TSTP Solution File: GRP156-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 11:17:46 EDT 2022
% Result : Unsatisfiable 0.51s 0.87s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Tue Jun 14 13:28:43 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.51/0.87 ============================== Prover9 ===============================
% 0.51/0.87 Prover9 (32) version 2009-11A, November 2009.
% 0.51/0.87 Process 4555 was started by sandbox on n032.cluster.edu,
% 0.51/0.87 Tue Jun 14 13:28:43 2022
% 0.51/0.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4402_n032.cluster.edu".
% 0.51/0.87 ============================== end of head ===========================
% 0.51/0.87
% 0.51/0.87 ============================== INPUT =================================
% 0.51/0.87
% 0.51/0.87 % Reading from file /tmp/Prover9_4402_n032.cluster.edu
% 0.51/0.87
% 0.51/0.87 set(prolog_style_variables).
% 0.51/0.87 set(auto2).
% 0.51/0.87 % set(auto2) -> set(auto).
% 0.51/0.87 % set(auto) -> set(auto_inference).
% 0.51/0.87 % set(auto) -> set(auto_setup).
% 0.51/0.87 % set(auto_setup) -> set(predicate_elim).
% 0.51/0.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.51/0.87 % set(auto) -> set(auto_limits).
% 0.51/0.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.51/0.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.51/0.87 % set(auto) -> set(auto_denials).
% 0.51/0.87 % set(auto) -> set(auto_process).
% 0.51/0.87 % set(auto2) -> assign(new_constants, 1).
% 0.51/0.87 % set(auto2) -> assign(fold_denial_max, 3).
% 0.51/0.87 % set(auto2) -> assign(max_weight, "200.000").
% 0.51/0.87 % set(auto2) -> assign(max_hours, 1).
% 0.51/0.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.51/0.87 % set(auto2) -> assign(max_seconds, 0).
% 0.51/0.87 % set(auto2) -> assign(max_minutes, 5).
% 0.51/0.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.51/0.87 % set(auto2) -> set(sort_initial_sos).
% 0.51/0.87 % set(auto2) -> assign(sos_limit, -1).
% 0.51/0.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.51/0.87 % set(auto2) -> assign(max_megs, 400).
% 0.51/0.87 % set(auto2) -> assign(stats, some).
% 0.51/0.87 % set(auto2) -> clear(echo_input).
% 0.51/0.87 % set(auto2) -> set(quiet).
% 0.51/0.87 % set(auto2) -> clear(print_initial_clauses).
% 0.51/0.87 % set(auto2) -> clear(print_given).
% 0.51/0.87 assign(lrs_ticks,-1).
% 0.51/0.87 assign(sos_limit,10000).
% 0.51/0.87 assign(order,kbo).
% 0.51/0.87 set(lex_order_vars).
% 0.51/0.87 clear(print_given).
% 0.51/0.87
% 0.51/0.87 % formulas(sos). % not echoed (17 formulas)
% 0.51/0.87
% 0.51/0.87 ============================== end of input ==========================
% 0.51/0.87
% 0.51/0.87 % From the command line: assign(max_seconds, 300).
% 0.51/0.87
% 0.51/0.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.51/0.87
% 0.51/0.87 % Formulas that are not ordinary clauses:
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% 0.51/0.87 ============================== end of process non-clausal formulas ===
% 0.51/0.87
% 0.51/0.87 ============================== PROCESS INITIAL CLAUSES ===============
% 0.51/0.87
% 0.51/0.87 ============================== PREDICATE ELIMINATION =================
% 0.51/0.87
% 0.51/0.87 ============================== end predicate elimination =============
% 0.51/0.87
% 0.51/0.87 Auto_denials:
% 0.51/0.87 % copying label prove_ax_mono1c to answer in negative clause
% 0.51/0.87
% 0.51/0.87 Term ordering decisions:
% 0.51/0.87
% 0.51/0.87 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.51/0.87 Function symbol KB weights: b=1. identity=1. a=1. c=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 0.51/0.87
% 0.51/0.87 ============================== end of process initial clauses ========
% 0.51/0.87
% 0.51/0.87 ============================== CLAUSES FOR SEARCH ====================
% 0.51/0.87
% 0.51/0.87 ============================== end of clauses for search =============
% 0.51/0.87
% 0.51/0.87 ============================== SEARCH ================================
% 0.51/0.87
% 0.51/0.87 % Starting search at 0.01 seconds.
% 0.51/0.87
% 0.51/0.87 ============================== PROOF =================================
% 0.51/0.87 % SZS status Unsatisfiable
% 0.51/0.87 % SZS output start Refutation
% 0.51/0.87
% 0.51/0.87 % Proof 1 at 0.05 (+ 0.00) seconds: prove_ax_mono1c.
% 0.51/0.87 % Length of proof is 32.
% 0.51/0.87 % Level of proof is 10.
% 0.51/0.87 % Maximum clause weight is 13.000.
% 0.51/0.87 % Given clauses 67.
% 0.51/0.87
% 0.51/0.87 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.51/0.87 4 least_upper_bound(a,b) = b # label(ax_mono1c_1) # label(hypothesis). [assumption].
% 0.51/0.87 5 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.51/0.87 6 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.51/0.87 7 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.51/0.87 9 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 0.51/0.87 10 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.51/0.87 15 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 0.51/0.87 16 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(15),flip(a)].
% 0.51/0.87 19 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.51/0.87 20 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(19),flip(a)].
% 0.51/0.87 21 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.51/0.87 22 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(21),flip(a)].
% 0.51/0.87 23 greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c) # label(prove_ax_mono1c) # label(negated_conjecture) # answer(prove_ax_mono1c). [assumption].
% 0.51/0.87 24 multiply(greatest_lower_bound(b,a),c) != multiply(a,c) # answer(prove_ax_mono1c). [copy(23),rewrite([6(7),22(7)])].
% 0.51/0.87 25 least_upper_bound(b,a) = b. [back_rewrite(4),rewrite([7(3)])].
% 0.51/0.87 26 multiply(inverse(A),multiply(A,B)) = B. [para(5(a,1),10(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.51/0.87 31 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(5(a,1),16(a,1,1))].
% 0.51/0.87 34 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)])].
% 0.51/0.87 42 multiply(inverse(inverse(A)),identity) = A. [para(5(a,1),26(a,1,2))].
% 0.51/0.87 48 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(26(a,1),26(a,1,2))].
% 0.51/0.87 49 multiply(A,identity) = A. [back_rewrite(42),rewrite([48(4)])].
% 0.51/0.87 62 inverse(inverse(A)) = A. [para(48(a,1),49(a,1)),rewrite([49(2)]),flip(a)].
% 0.51/0.87 95 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(31(a,1),9(a,1,2))].
% 0.51/0.87 109 least_upper_bound(identity,multiply(inverse(b),a)) = identity. [para(25(a,1),31(a,2,2)),rewrite([5(10)])].
% 0.51/0.87 220 multiply(least_upper_bound(inverse(b),inverse(a)),a) = identity. [para(34(a,1),109(a,1))].
% 0.51/0.87 230 inverse(least_upper_bound(inverse(b),inverse(a))) = a. [para(220(a,1),26(a,1,2)),rewrite([49(8)])].
% 0.51/0.87 233 least_upper_bound(inverse(b),inverse(a)) = inverse(a). [para(230(a,1),62(a,1,1)),flip(a)].
% 0.51/0.87 239 greatest_lower_bound(identity,multiply(b,inverse(a))) = identity. [para(233(a,1),95(a,1,2,2)),rewrite([62(4)])].
% 0.51/0.87 269 greatest_lower_bound(A,multiply(b,multiply(inverse(a),A))) = A. [para(239(a,1),22(a,2,1)),rewrite([1(2),10(5),1(8)])].
% 0.51/0.87 360 greatest_lower_bound(b,a) = a. [para(5(a,1),269(a,1,2,2)),rewrite([49(4),6(3)])].
% 0.51/0.87 364 $F # answer(prove_ax_mono1c). [back_rewrite(24),rewrite([360(3)]),xx(a)].
% 0.51/0.87
% 0.51/0.87 % SZS output end Refutation
% 0.51/0.87 ============================== end of proof ==========================
% 0.51/0.87
% 0.51/0.87 ============================== STATISTICS ============================
% 0.51/0.87
% 0.51/0.87 Given=67. Generated=1662. Kept=356. proofs=1.
% 0.51/0.87 Usable=61. Sos=249. Demods=243. Limbo=4, Disabled=59. Hints=0.
% 0.51/0.87 Megabytes=0.42.
% 0.51/0.87 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.51/0.87
% 0.51/0.87 ============================== end of statistics =====================
% 0.51/0.87
% 0.51/0.87 ============================== end of search =========================
% 0.51/0.87
% 0.51/0.87 THEOREM PROVED
% 0.51/0.87 % SZS status Unsatisfiable
% 0.51/0.87
% 0.51/0.87 Exiting with 1 proof.
% 0.51/0.87
% 0.51/0.87 Process 4555 exit (max_proofs) Tue Jun 14 13:28:43 2022
% 0.51/0.87 Prover9 interrupted
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