TSTP Solution File: GRP190-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:18:05 EDT 2022
% Result : Unsatisfiable 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 15:47:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.03 ============================== Prover9 ===============================
% 0.75/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.03 Process 28585 was started by sandbox2 on n018.cluster.edu,
% 0.75/1.03 Mon Jun 13 15:47:13 2022
% 0.75/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28312_n018.cluster.edu".
% 0.75/1.03 ============================== end of head ===========================
% 0.75/1.03
% 0.75/1.03 ============================== INPUT =================================
% 0.75/1.03
% 0.75/1.03 % Reading from file /tmp/Prover9_28312_n018.cluster.edu
% 0.75/1.03
% 0.75/1.03 set(prolog_style_variables).
% 0.75/1.03 set(auto2).
% 0.75/1.03 % set(auto2) -> set(auto).
% 0.75/1.03 % set(auto) -> set(auto_inference).
% 0.75/1.03 % set(auto) -> set(auto_setup).
% 0.75/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.03 % set(auto) -> set(auto_limits).
% 0.75/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.03 % set(auto) -> set(auto_denials).
% 0.75/1.03 % set(auto) -> set(auto_process).
% 0.75/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.03 % set(auto2) -> assign(stats, some).
% 0.75/1.03 % set(auto2) -> clear(echo_input).
% 0.75/1.03 % set(auto2) -> set(quiet).
% 0.75/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.03 % set(auto2) -> clear(print_given).
% 0.75/1.03 assign(lrs_ticks,-1).
% 0.75/1.03 assign(sos_limit,10000).
% 0.75/1.03 assign(order,kbo).
% 0.75/1.03 set(lex_order_vars).
% 0.75/1.03 clear(print_given).
% 0.75/1.03
% 0.75/1.03 % formulas(sos). % not echoed (17 formulas)
% 0.75/1.03
% 0.75/1.03 ============================== end of input ==========================
% 0.75/1.03
% 0.75/1.03 % From the command line: assign(max_seconds, 300).
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.03
% 0.75/1.03 % Formulas that are not ordinary clauses:
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% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials:
% 0.75/1.03 % copying label prove_p39c to answer in negative clause
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03
% 0.75/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.75/1.03 Function symbol KB weights: a=1. identity=1. b=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.01 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.04 (+ 0.00) seconds: prove_p39c.
% 0.75/1.03 % Length of proof is 24.
% 0.75/1.03 % Level of proof is 8.
% 0.75/1.03 % Maximum clause weight is 13.000.
% 0.75/1.03 % Given clauses 51.
% 0.75/1.03
% 0.75/1.03 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.75/1.03 4 least_upper_bound(a,b) = a # label(p39c_1) # label(hypothesis). [assumption].
% 0.75/1.03 5 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.75/1.03 7 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.75/1.03 9 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 0.75/1.03 10 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.75/1.03 15 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 0.75/1.03 16 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(15),flip(a)].
% 0.75/1.03 19 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.75/1.03 20 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(19),flip(a)].
% 0.75/1.03 23 greatest_lower_bound(inverse(a),inverse(b)) != inverse(a) # label(prove_p39c) # label(negated_conjecture) # answer(prove_p39c). [assumption].
% 0.75/1.03 24 multiply(inverse(A),multiply(A,B)) = B. [para(5(a,1),10(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.75/1.03 29 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(5(a,1),16(a,1,1))].
% 0.75/1.03 32 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(5(a,1),20(a,1,1)),rewrite([7(5)])].
% 0.75/1.03 40 multiply(inverse(inverse(A)),identity) = A. [para(5(a,1),24(a,1,2))].
% 0.75/1.03 46 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(24(a,1),24(a,1,2))].
% 0.75/1.03 47 multiply(A,identity) = A. [back_rewrite(40),rewrite([46(4)])].
% 0.75/1.03 60 inverse(inverse(A)) = A. [para(46(a,1),47(a,1)),rewrite([47(2)]),flip(a)].
% 0.75/1.03 92 least_upper_bound(identity,multiply(inverse(a),b)) = identity. [para(4(a,1),29(a,2,2)),rewrite([5(10)])].
% 0.75/1.03 218 multiply(least_upper_bound(inverse(a),inverse(b)),b) = identity. [para(32(a,1),92(a,1))].
% 0.75/1.03 228 inverse(least_upper_bound(inverse(a),inverse(b))) = b. [para(218(a,1),24(a,1,2)),rewrite([47(8)])].
% 0.75/1.03 231 least_upper_bound(inverse(a),inverse(b)) = inverse(b). [para(228(a,1),60(a,1,1)),flip(a)].
% 0.75/1.03 234 greatest_lower_bound(inverse(a),inverse(b)) = inverse(a). [para(231(a,1),9(a,1,2))].
% 0.75/1.03 235 $F # answer(prove_p39c). [resolve(234,a,23,a)].
% 0.75/1.03
% 0.75/1.03 % SZS output end Refutation
% 0.75/1.03 ============================== end of proof ==========================
% 0.75/1.03
% 0.75/1.03 ============================== STATISTICS ============================
% 0.75/1.03
% 0.75/1.03 Given=51. Generated=1098. Kept=228. proofs=1.
% 0.75/1.03 Usable=46. Sos=147. Demods=145. Limbo=0, Disabled=51. Hints=0.
% 0.75/1.03 Megabytes=0.27.
% 0.75/1.03 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of statistics =====================
% 0.75/1.03
% 0.75/1.03 ============================== end of search =========================
% 0.75/1.03
% 0.75/1.03 THEOREM PROVED
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03
% 0.75/1.03 Exiting with 1 proof.
% 0.75/1.03
% 0.75/1.03 Process 28585 exit (max_proofs) Mon Jun 13 15:47:13 2022
% 0.75/1.03 Prover9 interrupted
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