TSTP Solution File: GRP181-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:17:58 EDT 2022
% Result : Unsatisfiable 1.35s 1.63s
% Output : Refutation 1.35s
% 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 : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 23:03:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.35/1.63 ============================== Prover9 ===============================
% 1.35/1.63 Prover9 (32) version 2009-11A, November 2009.
% 1.35/1.63 Process 26990 was started by sandbox on n011.cluster.edu,
% 1.35/1.63 Mon Jun 13 23:03:34 2022
% 1.35/1.63 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26836_n011.cluster.edu".
% 1.35/1.63 ============================== end of head ===========================
% 1.35/1.63
% 1.35/1.63 ============================== INPUT =================================
% 1.35/1.63
% 1.35/1.63 % Reading from file /tmp/Prover9_26836_n011.cluster.edu
% 1.35/1.63
% 1.35/1.63 set(prolog_style_variables).
% 1.35/1.63 set(auto2).
% 1.35/1.63 % set(auto2) -> set(auto).
% 1.35/1.63 % set(auto) -> set(auto_inference).
% 1.35/1.63 % set(auto) -> set(auto_setup).
% 1.35/1.63 % set(auto_setup) -> set(predicate_elim).
% 1.35/1.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.35/1.63 % set(auto) -> set(auto_limits).
% 1.35/1.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.35/1.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.35/1.63 % set(auto) -> set(auto_denials).
% 1.35/1.63 % set(auto) -> set(auto_process).
% 1.35/1.63 % set(auto2) -> assign(new_constants, 1).
% 1.35/1.63 % set(auto2) -> assign(fold_denial_max, 3).
% 1.35/1.63 % set(auto2) -> assign(max_weight, "200.000").
% 1.35/1.63 % set(auto2) -> assign(max_hours, 1).
% 1.35/1.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.35/1.63 % set(auto2) -> assign(max_seconds, 0).
% 1.35/1.63 % set(auto2) -> assign(max_minutes, 5).
% 1.35/1.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.35/1.63 % set(auto2) -> set(sort_initial_sos).
% 1.35/1.63 % set(auto2) -> assign(sos_limit, -1).
% 1.35/1.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.35/1.63 % set(auto2) -> assign(max_megs, 400).
% 1.35/1.63 % set(auto2) -> assign(stats, some).
% 1.35/1.63 % set(auto2) -> clear(echo_input).
% 1.35/1.63 % set(auto2) -> set(quiet).
% 1.35/1.63 % set(auto2) -> clear(print_initial_clauses).
% 1.35/1.63 % set(auto2) -> clear(print_given).
% 1.35/1.63 assign(lrs_ticks,-1).
% 1.35/1.63 assign(sos_limit,10000).
% 1.35/1.63 assign(order,kbo).
% 1.35/1.63 set(lex_order_vars).
% 1.35/1.63 clear(print_given).
% 1.35/1.63
% 1.35/1.63 % formulas(sos). % not echoed (20 formulas)
% 1.35/1.63
% 1.35/1.63 ============================== end of input ==========================
% 1.35/1.63
% 1.35/1.63 % From the command line: assign(max_seconds, 300).
% 1.35/1.63
% 1.35/1.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.35/1.63
% 1.35/1.63 % Formulas that are not ordinary clauses:
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% 1.35/1.63 ============================== end of process non-clausal formulas ===
% 1.35/1.63
% 1.35/1.63 ============================== PROCESS INITIAL CLAUSES ===============
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% 1.35/1.63 ============================== PREDICATE ELIMINATION =================
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% 1.35/1.63 ============================== end predicate elimination =============
% 1.35/1.63
% 1.35/1.63 Auto_denials:
% 1.35/1.63 % copying label prove_p12x to answer in negative clause
% 1.35/1.63
% 1.35/1.63 Term ordering decisions:
% 1.35/1.63
% 1.35/1.63 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.35/1.63 Function symbol KB weights: c=1. a=1. b=1. identity=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
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% 1.35/1.63 ============================== end of process initial clauses ========
% 1.35/1.63
% 1.35/1.63 ============================== CLAUSES FOR SEARCH ====================
% 1.35/1.63
% 1.35/1.63 ============================== end of clauses for search =============
% 1.35/1.63
% 1.35/1.63 ============================== SEARCH ================================
% 1.35/1.63
% 1.35/1.63 % Starting search at 0.01 seconds.
% 1.35/1.63
% 1.35/1.63 ============================== PROOF =================================
% 1.35/1.63 % SZS status Unsatisfiable
% 1.35/1.63 % SZS output start Refutation
% 1.35/1.63
% 1.35/1.63 % Proof 1 at 0.61 (+ 0.02) seconds: prove_p12x.
% 1.35/1.63 % Length of proof is 28.
% 1.35/1.63 % Level of proof is 8.
% 1.35/1.63 % Maximum clause weight is 13.000.
% 1.35/1.63 % Given clauses 289.
% 1.35/1.63
% 1.35/1.63 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 1.35/1.63 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 1.35/1.63 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 1.35/1.63 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 1.35/1.63 9 greatest_lower_bound(a,c) = greatest_lower_bound(b,c) # label(p12x_1) # label(hypothesis). [assumption].
% 1.35/1.63 10 greatest_lower_bound(c,b) = greatest_lower_bound(c,a). [copy(9),rewrite([5(3),5(6)]),flip(a)].
% 1.35/1.63 11 least_upper_bound(a,c) = least_upper_bound(b,c) # label(p12x_2) # label(hypothesis). [assumption].
% 1.35/1.63 12 least_upper_bound(c,b) = least_upper_bound(c,a). [copy(11),rewrite([6(3),6(6)]),flip(a)].
% 1.35/1.63 13 inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)) # label(p12x_3) # label(hypothesis). [assumption].
% 1.35/1.63 15 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 1.35/1.63 20 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 1.35/1.63 21 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(20),flip(a)].
% 1.35/1.63 24 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 1.35/1.63 25 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(24),flip(a)].
% 1.35/1.63 28 a != b # label(prove_p12x) # label(negated_conjecture) # answer(prove_p12x). [assumption].
% 1.35/1.63 29 b != a # answer(prove_p12x). [copy(28),flip(a)].
% 1.35/1.63 36 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),15(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.35/1.63 41 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),21(a,1,1))].
% 1.35/1.63 46 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(4(a,1),25(a,1,1)),rewrite([6(5)])].
% 1.35/1.63 72 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(36(a,1),36(a,1,2))].
% 1.35/1.63 86 multiply(A,multiply(inverse(A),B)) = B. [para(72(a,1),36(a,1))].
% 1.35/1.63 106 multiply(greatest_lower_bound(A,B),multiply(least_upper_bound(inverse(A),inverse(B)),C)) = C. [para(13(a,1),86(a,1,2,1))].
% 1.35/1.63 251 least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(c,a)). [para(12(a,1),41(a,2,2))].
% 1.35/1.63 2450 multiply(greatest_lower_bound(A,B),least_upper_bound(identity,multiply(inverse(A),B))) = B. [para(46(a,2),106(a,1,2))].
% 1.35/1.63 4273 multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))) = b. [para(10(a,1),2450(a,1,1)),rewrite([251(9)])].
% 1.35/1.63 4292 multiply(greatest_lower_bound(A,B),multiply(inverse(A),least_upper_bound(A,B))) = B. [para(41(a,1),2450(a,1,2))].
% 1.35/1.63 4333 b = a. [back_rewrite(4273),rewrite([4292(10)]),flip(a)].
% 1.35/1.63 4334 $F # answer(prove_p12x). [resolve(4333,a,29,a)].
% 1.35/1.63
% 1.35/1.63 % SZS output end Refutation
% 1.35/1.63 ============================== end of proof ==========================
% 1.35/1.63
% 1.35/1.63 ============================== STATISTICS ============================
% 1.35/1.63
% 1.35/1.63 Given=289. Generated=21568. Kept=4324. proofs=1.
% 1.35/1.63 Usable=265. Sos=3247. Demods=3071. Limbo=41, Disabled=790. Hints=0.
% 1.35/1.63 Megabytes=4.93.
% 1.35/1.63 User_CPU=0.61, System_CPU=0.02, Wall_clock=1.
% 1.35/1.63
% 1.35/1.63 ============================== end of statistics =====================
% 1.35/1.63
% 1.35/1.63 ============================== end of search =========================
% 1.35/1.63
% 1.35/1.63 THEOREM PROVED
% 1.35/1.63 % SZS status Unsatisfiable
% 1.35/1.63
% 1.35/1.63 Exiting with 1 proof.
% 1.35/1.63
% 1.35/1.63 Process 26990 exit (max_proofs) Mon Jun 13 23:03:35 2022
% 1.35/1.63 Prover9 interrupted
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