TSTP Solution File: GRP093-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:17:07 EDT 2022
% Result : Unsatisfiable 0.57s 0.85s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Tue Jun 14 07:42:57 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.57/0.85 ============================== Prover9 ===============================
% 0.57/0.85 Prover9 (32) version 2009-11A, November 2009.
% 0.57/0.85 Process 8260 was started by sandbox on n032.cluster.edu,
% 0.57/0.85 Tue Jun 14 07:42:58 2022
% 0.57/0.85 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8105_n032.cluster.edu".
% 0.57/0.85 ============================== end of head ===========================
% 0.57/0.85
% 0.57/0.85 ============================== INPUT =================================
% 0.57/0.85
% 0.57/0.85 % Reading from file /tmp/Prover9_8105_n032.cluster.edu
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% 0.57/0.85 set(prolog_style_variables).
% 0.57/0.85 set(auto2).
% 0.57/0.85 % set(auto2) -> set(auto).
% 0.57/0.85 % set(auto) -> set(auto_inference).
% 0.57/0.85 % set(auto) -> set(auto_setup).
% 0.57/0.85 % set(auto_setup) -> set(predicate_elim).
% 0.57/0.85 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.57/0.85 % set(auto) -> set(auto_limits).
% 0.57/0.85 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.57/0.85 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.57/0.85 % set(auto) -> set(auto_denials).
% 0.57/0.85 % set(auto) -> set(auto_process).
% 0.57/0.85 % set(auto2) -> assign(new_constants, 1).
% 0.57/0.85 % set(auto2) -> assign(fold_denial_max, 3).
% 0.57/0.85 % set(auto2) -> assign(max_weight, "200.000").
% 0.57/0.85 % set(auto2) -> assign(max_hours, 1).
% 0.57/0.85 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.57/0.85 % set(auto2) -> assign(max_seconds, 0).
% 0.57/0.85 % set(auto2) -> assign(max_minutes, 5).
% 0.57/0.85 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.57/0.85 % set(auto2) -> set(sort_initial_sos).
% 0.57/0.85 % set(auto2) -> assign(sos_limit, -1).
% 0.57/0.85 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.57/0.85 % set(auto2) -> assign(max_megs, 400).
% 0.57/0.85 % set(auto2) -> assign(stats, some).
% 0.57/0.85 % set(auto2) -> clear(echo_input).
% 0.57/0.85 % set(auto2) -> set(quiet).
% 0.57/0.85 % set(auto2) -> clear(print_initial_clauses).
% 0.57/0.85 % set(auto2) -> clear(print_given).
% 0.57/0.85 assign(lrs_ticks,-1).
% 0.57/0.85 assign(sos_limit,10000).
% 0.57/0.85 assign(order,kbo).
% 0.57/0.85 set(lex_order_vars).
% 0.57/0.85 clear(print_given).
% 0.57/0.85
% 0.57/0.85 % formulas(sos). % not echoed (5 formulas)
% 0.57/0.85
% 0.57/0.85 ============================== end of input ==========================
% 0.57/0.85
% 0.57/0.85 % From the command line: assign(max_seconds, 300).
% 0.57/0.85
% 0.57/0.85 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.57/0.85
% 0.57/0.85 % Formulas that are not ordinary clauses:
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% 0.57/0.85 ============================== end of process non-clausal formulas ===
% 0.57/0.85
% 0.57/0.85 ============================== PROCESS INITIAL CLAUSES ===============
% 0.57/0.85
% 0.57/0.85 ============================== PREDICATE ELIMINATION =================
% 0.57/0.85
% 0.57/0.85 ============================== end predicate elimination =============
% 0.57/0.85
% 0.57/0.85 Auto_denials:
% 0.57/0.85 % copying label prove_these_axioms to answer in negative clause
% 0.57/0.85
% 0.57/0.85 Term ordering decisions:
% 0.57/0.85
% 0.57/0.85 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 0.57/0.85 Function symbol KB weights: identity=1. a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.57/0.85
% 0.57/0.85 ============================== end of process initial clauses ========
% 0.57/0.85
% 0.57/0.85 ============================== CLAUSES FOR SEARCH ====================
% 0.57/0.85
% 0.57/0.85 ============================== end of clauses for search =============
% 0.57/0.85
% 0.57/0.85 ============================== SEARCH ================================
% 0.57/0.85
% 0.57/0.85 % Starting search at 0.01 seconds.
% 0.57/0.85
% 0.57/0.85 ============================== PROOF =================================
% 0.57/0.85 % SZS status Unsatisfiable
% 0.57/0.85 % SZS output start Refutation
% 0.57/0.85
% 0.57/0.85 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms.
% 0.57/0.85 % Length of proof is 35.
% 0.57/0.85 % Level of proof is 10.
% 0.57/0.85 % Maximum clause weight is 37.000.
% 0.57/0.85 % Given clauses 23.
% 0.57/0.85
% 0.57/0.85 1 identity = divide(A,A) # label(identity) # label(axiom). [assumption].
% 0.57/0.85 2 divide(A,A) = identity. [copy(1),flip(a)].
% 0.57/0.85 3 inverse(A) = divide(identity,A) # label(inverse) # label(axiom). [assumption].
% 0.57/0.85 4 multiply(A,B) = divide(A,divide(identity,B)) # label(multiply) # label(axiom). [assumption].
% 0.57/0.85 5 divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.57/0.85 6 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)) | multiply(a4,b4) != multiply(b4,a4) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.57/0.85 7 divide(identity,divide(identity,a2)) != a2 | divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) | divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4)) # answer(prove_these_axioms). [copy(6),rewrite([3(2),4(5),2(7),3(3),4(6),2(8),3(5),4(8),2(10),4(6),4(13),4(17),4(23),4(26),4(32),4(37)]),flip(d),xx(a)].
% 0.57/0.85 8 divide(divide(identity,divide(divide(identity,A),B)),A) = B. [para(2(a,1),5(a,1,1,2,1,1))].
% 0.57/0.85 9 divide(divide(identity,divide(identity,A)),divide(A,B)) = B. [para(2(a,1),5(a,1,1,2,1))].
% 0.57/0.85 11 divide(divide(divide(A,B),C),A) = divide(divide(identity,divide(B,identity)),C). [para(5(a,1),5(a,1,1,2,1)),flip(a)].
% 0.57/0.85 14 divide(divide(identity,divide(A,identity)),B) = divide(divide(identity,B),A). [para(8(a,1),5(a,1,1,2,1))].
% 0.57/0.85 16 divide(divide(identity,A),divide(divide(identity,B),A)) = B. [para(8(a,1),8(a,1,1,2))].
% 0.57/0.85 17 divide(divide(divide(A,B),C),A) = divide(divide(identity,C),B). [back_rewrite(11),rewrite([14(8)])].
% 0.57/0.85 18 divide(identity,divide(identity,A)) = A. [para(2(a,1),9(a,1,1,2)),rewrite([2(3)])].
% 0.57/0.85 19 divide(A,identity) = A. [para(2(a,1),9(a,1,2)),rewrite([18(4)])].
% 0.57/0.85 20 divide(divide(identity,A),divide(identity,B)) = divide(B,A). [para(9(a,1),8(a,1,1,2))].
% 0.57/0.85 22 divide(A,divide(A,B)) = B. [back_rewrite(9),rewrite([18(4)])].
% 0.57/0.85 23 divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) | divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4)) # answer(prove_these_axioms). [back_rewrite(7),rewrite([22(5)]),xx(a)].
% 0.57/0.85 24 divide(divide(identity,A),B) = divide(divide(identity,B),A). [back_rewrite(14),rewrite([19(3)])].
% 0.57/0.85 26 divide(divide(identity,A),divide(B,A)) = divide(identity,B). [para(22(a,1),16(a,1,2,1))].
% 0.57/0.85 27 divide(A,divide(identity,B)) = divide(B,divide(identity,A)). [para(22(a,1),20(a,1,1))].
% 0.57/0.85 28 divide(c3,divide(identity,divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) # answer(prove_these_axioms). [back_rewrite(23),rewrite([27(9),27(24)]),xx(b)].
% 0.57/0.85 29 divide(divide(A,B),A) = divide(identity,B). [para(2(a,1),17(a,2,1)),rewrite([19(3)])].
% 0.57/0.85 32 divide(divide(identity,A),divide(B,C)) = divide(divide(C,A),B). [para(22(a,1),17(a,1,1,1)),flip(a)].
% 0.57/0.85 33 divide(divide(A,B),divide(C,B)) = divide(A,C). [para(22(a,1),17(a,1,1)),rewrite([24(6),32(6)]),flip(a)].
% 0.57/0.85 37 divide(A,divide(identity,divide(divide(identity,B),C))) = divide(divide(A,C),B). [para(26(a,1),17(a,1,1,1)),rewrite([27(6),32(10)])].
% 0.57/0.85 41 divide(identity,divide(A,B)) = divide(B,A). [para(22(a,1),29(a,1,1)),flip(a)].
% 0.57/0.85 45 divide(A,divide(B,divide(identity,C))) = divide(divide(A,C),B). [back_rewrite(37),rewrite([41(5),27(3)])].
% 0.57/0.85 49 divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,b3),c3)) # answer(prove_these_axioms). [back_rewrite(28),rewrite([45(8),24(6),45(15),24(13)])].
% 0.57/0.85 55 divide(divide(divide(identity,A),B),divide(C,D)) = divide(divide(divide(D,B),A),C). [para(17(a,1),33(a,1,1))].
% 0.57/0.85 57 divide(A,divide(B,C)) = divide(C,divide(B,A)). [para(29(a,1),33(a,1,2)),rewrite([27(4),41(3)])].
% 0.57/0.85 61 divide(A,divide(B,divide(divide(identity,C),D))) = divide(divide(divide(A,B),C),D). [back_rewrite(55),rewrite([57(5),57(4)])].
% 0.57/0.85 63 divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(divide(identity,b3),c3)) # answer(prove_these_axioms). [back_rewrite(49),rewrite([57(7)])].
% 0.57/0.85 69 divide(A,divide(divide(identity,B),C)) = divide(B,divide(divide(identity,A),C)). [para(17(a,1),45(a,1,2)),rewrite([57(10),57(9),61(9),29(6)])].
% 0.57/0.85 70 $F # answer(prove_these_axioms). [resolve(69,a,63,a)].
% 0.57/0.85
% 0.57/0.85 % SZS output end Refutation
% 0.57/0.85 ============================== end of proof ==========================
% 0.57/0.85
% 0.57/0.85 ============================== STATISTICS ============================
% 0.57/0.85
% 0.57/0.85 Given=23. Generated=383. Kept=67. proofs=1.
% 0.57/0.85 Usable=9. Sos=11. Demods=17. Limbo=1, Disabled=50. Hints=0.
% 0.57/0.85 Megabytes=0.08.
% 0.57/0.85 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.57/0.85
% 0.57/0.85 ============================== end of statistics =====================
% 0.57/0.85
% 0.57/0.85 ============================== end of search =========================
% 0.57/0.85
% 0.57/0.85 THEOREM PROVED
% 0.57/0.85 % SZS status Unsatisfiable
% 0.57/0.85
% 0.57/0.85 Exiting with 1 proof.
% 0.57/0.85
% 0.57/0.85 Process 8260 exit (max_proofs) Tue Jun 14 07:42:58 2022
% 0.57/0.85 Prover9 interrupted
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