TSTP Solution File: GRP171-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 11:17:53 EDT 2022
% Result : Unsatisfiable 0.71s 1.06s
% 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 : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 22:33:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.06 ============================== Prover9 ===============================
% 0.71/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.06 Process 23695 was started by sandbox2 on n024.cluster.edu,
% 0.71/1.06 Mon Jun 13 22:33:04 2022
% 0.71/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23542_n024.cluster.edu".
% 0.71/1.06 ============================== end of head ===========================
% 0.71/1.06
% 0.71/1.06 ============================== INPUT =================================
% 0.71/1.06
% 0.71/1.06 % Reading from file /tmp/Prover9_23542_n024.cluster.edu
% 0.71/1.06
% 0.71/1.06 set(prolog_style_variables).
% 0.71/1.06 set(auto2).
% 0.71/1.06 % set(auto2) -> set(auto).
% 0.71/1.06 % set(auto) -> set(auto_inference).
% 0.71/1.06 % set(auto) -> set(auto_setup).
% 0.71/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.06 % set(auto) -> set(auto_limits).
% 0.71/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.06 % set(auto) -> set(auto_denials).
% 0.71/1.06 % set(auto) -> set(auto_process).
% 0.71/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.06 % set(auto2) -> assign(stats, some).
% 0.71/1.06 % set(auto2) -> clear(echo_input).
% 0.71/1.06 % set(auto2) -> set(quiet).
% 0.71/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.06 % set(auto2) -> clear(print_given).
% 0.71/1.06 assign(lrs_ticks,-1).
% 0.71/1.06 assign(sos_limit,10000).
% 0.71/1.06 assign(order,kbo).
% 0.71/1.06 set(lex_order_vars).
% 0.71/1.06 clear(print_given).
% 0.71/1.06
% 0.71/1.06 % formulas(sos). % not echoed (18 formulas)
% 0.71/1.06
% 0.71/1.06 ============================== end of input ==========================
% 0.71/1.06
% 0.71/1.06 % From the command line: assign(max_seconds, 300).
% 0.71/1.06
% 0.71/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.06
% 0.71/1.06 % Formulas that are not ordinary clauses:
% 0.71/1.06
% 0.71/1.06 ============================== end of process non-clausal formulas ===
% 0.71/1.06
% 0.71/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.06
% 0.71/1.06 ============================== PREDICATE ELIMINATION =================
% 0.71/1.06
% 0.71/1.06 ============================== end predicate elimination =============
% 0.71/1.06
% 0.71/1.06 Auto_denials:
% 0.71/1.06 % copying label prove_p04a to answer in negative clause
% 0.71/1.06
% 0.71/1.06 Term ordering decisions:
% 0.71/1.06
% 0.71/1.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.71/1.06 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 0.71/1.06
% 0.71/1.06 ============================== end of process initial clauses ========
% 0.71/1.06
% 0.71/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.06
% 0.71/1.06 ============================== end of clauses for search =============
% 0.71/1.06
% 0.71/1.06 ============================== SEARCH ================================
% 0.71/1.06
% 0.71/1.06 % Starting search at 0.01 seconds.
% 0.71/1.06
% 0.71/1.06 ============================== PROOF =================================
% 0.71/1.06 % SZS status Unsatisfiable
% 0.71/1.06 % SZS output start Refutation
% 0.71/1.06
% 0.71/1.06 % Proof 1 at 0.10 (+ 0.01) seconds: prove_p04a.
% 0.71/1.06 % Length of proof is 33.
% 0.71/1.06 % Level of proof is 8.
% 0.71/1.06 % Maximum clause weight is 13.000.
% 0.71/1.06 % Given clauses 99.
% 0.71/1.06
% 0.71/1.06 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.71/1.06 4 least_upper_bound(identity,a) = a # label(p04a_1) # label(hypothesis). [assumption].
% 0.71/1.06 5 least_upper_bound(identity,b) = b # label(p04a_2) # label(hypothesis). [assumption].
% 0.71/1.06 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.71/1.06 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.71/1.06 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.71/1.06 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 0.71/1.06 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 0.71/1.06 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.71/1.06 12 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C) # label(associativity_of_glb) # label(axiom). [assumption].
% 0.71/1.06 13 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(12),rewrite([7(4)])].
% 0.71/1.06 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.71/1.06 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 0.71/1.06 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.71/1.06 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 0.71/1.06 24 least_upper_bound(identity,multiply(a,b)) != multiply(a,b) # label(prove_p04a) # label(negated_conjecture) # answer(prove_p04a). [assumption].
% 0.71/1.06 25 greatest_lower_bound(identity,a) = identity. [para(4(a,1),10(a,1,2))].
% 0.71/1.06 26 greatest_lower_bound(identity,b) = identity. [para(5(a,1),10(a,1,2))].
% 0.71/1.06 27 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.71/1.06 37 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 0.71/1.06 44 greatest_lower_bound(A,multiply(a,A)) = A. [para(25(a,1),23(a,2,1)),rewrite([1(2),1(5)])].
% 0.71/1.06 45 greatest_lower_bound(A,multiply(b,A)) = A. [para(26(a,1),23(a,2,1)),rewrite([1(2),1(5)])].
% 0.71/1.06 46 greatest_lower_bound(A,greatest_lower_bound(B,multiply(a,A))) = greatest_lower_bound(A,B). [para(44(a,1),13(a,2,2)),rewrite([7(3),7(5)])].
% 0.71/1.06 49 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),27(a,1,2))].
% 0.71/1.06 55 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(27(a,1),27(a,1,2))].
% 0.71/1.06 56 multiply(A,identity) = A. [back_rewrite(49),rewrite([55(4)])].
% 0.71/1.06 67 multiply(A,inverse(A)) = identity. [para(55(a,1),6(a,1))].
% 0.71/1.06 80 greatest_lower_bound(identity,inverse(b)) = inverse(b). [para(67(a,1),45(a,1,2)),rewrite([7(4)])].
% 0.71/1.06 216 multiply(least_upper_bound(a,inverse(b)),b) != multiply(a,b) # answer(prove_p04a). [para(37(a,1),24(a,1))].
% 0.71/1.06 541 greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = inverse(b). [para(80(a,1),46(a,2)),rewrite([56(6),7(5)])].
% 0.71/1.06 585 greatest_lower_bound(a,inverse(b)) = inverse(b). [para(541(a,1),13(a,2)),rewrite([7(5),80(5)])].
% 0.71/1.06 586 least_upper_bound(a,inverse(b)) = a. [para(585(a,1),9(a,1,2))].
% 0.71/1.06 591 $F # answer(prove_p04a). [back_rewrite(216),rewrite([586(4)]),xx(a)].
% 0.71/1.06
% 0.71/1.06 % SZS output end Refutation
% 0.71/1.06 ============================== end of proof ==========================
% 0.71/1.06
% 0.71/1.06 ============================== STATISTICS ============================
% 0.71/1.06
% 0.71/1.06 Given=99. Generated=2814. Kept=584. proofs=1.
% 0.71/1.06 Usable=90. Sos=427. Demods=421. Limbo=5, Disabled=80. Hints=0.
% 0.71/1.06 Megabytes=0.65.
% 0.71/1.06 User_CPU=0.10, System_CPU=0.01, Wall_clock=0.
% 0.71/1.06
% 0.71/1.06 ============================== end of statistics =====================
% 0.71/1.06
% 0.71/1.06 ============================== end of search =========================
% 0.71/1.06
% 0.71/1.06 THEOREM PROVED
% 0.71/1.06 % SZS status Unsatisfiable
% 0.71/1.06
% 0.71/1.06 Exiting with 1 proof.
% 0.71/1.06
% 0.71/1.06 Process 23695 exit (max_proofs) Mon Jun 13 22:33:04 2022
% 0.71/1.06 Prover9 interrupted
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