TSTP Solution File: GRP174-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:17:54 EDT 2022
% Result : Unsatisfiable 0.71s 0.98s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 08:20:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.71/0.98 ============================== Prover9 ===============================
% 0.71/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.71/0.98 Process 17375 was started by sandbox on n027.cluster.edu,
% 0.71/0.98 Tue Jun 14 08:20:48 2022
% 0.71/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17222_n027.cluster.edu".
% 0.71/0.98 ============================== end of head ===========================
% 0.71/0.98
% 0.71/0.98 ============================== INPUT =================================
% 0.71/0.98
% 0.71/0.98 % Reading from file /tmp/Prover9_17222_n027.cluster.edu
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% 0.71/0.98 set(prolog_style_variables).
% 0.71/0.98 set(auto2).
% 0.71/0.98 % set(auto2) -> set(auto).
% 0.71/0.98 % set(auto) -> set(auto_inference).
% 0.71/0.98 % set(auto) -> set(auto_setup).
% 0.71/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.71/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/0.98 % set(auto) -> set(auto_limits).
% 0.71/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/0.98 % set(auto) -> set(auto_denials).
% 0.71/0.98 % set(auto) -> set(auto_process).
% 0.71/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.98 % set(auto2) -> assign(stats, some).
% 0.71/0.98 % set(auto2) -> clear(echo_input).
% 0.71/0.98 % set(auto2) -> set(quiet).
% 0.71/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.98 % set(auto2) -> clear(print_given).
% 0.71/0.98 assign(lrs_ticks,-1).
% 0.71/0.98 assign(sos_limit,10000).
% 0.71/0.98 assign(order,kbo).
% 0.71/0.98 set(lex_order_vars).
% 0.71/0.98 clear(print_given).
% 0.71/0.98
% 0.71/0.98 % formulas(sos). % not echoed (18 formulas)
% 0.71/0.98
% 0.71/0.98 ============================== end of input ==========================
% 0.71/0.98
% 0.71/0.98 % From the command line: assign(max_seconds, 300).
% 0.71/0.98
% 0.71/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.98
% 0.71/0.98 % Formulas that are not ordinary clauses:
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% 0.71/0.98 ============================== end of process non-clausal formulas ===
% 0.71/0.98
% 0.71/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/0.98
% 0.71/0.98 ============================== PREDICATE ELIMINATION =================
% 0.71/0.98
% 0.71/0.98 ============================== end predicate elimination =============
% 0.71/0.98
% 0.71/0.98 Auto_denials:
% 0.71/0.98 % copying label prove_p05b to answer in negative clause
% 0.71/0.98
% 0.71/0.98 Term ordering decisions:
% 0.71/0.98
% 0.71/0.98 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.71/0.98 Function symbol KB weights: a=1. identity=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 0.71/0.98
% 0.71/0.98 ============================== end of process initial clauses ========
% 0.71/0.98
% 0.71/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.71/0.98
% 0.71/0.98 ============================== end of clauses for search =============
% 0.71/0.98
% 0.71/0.98 ============================== SEARCH ================================
% 0.71/0.98
% 0.71/0.98 % Starting search at 0.01 seconds.
% 0.71/0.98
% 0.71/0.98 ============================== PROOF =================================
% 0.71/0.98 % SZS status Unsatisfiable
% 0.71/0.98 % SZS output start Refutation
% 0.71/0.98
% 0.71/0.98 % Proof 1 at 0.02 (+ 0.00) seconds: prove_p05b.
% 0.71/0.98 % Length of proof is 25.
% 0.71/0.98 % Level of proof is 6.
% 0.71/0.98 % Maximum clause weight is 13.000.
% 0.71/0.98 % Given clauses 28.
% 0.71/0.98
% 0.71/0.98 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.71/0.98 4 greatest_lower_bound(identity,a) = a # label(p05b_1) # label(hypothesis). [assumption].
% 0.71/0.98 5 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.71/0.98 6 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.71/0.98 7 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.71/0.98 8 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 0.71/0.98 10 greatest_lower_bound(identity,inverse(a)) = inverse(a) # label(p05b_2) # label(hypothesis). [assumption].
% 0.71/0.98 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.71/0.98 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.71/0.98 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 0.71/0.98 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.71/0.98 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 0.71/0.98 24 identity != a # label(prove_p05b) # label(negated_conjecture) # answer(prove_p05b). [assumption].
% 0.71/0.98 25 greatest_lower_bound(a,identity) = a. [back_rewrite(4),rewrite([6(3)])].
% 0.71/0.98 26 least_upper_bound(identity,inverse(a)) = identity. [para(10(a,1),8(a,1,2))].
% 0.71/0.98 27 multiply(inverse(A),multiply(A,B)) = B. [para(5(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.71/0.98 43 greatest_lower_bound(A,multiply(a,A)) = multiply(a,A). [para(25(a,1),23(a,2,1)),rewrite([1(4),6(3)])].
% 0.71/0.98 44 least_upper_bound(A,multiply(inverse(a),A)) = A. [para(26(a,1),21(a,2,1)),rewrite([1(2),1(6)])].
% 0.71/0.98 46 multiply(inverse(inverse(A)),identity) = A. [para(5(a,1),27(a,1,2))].
% 0.71/0.98 52 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(27(a,1),27(a,1,2))].
% 0.71/0.98 53 multiply(A,identity) = A. [back_rewrite(46),rewrite([52(4)])].
% 0.71/0.98 59 least_upper_bound(A,multiply(a,A)) = multiply(a,A). [para(27(a,1),44(a,1,2)),rewrite([7(3)])].
% 0.71/0.98 61 multiply(a,A) = A. [para(43(a,1),8(a,1,2)),rewrite([59(3)])].
% 0.71/0.98 65 identity = a. [para(61(a,1),53(a,1))].
% 0.71/0.98 66 $F # answer(prove_p05b). [resolve(65,a,24,a)].
% 0.71/0.98
% 0.71/0.98 % SZS output end Refutation
% 0.71/0.98 ============================== end of proof ==========================
% 0.71/0.98
% 0.71/0.98 ============================== STATISTICS ============================
% 0.71/0.98
% 0.71/0.98 Given=28. Generated=381. Kept=59. proofs=1.
% 0.71/0.98 Usable=27. Sos=23. Demods=46. Limbo=3, Disabled=23. Hints=0.
% 0.71/0.98 Megabytes=0.07.
% 0.71/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.71/0.98
% 0.71/0.98 ============================== end of statistics =====================
% 0.71/0.98
% 0.71/0.98 ============================== end of search =========================
% 0.71/0.98
% 0.71/0.98 THEOREM PROVED
% 0.71/0.98 % SZS status Unsatisfiable
% 0.71/0.98
% 0.71/0.98 Exiting with 1 proof.
% 0.71/0.98
% 0.71/0.98 Process 17375 exit (max_proofs) Tue Jun 14 08:20:48 2022
% 0.71/0.98 Prover9 interrupted
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