TSTP Solution File: GRP193-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:18:06 EDT 2022
% Result : Unsatisfiable 0.81s 1.10s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 09:12:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.81/1.10 ============================== Prover9 ===============================
% 0.81/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.10 Process 16373 was started by sandbox on n019.cluster.edu,
% 0.81/1.10 Tue Jun 14 09:12:10 2022
% 0.81/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16219_n019.cluster.edu".
% 0.81/1.10 ============================== end of head ===========================
% 0.81/1.10
% 0.81/1.10 ============================== INPUT =================================
% 0.81/1.10
% 0.81/1.10 % Reading from file /tmp/Prover9_16219_n019.cluster.edu
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% 0.81/1.10 set(prolog_style_variables).
% 0.81/1.10 set(auto2).
% 0.81/1.10 % set(auto2) -> set(auto).
% 0.81/1.10 % set(auto) -> set(auto_inference).
% 0.81/1.10 % set(auto) -> set(auto_setup).
% 0.81/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.10 % set(auto) -> set(auto_limits).
% 0.81/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.10 % set(auto) -> set(auto_denials).
% 0.81/1.10 % set(auto) -> set(auto_process).
% 0.81/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.10 % set(auto2) -> assign(stats, some).
% 0.81/1.10 % set(auto2) -> clear(echo_input).
% 0.81/1.10 % set(auto2) -> set(quiet).
% 0.81/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.10 % set(auto2) -> clear(print_given).
% 0.81/1.10 assign(lrs_ticks,-1).
% 0.81/1.10 assign(sos_limit,10000).
% 0.81/1.10 assign(order,kbo).
% 0.81/1.10 set(lex_order_vars).
% 0.81/1.10 clear(print_given).
% 0.81/1.10
% 0.81/1.10 % formulas(sos). % not echoed (21 formulas)
% 0.81/1.10
% 0.81/1.10 ============================== end of input ==========================
% 0.81/1.10
% 0.81/1.10 % From the command line: assign(max_seconds, 300).
% 0.81/1.10
% 0.81/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.10
% 0.81/1.10 % Formulas that are not ordinary clauses:
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% 0.81/1.10 ============================== end of process non-clausal formulas ===
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% 0.81/1.10 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.81/1.10 ============================== PREDICATE ELIMINATION =================
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% 0.81/1.10 ============================== end predicate elimination =============
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% 0.81/1.10 Auto_denials:
% 0.81/1.10 % copying label prove_p8_9b to answer in negative clause
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% 0.81/1.10 Term ordering decisions:
% 0.81/1.10
% 0.81/1.10 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.81/1.10 Function symbol KB weights: identity=1. a=1. b=1. c=1. greatest_lower_bound=1. multiply=1. least_upper_bound=1. inverse=0.
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% 0.81/1.10 ============================== end of process initial clauses ========
% 0.81/1.10
% 0.81/1.10 ============================== CLAUSES FOR SEARCH ====================
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% 0.81/1.10 ============================== end of clauses for search =============
% 0.81/1.10
% 0.81/1.10 ============================== SEARCH ================================
% 0.81/1.10
% 0.81/1.10 % Starting search at 0.01 seconds.
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% 0.81/1.10 ============================== PROOF =================================
% 0.81/1.10 % SZS status Unsatisfiable
% 0.81/1.10 % SZS output start Refutation
% 0.81/1.10
% 0.81/1.10 % Proof 1 at 0.10 (+ 0.01) seconds: prove_p8_9b.
% 0.81/1.10 % Length of proof is 21.
% 0.81/1.10 % Level of proof is 5.
% 0.81/1.10 % Maximum clause weight is 15.000.
% 0.81/1.10 % Given clauses 102.
% 0.81/1.10
% 0.81/1.10 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.81/1.10 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 0.81/1.10 5 greatest_lower_bound(identity,b) = identity # label(p8_9b_2) # label(hypothesis). [assumption].
% 0.81/1.10 7 greatest_lower_bound(a,b) = identity # label(p8_9b_4) # label(hypothesis). [assumption].
% 0.81/1.10 9 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.81/1.10 14 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].
% 0.81/1.10 15 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(14),rewrite([9(4)])].
% 0.81/1.10 20 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 0.81/1.10 21 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(20),flip(a)].
% 0.81/1.10 24 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.81/1.10 25 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(24),flip(a)].
% 0.81/1.10 26 greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) # label(p8_9b_5) # label(hypothesis). [assumption].
% 0.81/1.10 27 greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)). [copy(26),rewrite([7(8),1(10),9(9),15(9,R),9(8)])].
% 0.81/1.10 28 greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) # label(prove_p8_9b) # label(negated_conjecture) # answer(prove_p8_9b). [assumption].
% 0.81/1.10 31 greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B). [para(15(a,1),3(a,1)),rewrite([9(1),9(2),15(2,R),3(1),9(3)])].
% 0.81/1.10 41 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(1(a,1),25(a,1,1)),rewrite([9(4)])].
% 0.81/1.10 43 greatest_lower_bound(A,multiply(b,A)) = A. [para(5(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 0.81/1.10 48 greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)). [para(27(a,1),15(a,1)),rewrite([31(13),9(12)]),flip(a)].
% 0.81/1.10 51 greatest_lower_bound(A,greatest_lower_bound(B,multiply(b,A))) = greatest_lower_bound(A,B). [para(43(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 0.81/1.10 597 greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c). [para(48(a,1),51(a,2)),rewrite([21(12),15(9,R),3(8),41(9),9(3),5(3),1(5)]),flip(a)].
% 0.81/1.10 598 $F # answer(prove_p8_9b). [resolve(597,a,28,a)].
% 0.81/1.10
% 0.81/1.10 % SZS output end Refutation
% 0.81/1.10 ============================== end of proof ==========================
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% 0.81/1.10 ============================== STATISTICS ============================
% 0.81/1.10
% 0.81/1.10 Given=102. Generated=2777. Kept=590. proofs=1.
% 0.81/1.10 Usable=94. Sos=407. Demods=421. Limbo=17, Disabled=92. Hints=0.
% 0.81/1.10 Megabytes=0.64.
% 0.81/1.10 User_CPU=0.10, System_CPU=0.01, Wall_clock=0.
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% 0.81/1.10 ============================== end of statistics =====================
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% 0.81/1.10 ============================== end of search =========================
% 0.81/1.10
% 0.81/1.10 THEOREM PROVED
% 0.81/1.10 % SZS status Unsatisfiable
% 0.81/1.10
% 0.81/1.10 Exiting with 1 proof.
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% 0.81/1.10 Process 16373 exit (max_proofs) Tue Jun 14 09:12:10 2022
% 0.81/1.10 Prover9 interrupted
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