TSTP Solution File: GRP159-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP159-1 : 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 11:17:47 EDT 2022
% Result : Unsatisfiable 0.45s 0.78s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.07 % Command : tptp2X_and_run_prover9 %d %s
% 0.07/0.26 % Computer : n018.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jun 13 22:17:13 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.45/0.78 ============================== Prover9 ===============================
% 0.45/0.78 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.78 Process 7472 was started by sandbox2 on n018.cluster.edu,
% 0.45/0.78 Mon Jun 13 22:17:13 2022
% 0.45/0.78 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7167_n018.cluster.edu".
% 0.45/0.78 ============================== end of head ===========================
% 0.45/0.78
% 0.45/0.78 ============================== INPUT =================================
% 0.45/0.78
% 0.45/0.78 % Reading from file /tmp/Prover9_7167_n018.cluster.edu
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% 0.45/0.78 set(prolog_style_variables).
% 0.45/0.78 set(auto2).
% 0.45/0.78 % set(auto2) -> set(auto).
% 0.45/0.78 % set(auto) -> set(auto_inference).
% 0.45/0.78 % set(auto) -> set(auto_setup).
% 0.45/0.78 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.78 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.78 % set(auto) -> set(auto_limits).
% 0.45/0.78 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.78 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.78 % set(auto) -> set(auto_denials).
% 0.45/0.78 % set(auto) -> set(auto_process).
% 0.45/0.78 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.78 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.78 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.78 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.78 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.78 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.78 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.78 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.78 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.78 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.78 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.78 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.78 % set(auto2) -> assign(stats, some).
% 0.45/0.78 % set(auto2) -> clear(echo_input).
% 0.45/0.78 % set(auto2) -> set(quiet).
% 0.45/0.78 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.78 % set(auto2) -> clear(print_given).
% 0.45/0.78 assign(lrs_ticks,-1).
% 0.45/0.78 assign(sos_limit,10000).
% 0.45/0.78 assign(order,kbo).
% 0.45/0.78 set(lex_order_vars).
% 0.45/0.78 clear(print_given).
% 0.45/0.78
% 0.45/0.78 % formulas(sos). % not echoed (17 formulas)
% 0.45/0.78
% 0.45/0.78 ============================== end of input ==========================
% 0.45/0.78
% 0.45/0.78 % From the command line: assign(max_seconds, 300).
% 0.45/0.78
% 0.45/0.78 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.78
% 0.45/0.78 % Formulas that are not ordinary clauses:
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% 0.45/0.78 ============================== end of process non-clausal formulas ===
% 0.45/0.78
% 0.45/0.78 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.45/0.78 ============================== PREDICATE ELIMINATION =================
% 0.45/0.78
% 0.45/0.78 ============================== end predicate elimination =============
% 0.45/0.78
% 0.45/0.78 Auto_denials:
% 0.45/0.78 % copying label prove_ax_mono2c to answer in negative clause
% 0.45/0.78
% 0.45/0.78 Term ordering decisions:
% 0.45/0.78
% 0.45/0.78 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.45/0.78 Function symbol KB weights: a=1. identity=1. b=1. c=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
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% 0.45/0.78 ============================== end of process initial clauses ========
% 0.45/0.78
% 0.45/0.78 ============================== CLAUSES FOR SEARCH ====================
% 0.45/0.78
% 0.45/0.78 ============================== end of clauses for search =============
% 0.45/0.78
% 0.45/0.78 ============================== SEARCH ================================
% 0.45/0.78
% 0.45/0.78 % Starting search at 0.01 seconds.
% 0.45/0.78
% 0.45/0.78 ============================== PROOF =================================
% 0.45/0.78 % SZS status Unsatisfiable
% 0.45/0.78 % SZS output start Refutation
% 0.45/0.78
% 0.45/0.78 % Proof 1 at 0.05 (+ 0.00) seconds: prove_ax_mono2c.
% 0.45/0.78 % Length of proof is 35.
% 0.45/0.78 % Level of proof is 10.
% 0.45/0.78 % Maximum clause weight is 13.000.
% 0.45/0.78 % Given clauses 57.
% 0.45/0.78
% 0.45/0.78 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.45/0.78 4 greatest_lower_bound(a,b) = a # label(ax_mono2c_1) # label(hypothesis). [assumption].
% 0.45/0.78 5 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.45/0.78 6 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.45/0.78 7 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.45/0.78 8 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 0.45/0.78 10 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.45/0.78 15 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 0.45/0.78 16 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(15),flip(a)].
% 0.45/0.78 17 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 0.45/0.78 18 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(17),flip(a)].
% 0.45/0.78 19 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.45/0.78 20 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(19),flip(a)].
% 0.45/0.78 21 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.45/0.78 22 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(21),flip(a)].
% 0.45/0.78 23 least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b) # label(prove_ax_mono2c) # label(negated_conjecture) # answer(prove_ax_mono2c). [assumption].
% 0.45/0.78 24 multiply(c,least_upper_bound(a,b)) != multiply(c,b) # answer(prove_ax_mono2c). [copy(23),rewrite([16(7)])].
% 0.45/0.78 25 multiply(inverse(A),multiply(A,B)) = B. [para(5(a,1),10(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.45/0.78 30 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(5(a,1),16(a,1,1))].
% 0.45/0.78 31 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(5(a,1),18(a,1,1))].
% 0.45/0.78 33 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)])].
% 0.45/0.78 41 multiply(inverse(inverse(A)),identity) = A. [para(5(a,1),25(a,1,2))].
% 0.45/0.78 47 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(25(a,1),25(a,1,2))].
% 0.45/0.78 48 multiply(A,identity) = A. [back_rewrite(41),rewrite([47(4)])].
% 0.45/0.78 56 multiply(A,inverse(A)) = identity. [para(47(a,1),5(a,1))].
% 0.45/0.78 62 inverse(inverse(A)) = A. [para(47(a,1),48(a,1)),rewrite([48(2)]),flip(a)].
% 0.45/0.78 93 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(8(a,1),30(a,2,2)),rewrite([5(7)])].
% 0.45/0.78 124 greatest_lower_bound(identity,multiply(inverse(a),b)) = identity. [para(4(a,1),31(a,2,2)),rewrite([5(10)])].
% 0.45/0.78 147 greatest_lower_bound(A,multiply(inverse(a),multiply(b,A))) = A. [para(124(a,1),22(a,2,1)),rewrite([1(2),10(5),1(8)])].
% 0.45/0.78 232 greatest_lower_bound(inverse(a),inverse(b)) = inverse(b). [para(56(a,1),147(a,1,2,2)),rewrite([48(6),6(5)])].
% 0.45/0.78 236 least_upper_bound(identity,multiply(a,inverse(b))) = identity. [para(232(a,1),93(a,1,2,2)),rewrite([62(4)])].
% 0.45/0.78 270 multiply(least_upper_bound(a,b),inverse(b)) = identity. [para(236(a,1),33(a,1)),rewrite([62(5)]),flip(a)].
% 0.45/0.78 276 inverse(least_upper_bound(a,b)) = inverse(b). [para(270(a,1),25(a,1,2)),rewrite([48(6)])].
% 0.45/0.78 282 least_upper_bound(a,b) = b. [para(276(a,1),62(a,1,1)),rewrite([62(3)]),flip(a)].
% 0.45/0.78 287 $F # answer(prove_ax_mono2c). [back_rewrite(24),rewrite([282(4)]),xx(a)].
% 0.45/0.78
% 0.45/0.78 % SZS output end Refutation
% 0.45/0.78 ============================== end of proof ==========================
% 0.45/0.78
% 0.45/0.78 ============================== STATISTICS ============================
% 0.45/0.78
% 0.45/0.78 Given=57. Generated=1289. Kept=279. proofs=1.
% 0.45/0.78 Usable=51. Sos=185. Demods=183. Limbo=5, Disabled=55. Hints=0.
% 0.45/0.78 Megabytes=0.34.
% 0.45/0.78 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.45/0.78
% 0.45/0.78 ============================== end of statistics =====================
% 0.45/0.78
% 0.45/0.78 ============================== end of search =========================
% 0.45/0.78
% 0.45/0.78 THEOREM PROVED
% 0.45/0.78 % SZS status Unsatisfiable
% 0.45/0.78
% 0.45/0.78 Exiting with 1 proof.
% 0.45/0.78
% 0.45/0.78 Process 7472 exit (max_proofs) Mon Jun 13 22:17:13 2022
% 0.45/0.78 Prover9 interrupted
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