 2.64/2.92 170 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(37(a,1),10(a,1,2))].
% 2.64/2.92 188 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(37(a,2),29(a,1,2))].
% 2.64/2.92 243 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(5(a,1),170(a,1,2,1,2))].
% 2.64/2.92 364 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(41(a,1),9(a,1,2))].
% 2.64/2.92 411 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(5(a,1),364(a,1,2,1,2))].
% 2.64/2.92 439 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(93(a,1),411(a,1,2,1)),rewrite([11(6),5(6),2(6)])].
% 2.64/2.92 530 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(8(a,1),439(a,1,2,1,1))].
% 2.64/2.92 996 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(243(a,1),56(a,1,2)),rewrite([50(4),50(7)]),flip(a)].
% 2.64/2.92 11360 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(530(a,1),188(a,1,2)),rewrite([8(4),50(7)])].
% 2.64/2.92 11393 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(11360(a,1),996(a,1,2)),rewrite([5(3),7(2),11360(7)])].
% 2.64/2.92 11394 $F # answer(prove_p38b). [resolve(11393,a,25,a)].
% 2.64/2.92
% 2.64/2.92 % SZS output end Refutation
% 2.64/2.92 ============================== end of proof ==========================
% 2.64/2.92
% 2.64/2.92 ============================== STATISTICS ============================
% 2.64/2.92
% 2.64/2.92 Given=487. Generated=96389. Kept=11387. proofs=1.
% 2.64/2.92 Usable=468. Sos=9291. Demods=8515. Limbo=3, Disabled=1643. Hints=0.
% 2.64/2.92 Megabytes=13.07.
% 2.64/2.92 User_CPU=1.86, System_CPU=0.06, Wall_clock=2.
% 2.64/2.92
% 2.64/2.92 ============================== end of statistics =====================
% 2.64/2.92
% 2.64/2.92 ============================== end of search =========================
% 2.64/2.92
% 2.64/2.92 THEOREM PROVED
% 2.64/2.92 % SZS status Unsatisfiable
% 2.64/2.92
% 2.64/2.92 Exiting with 1 proof.
% 2.64/2.92
% 2.64/2.92 Process 31368 exit (max_proofs) Tue Jun 14 06:13:11 2022
% 2.64/2.92 Prover9 interrupted
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