TSTP Solution File: GRP181-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:17:59 EDT 2022
% Result : Unsatisfiable 1.27s 1.58s
% Output : Refutation 1.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.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 08:26:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.27/1.58 ============================== Prover9 ===============================
% 1.27/1.58 Prover9 (32) version 2009-11A, November 2009.
% 1.27/1.58 Process 15030 was started by sandbox2 on n009.cluster.edu,
% 1.27/1.58 Mon Jun 13 08:26:53 2022
% 1.27/1.58 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14714_n009.cluster.edu".
% 1.27/1.58 ============================== end of head ===========================
% 1.27/1.58
% 1.27/1.58 ============================== INPUT =================================
% 1.27/1.58
% 1.27/1.58 % Reading from file /tmp/Prover9_14714_n009.cluster.edu
% 1.27/1.58
% 1.27/1.58 set(prolog_style_variables).
% 1.27/1.58 set(auto2).
% 1.27/1.58 % set(auto2) -> set(auto).
% 1.27/1.58 % set(auto) -> set(auto_inference).
% 1.27/1.58 % set(auto) -> set(auto_setup).
% 1.27/1.58 % set(auto_setup) -> set(predicate_elim).
% 1.27/1.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.27/1.58 % set(auto) -> set(auto_limits).
% 1.27/1.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.27/1.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.27/1.58 % set(auto) -> set(auto_denials).
% 1.27/1.58 % set(auto) -> set(auto_process).
% 1.27/1.58 % set(auto2) -> assign(new_constants, 1).
% 1.27/1.58 % set(auto2) -> assign(fold_denial_max, 3).
% 1.27/1.58 % set(auto2) -> assign(max_weight, "200.000").
% 1.27/1.58 % set(auto2) -> assign(max_hours, 1).
% 1.27/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.27/1.58 % set(auto2) -> assign(max_seconds, 0).
% 1.27/1.58 % set(auto2) -> assign(max_minutes, 5).
% 1.27/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.27/1.58 % set(auto2) -> set(sort_initial_sos).
% 1.27/1.58 % set(auto2) -> assign(sos_limit, -1).
% 1.27/1.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.27/1.58 % set(auto2) -> assign(max_megs, 400).
% 1.27/1.58 % set(auto2) -> assign(stats, some).
% 1.27/1.58 % set(auto2) -> clear(echo_input).
% 1.27/1.58 % set(auto2) -> set(quiet).
% 1.27/1.58 % set(auto2) -> clear(print_initial_clauses).
% 1.27/1.58 % set(auto2) -> clear(print_given).
% 1.27/1.58 assign(lrs_ticks,-1).
% 1.27/1.58 assign(sos_limit,10000).
% 1.27/1.58 assign(order,kbo).
% 1.27/1.58 set(lex_order_vars).
% 1.27/1.58 clear(print_given).
% 1.27/1.58
% 1.27/1.58 % formulas(sos). % not echoed (23 formulas)
% 1.27/1.58
% 1.27/1.58 ============================== end of input ==========================
% 1.27/1.58
% 1.27/1.58 % From the command line: assign(max_seconds, 300).
% 1.27/1.58
% 1.27/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.27/1.58
% 1.27/1.58 % Formulas that are not ordinary clauses:
% 1.27/1.58
% 1.27/1.58 ============================== end of process non-clausal formulas ===
% 1.27/1.58
% 1.27/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.58
% 1.27/1.58 ============================== PREDICATE ELIMINATION =================
% 1.27/1.58
% 1.27/1.58 ============================== end predicate elimination =============
% 1.27/1.58
% 1.27/1.58 Auto_denials:
% 1.27/1.58 % copying label prove_p12x to answer in negative clause
% 1.27/1.58
% 1.27/1.58 Term ordering decisions:
% 1.27/1.58
% 1.27/1.58 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.27/1.58 Function symbol KB weights: c=1. identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 1.27/1.58
% 1.27/1.58 ============================== end of process initial clauses ========
% 1.27/1.58
% 1.27/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.58
% 1.27/1.58 ============================== end of clauses for search =============
% 1.27/1.58
% 1.27/1.58 ============================== SEARCH ================================
% 1.27/1.58
% 1.27/1.58 % Starting search at 0.01 seconds.
% 1.27/1.58
% 1.27/1.58 ============================== PROOF =================================
% 1.27/1.58 % SZS status Unsatisfiable
% 1.27/1.58 % SZS output start Refutation
% 1.27/1.58
% 1.27/1.58 % Proof 1 at 0.58 (+ 0.02) seconds: prove_p12x.
% 1.27/1.58 % Length of proof is 28.
% 1.27/1.58 % Level of proof is 7.
% 1.27/1.58 % Maximum clause weight is 13.000.
% 1.27/1.58 % Given clauses 291.
% 1.27/1.58
% 1.27/1.58 2 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 1.27/1.58 5 inverse(inverse(A)) = A # label(p12x_2) # label(hypothesis). [assumption].
% 1.27/1.58 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 1.27/1.58 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 1.27/1.58 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 1.27/1.58 11 greatest_lower_bound(a,c) = greatest_lower_bound(b,c) # label(p12x_4) # label(hypothesis). [assumption].
% 1.27/1.58 12 greatest_lower_bound(c,b) = greatest_lower_bound(c,a). [copy(11),rewrite([7(3),7(6)]),flip(a)].
% 1.27/1.58 13 least_upper_bound(a,c) = least_upper_bound(b,c) # label(p12x_5) # label(hypothesis). [assumption].
% 1.27/1.58 14 least_upper_bound(c,b) = least_upper_bound(c,a). [copy(13),rewrite([8(3),8(6)]),flip(a)].
% 1.27/1.58 16 inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)) # label(p12x_6) # label(hypothesis). [assumption].
% 1.27/1.58 18 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 1.27/1.58 23 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 1.27/1.58 24 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(23),flip(a)].
% 1.27/1.58 27 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 1.27/1.58 28 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(27),flip(a)].
% 1.27/1.58 31 a != b # label(prove_p12x) # label(negated_conjecture) # answer(prove_p12x). [assumption].
% 1.27/1.58 32 b != a # answer(prove_p12x). [copy(31),flip(a)].
% 1.27/1.58 33 multiply(A,inverse(A)) = identity. [para(5(a,1),6(a,1,1))].
% 1.27/1.58 47 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),24(a,1,1))].
% 1.27/1.58 50 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),28(a,1,1)),rewrite([8(5)])].
% 1.27/1.58 60 multiply(A,multiply(inverse(A),B)) = B. [para(33(a,1),18(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.27/1.58 76 multiply(greatest_lower_bound(A,B),multiply(least_upper_bound(inverse(A),inverse(B)),C)) = C. [para(16(a,1),60(a,1,2,1))].
% 1.27/1.58 227 least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(c,a)). [para(14(a,1),47(a,2,2))].
% 1.27/1.58 1587 multiply(greatest_lower_bound(A,B),least_upper_bound(identity,multiply(inverse(A),B))) = B. [para(50(a,2),76(a,1,2))].
% 1.27/1.58 4156 multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))) = b. [para(12(a,1),1587(a,1,1)),rewrite([227(9)])].
% 1.27/1.58 4175 multiply(greatest_lower_bound(A,B),multiply(inverse(A),least_upper_bound(A,B))) = B. [para(47(a,1),1587(a,1,2))].
% 1.27/1.58 4221 b = a. [back_rewrite(4156),rewrite([4175(10)]),flip(a)].
% 1.27/1.58 4222 $F # answer(prove_p12x). [resolve(4221,a,32,a)].
% 1.27/1.58
% 1.27/1.58 % SZS output end Refutation
% 1.27/1.58 ============================== end of proof ==========================
% 1.27/1.58
% 1.27/1.58 ============================== STATISTICS ============================
% 1.27/1.58
% 1.27/1.58 Given=291. Generated=21568. Kept=4212. proofs=1.
% 1.27/1.58 Usable=274. Sos=3281. Demods=3173. Limbo=46, Disabled=633. Hints=0.
% 1.27/1.58 Megabytes=4.86.
% 1.27/1.58 User_CPU=0.58, System_CPU=0.02, Wall_clock=1.
% 1.27/1.58
% 1.27/1.58 ============================== end of statistics =====================
% 1.27/1.58
% 1.27/1.58 ============================== end of search =========================
% 1.27/1.58
% 1.27/1.58 THEOREM PROVED
% 1.27/1.58 % SZS status Unsatisfiable
% 1.27/1.58
% 1.27/1.58 Exiting with 1 proof.
% 1.27/1.58
% 1.27/1.58 Process 15030 exit (max_proofs) Mon Jun 13 08:26:54 2022
% 1.27/1.58 Prover9 interrupted
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