TSTP Solution File: GRP172-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 0.83s 1.24s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 13:42:26 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.83/1.23 ============================== Prover9 ===============================
% 0.83/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.23 Process 23898 was started by sandbox on n006.cluster.edu,
% 0.83/1.23 Tue Jun 14 13:42:27 2022
% 0.83/1.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23743_n006.cluster.edu".
% 0.83/1.23 ============================== end of head ===========================
% 0.83/1.23
% 0.83/1.23 ============================== INPUT =================================
% 0.83/1.23
% 0.83/1.23 % Reading from file /tmp/Prover9_23743_n006.cluster.edu
% 0.83/1.23
% 0.83/1.23 set(prolog_style_variables).
% 0.83/1.23 set(auto2).
% 0.83/1.23 % set(auto2) -> set(auto).
% 0.83/1.23 % set(auto) -> set(auto_inference).
% 0.83/1.23 % set(auto) -> set(auto_setup).
% 0.83/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.23 % set(auto) -> set(auto_limits).
% 0.83/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.23 % set(auto) -> set(auto_denials).
% 0.83/1.23 % set(auto) -> set(auto_process).
% 0.83/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.23 % set(auto2) -> assign(stats, some).
% 0.83/1.23 % set(auto2) -> clear(echo_input).
% 0.83/1.23 % set(auto2) -> set(quiet).
% 0.83/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.23 % set(auto2) -> clear(print_given).
% 0.83/1.23 assign(lrs_ticks,-1).
% 0.83/1.23 assign(sos_limit,10000).
% 0.83/1.23 assign(order,kbo).
% 0.83/1.23 set(lex_order_vars).
% 0.83/1.23 clear(print_given).
% 0.83/1.23
% 0.83/1.23 % formulas(sos). % not echoed (18 formulas)
% 0.83/1.23
% 0.83/1.23 ============================== end of input ==========================
% 0.83/1.23
% 0.83/1.23 % From the command line: assign(max_seconds, 300).
% 0.83/1.23
% 0.83/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.24
% 0.83/1.24 % Formulas that are not ordinary clauses:
% 0.83/1.24
% 0.83/1.24 ============================== end of process non-clausal formulas ===
% 0.83/1.24
% 0.83/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.24
% 0.83/1.24 ============================== PREDICATE ELIMINATION =================
% 0.83/1.24
% 0.83/1.24 ============================== end predicate elimination =============
% 0.83/1.24
% 0.83/1.24 Auto_denials:
% 0.83/1.24 % copying label prove_p04b to answer in negative clause
% 0.83/1.24
% 0.83/1.24 Term ordering decisions:
% 0.83/1.24
% 0.83/1.24 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.83/1.24 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 0.83/1.24
% 0.83/1.24 ============================== end of process initial clauses ========
% 0.83/1.24
% 0.83/1.24 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.24
% 0.83/1.24 ============================== end of clauses for search =============
% 0.83/1.24
% 0.83/1.24 ============================== SEARCH ================================
% 0.83/1.24
% 0.83/1.24 % Starting search at 0.01 seconds.
% 0.83/1.24
% 0.83/1.24 ============================== PROOF =================================
% 0.83/1.24 % SZS status Unsatisfiable
% 0.83/1.24 % SZS output start Refutation
% 0.83/1.24
% 0.83/1.24 % Proof 1 at 0.16 (+ 0.00) seconds: prove_p04b.
% 0.83/1.24 % Length of proof is 25.
% 0.83/1.24 % Level of proof is 7.
% 0.83/1.24 % Maximum clause weight is 13.000.
% 0.83/1.24 % Given clauses 129.
% 0.83/1.24
% 0.83/1.24 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.83/1.24 4 greatest_lower_bound(identity,a) = identity # label(p04b_1) # label(hypothesis). [assumption].
% 0.83/1.24 5 greatest_lower_bound(identity,b) = identity # label(p04b_2) # label(hypothesis). [assumption].
% 0.83/1.24 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.83/1.24 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.83/1.24 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.83/1.24 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].
% 0.83/1.24 13 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(12),rewrite([7(4)])].
% 0.83/1.24 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.83/1.24 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 0.83/1.24 24 greatest_lower_bound(identity,multiply(a,b)) != identity # label(prove_p04b) # label(negated_conjecture) # answer(prove_p04b). [assumption].
% 0.83/1.24 25 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.83/1.24 37 greatest_lower_bound(A,multiply(a,A)) = A. [para(4(a,1),23(a,2,1)),rewrite([1(2),1(5)])].
% 0.83/1.24 38 greatest_lower_bound(A,multiply(b,A)) = A. [para(5(a,1),23(a,2,1)),rewrite([1(2),1(5)])].
% 0.83/1.24 39 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),23(a,1,1)),rewrite([7(5)])].
% 0.83/1.24 43 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),25(a,1,2))].
% 0.83/1.24 49 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(25(a,1),25(a,1,2))].
% 0.83/1.24 50 multiply(A,identity) = A. [back_rewrite(43),rewrite([49(4)])].
% 0.83/1.24 54 greatest_lower_bound(A,greatest_lower_bound(B,multiply(a,A))) = greatest_lower_bound(A,B). [para(37(a,1),13(a,2,2)),rewrite([7(3),7(5)])].
% 0.83/1.24 56 multiply(A,inverse(A)) = identity. [para(49(a,1),6(a,1))].
% 0.83/1.24 69 greatest_lower_bound(identity,inverse(b)) = inverse(b). [para(56(a,1),38(a,1,2)),rewrite([7(4)])].
% 0.83/1.24 385 multiply(greatest_lower_bound(a,inverse(b)),b) != identity # answer(prove_p04b). [para(39(a,1),24(a,1))].
% 0.83/1.24 1024 greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = inverse(b). [para(69(a,1),54(a,2)),rewrite([50(6),7(5)])].
% 0.83/1.24 1102 greatest_lower_bound(a,inverse(b)) = inverse(b). [para(1024(a,1),13(a,2)),rewrite([7(5),69(5)])].
% 0.83/1.24 1103 $F # answer(prove_p04b). [back_rewrite(385),rewrite([1102(4),6(4)]),xx(a)].
% 0.83/1.24
% 0.83/1.24 % SZS output end Refutation
% 0.83/1.24 ============================== end of proof ==========================
% 0.83/1.24
% 0.83/1.24 ============================== STATISTICS ============================
% 0.83/1.24
% 0.83/1.24 Given=129. Generated=4883. Kept=1096. proofs=1.
% 0.83/1.24 Usable=118. Sos=888. Demods=798. Limbo=1, Disabled=107. Hints=0.
% 0.83/1.24 Megabytes=1.22.
% 0.83/1.24 User_CPU=0.16, System_CPU=0.00, Wall_clock=0.
% 0.83/1.24
% 0.83/1.24 ============================== end of statistics =====================
% 0.83/1.24
% 0.83/1.24 ============================== end of search =========================
% 0.83/1.24
% 0.83/1.24 THEOREM PROVED
% 0.83/1.24 % SZS status Unsatisfiable
% 0.83/1.24
% 0.83/1.24 Exiting with 1 proof.
% 0.83/1.24
% 0.83/1.24 Process 23898 exit (max_proofs) Tue Jun 14 13:42:27 2022
% 0.83/1.24 Prover9 interrupted
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