TSTP Solution File: GRP063-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP063-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:17:00 EDT 2022
% Result : Unsatisfiable 0.71s 0.97s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP063-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:21:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 27571 was started by sandbox2 on n009.cluster.edu,
% 0.42/0.97 Mon Jun 13 06:21:38 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27418_n009.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_27418_n009.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.97 % set(auto2) -> assign(stats, some).
% 0.71/0.97 % set(auto2) -> clear(echo_input).
% 0.71/0.97 % set(auto2) -> set(quiet).
% 0.71/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.97 % set(auto2) -> clear(print_given).
% 0.71/0.97 assign(lrs_ticks,-1).
% 0.71/0.97 assign(sos_limit,10000).
% 0.71/0.97 assign(order,kbo).
% 0.71/0.97 set(lex_order_vars).
% 0.71/0.97 clear(print_given).
% 0.71/0.97
% 0.71/0.97 % formulas(sos). % not echoed (4 formulas)
% 0.71/0.97
% 0.71/0.97 ============================== end of input ==========================
% 0.71/0.97
% 0.71/0.97 % From the command line: assign(max_seconds, 300).
% 0.71/0.97
% 0.71/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.97
% 0.71/0.97 % Formulas that are not ordinary clauses:
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% 0.71/0.97 ============================== end of process non-clausal formulas ===
% 0.71/0.97
% 0.71/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/0.97
% 0.71/0.97 ============================== PREDICATE ELIMINATION =================
% 0.71/0.97
% 0.71/0.97 ============================== end predicate elimination =============
% 0.71/0.97
% 0.71/0.97 Auto_denials:
% 0.71/0.97 % copying label prove_these_axioms to answer in negative clause
% 0.71/0.97
% 0.71/0.97 Term ordering decisions:
% 0.71/0.97
% 0.71/0.97 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.71/0.97 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.71/0.97
% 0.71/0.97 ============================== end of process initial clauses ========
% 0.71/0.97
% 0.71/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.71/0.97
% 0.71/0.97 ============================== end of clauses for search =============
% 0.71/0.97
% 0.71/0.97 ============================== SEARCH ================================
% 0.71/0.97
% 0.71/0.97 % Starting search at 0.01 seconds.
% 0.71/0.97
% 0.71/0.97 ============================== PROOF =================================
% 0.71/0.97 % SZS status Unsatisfiable
% 0.71/0.97 % SZS output start Refutation
% 0.71/0.97
% 0.71/0.97 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms.
% 0.71/0.97 % Length of proof is 36.
% 0.71/0.97 % Level of proof is 16.
% 0.71/0.97 % Maximum clause weight is 31.000.
% 0.71/0.97 % Given clauses 28.
% 0.71/0.97
% 0.71/0.97 1 inverse(A) = divide(divide(B,B),A) # label(inverse) # label(axiom). [assumption].
% 0.71/0.97 2 divide(divide(A,A),B) = inverse(B). [copy(1),flip(a)].
% 0.71/0.97 3 multiply(A,B) = divide(A,divide(divide(C,C),B)) # label(multiply) # label(axiom). [assumption].
% 0.71/0.97 4 multiply(A,B) = divide(A,inverse(B)). [copy(3),rewrite([2(3)])].
% 0.71/0.97 5 divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.71/0.97 6 divide(A,divide(divide(inverse(B),C),divide(inverse(A),C))) = B. [copy(5),rewrite([2(2),2(4)])].
% 0.71/0.97 7 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.71/0.97 8 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | inverse(inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [copy(7),rewrite([4(4),4(9),4(15),4(18),2(19),4(19),4(22),4(27),4(29)]),flip(a)].
% 0.71/0.97 9 divide(inverse(divide(A,A)),B) = inverse(B). [para(2(a,1),2(a,1,1))].
% 0.71/0.97 10 inverse(divide(divide(inverse(A),B),inverse(B))) = A. [para(6(a,1),2(a,1)),rewrite([9(5)]),flip(a)].
% 0.71/0.97 20 inverse(divide(A,inverse(divide(divide(inverse(A),B),divide(inverse(inverse(C)),B))))) = C. [para(6(a,1),10(a,1,1,1))].
% 0.71/0.97 21 inverse(divide(inverse(A),inverse(A))) = divide(B,B). [para(9(a,1),10(a,1,1,1))].
% 0.71/0.97 24 inverse(divide(inverse(A),inverse(A))) = c_0. [new_symbol(21)].
% 0.71/0.97 25 divide(A,A) = c_0. [back_rewrite(21),rewrite([24(4)]),flip(a)].
% 0.71/0.97 26 inverse(c_0) = c_0. [back_rewrite(24),rewrite([25(3)])].
% 0.71/0.97 29 inverse(inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [back_rewrite(8),rewrite([25(5),25(6)]),xx(a)].
% 0.71/0.97 30 inverse(divide(divide(inverse(A),c_0),c_0)) = A. [para(26(a,1),10(a,1,1,2))].
% 0.71/0.97 31 divide(A,divide(divide(inverse(B),inverse(A)),c_0)) = B. [para(25(a,1),6(a,1,2,2))].
% 0.71/0.97 32 divide(A,c_0) = A. [para(25(a,1),6(a,1,2))].
% 0.71/0.97 33 divide(A,divide(inverse(B),inverse(A))) = B. [back_rewrite(31),rewrite([32(5)])].
% 0.71/0.97 34 inverse(inverse(A)) = A. [back_rewrite(30),rewrite([32(3),32(3)])].
% 0.71/0.97 35 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [back_rewrite(29),rewrite([34(3)]),xx(a)].
% 0.71/0.97 36 inverse(divide(A,inverse(divide(divide(inverse(A),B),divide(C,B))))) = C. [back_rewrite(20),rewrite([34(4)])].
% 0.71/0.97 46 inverse(divide(divide(A,B),inverse(B))) = inverse(A). [para(34(a,1),10(a,1,1,1,1))].
% 0.71/0.97 51 divide(A,divide(B,inverse(A))) = inverse(B). [para(34(a,1),33(a,1,2,1))].
% 0.71/0.97 53 divide(inverse(A),divide(B,A)) = inverse(B). [para(34(a,1),51(a,1,2,2))].
% 0.71/0.97 56 inverse(divide(A,inverse(divide(inverse(B),divide(C,divide(B,A)))))) = C. [para(51(a,1),36(a,1,1,2,1,1)),rewrite([34(3)])].
% 0.71/0.97 59 divide(inverse(divide(A,B)),inverse(A)) = B. [para(53(a,1),53(a,1,2)),rewrite([34(6)])].
% 0.71/0.97 60 divide(inverse(divide(inverse(A),B)),A) = B. [para(34(a,1),59(a,1,2))].
% 0.71/0.97 61 divide(divide(A,B),inverse(B)) = A. [para(46(a,1),34(a,1,1)),rewrite([34(2)]),flip(a)].
% 0.71/0.97 65 inverse(divide(A,B)) = divide(B,A). [para(59(a,1),46(a,1,1,1)),rewrite([34(2),34(5)])].
% 0.71/0.97 66 divide(divide(A,inverse(B)),B) = A. [para(46(a,1),60(a,1,1,1,1)),rewrite([65(3),61(5)])].
% 0.71/0.97 68 divide(divide(divide(A,divide(B,C)),inverse(B)),C) = A. [back_rewrite(56),rewrite([65(5),65(6)])].
% 0.71/0.97 72 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) # answer(prove_these_axioms). [back_rewrite(35),rewrite([65(13)])].
% 0.71/0.97 104 divide(divide(A,inverse(B)),C) = divide(A,divide(C,B)). [para(66(a,1),68(a,1,1,1)),rewrite([65(5)])].
% 0.71/0.97 105 $F # answer(prove_these_axioms). [resolve(104,a,72,a)].
% 0.71/0.97
% 0.71/0.97 % SZS output end Refutation
% 0.71/0.97 ============================== end of proof ==========================
% 0.71/0.97
% 0.71/0.97 ============================== STATISTICS ============================
% 0.71/0.97
% 0.71/0.97 Given=28. Generated=401. Kept=100. proofs=1.
% 0.71/0.97 Usable=14. Sos=25. Demods=46. Limbo=8, Disabled=56. Hints=0.
% 0.71/0.97 Megabytes=0.13.
% 0.71/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.71/0.97
% 0.71/0.97 ============================== end of statistics =====================
% 0.71/0.97
% 0.71/0.97 ============================== end of search =========================
% 0.71/0.97
% 0.71/0.97 THEOREM PROVED
% 0.71/0.97 % SZS status Unsatisfiable
% 0.71/0.97
% 0.71/0.97 Exiting with 1 proof.
% 0.71/0.97
% 0.71/0.97 Process 27571 exit (max_proofs) Mon Jun 13 06:21:38 2022
% 0.71/0.97 Prover9 interrupted
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