TSTP Solution File: GRP087-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:17:06 EDT 2022
% Result : Unsatisfiable 0.75s 1.05s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:12:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.05 ============================== Prover9 ===============================
% 0.75/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.05 Process 17790 was started by sandbox2 on n020.cluster.edu,
% 0.75/1.05 Mon Jun 13 08:12:50 2022
% 0.75/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17636_n020.cluster.edu".
% 0.75/1.05 ============================== end of head ===========================
% 0.75/1.05
% 0.75/1.05 ============================== INPUT =================================
% 0.75/1.05
% 0.75/1.05 % Reading from file /tmp/Prover9_17636_n020.cluster.edu
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% 0.75/1.05 set(prolog_style_variables).
% 0.75/1.05 set(auto2).
% 0.75/1.05 % set(auto2) -> set(auto).
% 0.75/1.05 % set(auto) -> set(auto_inference).
% 0.75/1.05 % set(auto) -> set(auto_setup).
% 0.75/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.05 % set(auto) -> set(auto_limits).
% 0.75/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.05 % set(auto) -> set(auto_denials).
% 0.75/1.05 % set(auto) -> set(auto_process).
% 0.75/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.05 % set(auto2) -> assign(stats, some).
% 0.75/1.05 % set(auto2) -> clear(echo_input).
% 0.75/1.05 % set(auto2) -> set(quiet).
% 0.75/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.05 % set(auto2) -> clear(print_given).
% 0.75/1.05 assign(lrs_ticks,-1).
% 0.75/1.05 assign(sos_limit,10000).
% 0.75/1.05 assign(order,kbo).
% 0.75/1.05 set(lex_order_vars).
% 0.75/1.05 clear(print_given).
% 0.75/1.05
% 0.75/1.05 % formulas(sos). % not echoed (2 formulas)
% 0.75/1.05
% 0.75/1.05 ============================== end of input ==========================
% 0.75/1.05
% 0.75/1.05 % From the command line: assign(max_seconds, 300).
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.05
% 0.75/1.05 % Formulas that are not ordinary clauses:
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% 0.75/1.05 ============================== end of process non-clausal formulas ===
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.75/1.05 ============================== PREDICATE ELIMINATION =================
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% 0.75/1.05 ============================== end predicate elimination =============
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% 0.75/1.05 Auto_denials:
% 0.75/1.05 % copying label prove_these_axioms to answer in negative clause
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% 0.75/1.05 Term ordering decisions:
% 0.75/1.05
% 0.75/1.05 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.75/1.05 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. multiply=1. inverse=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of process initial clauses ========
% 0.75/1.05
% 0.75/1.05 ============================== CLAUSES FOR SEARCH ====================
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% 0.75/1.05 ============================== end of clauses for search =============
% 0.75/1.05
% 0.75/1.05 ============================== SEARCH ================================
% 0.75/1.05
% 0.75/1.05 % Starting search at 0.01 seconds.
% 0.75/1.05
% 0.75/1.05 ============================== PROOF =================================
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05 % SZS output start Refutation
% 0.75/1.05
% 0.75/1.05 % Proof 1 at 0.06 (+ 0.00) seconds: prove_these_axioms.
% 0.75/1.05 % Length of proof is 28.
% 0.75/1.05 % Level of proof is 14.
% 0.75/1.05 % Maximum clause weight is 35.000.
% 0.75/1.05 % Given clauses 29.
% 0.75/1.05
% 0.75/1.05 1 multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.05 2 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].
% 0.75/1.05 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(b4,a4) != multiply(a4,b4) # answer(prove_these_axioms). [copy(2),flip(a),flip(d)].
% 0.75/1.05 4 multiply(A,multiply(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C. [para(1(a,1),1(a,1,2,1,1,1))].
% 0.75/1.05 5 multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)). [para(1(a,1),1(a,1,2,1)),flip(a)].
% 0.75/1.05 9 multiply(multiply(inverse(A),B),A) = B. [para(1(a,1),4(a,1,2))].
% 0.75/1.05 13 multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A). [para(1(a,1),9(a,1,1)),flip(a)].
% 0.75/1.05 14 multiply(multiply(inverse(A),B),multiply(multiply(inverse(C),D),multiply(multiply(inverse(B),C),A))) = D. [para(9(a,1),4(a,1,2,2,1,1,1))].
% 0.75/1.05 15 multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(B,C). [para(4(a,1),9(a,1,1)),rewrite([13(8)]),flip(a)].
% 0.75/1.05 17 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [back_rewrite(5),rewrite([13(6)])].
% 0.75/1.05 18 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(15),rewrite([17(4)])].
% 0.75/1.05 24 multiply(multiply(A,B),C) = multiply(B,multiply(A,C)). [para(1(a,1),18(a,1,2,1)),rewrite([13(7)]),flip(a)].
% 0.75/1.05 27 multiply(A,multiply(inverse(inverse(B)),C)) = multiply(A,multiply(C,B)). [para(18(a,1),9(a,1,1)),rewrite([24(2),17(2),24(6)]),flip(a)].
% 0.75/1.05 28 multiply(A,B) = multiply(B,A). [para(9(a,1),18(a,1,2))].
% 0.75/1.05 33 multiply(A,multiply(B,multiply(C,inverse(A)))) = multiply(B,C). [para(18(a,1),17(a,2)),rewrite([28(2),17(4),28(3),17(3)])].
% 0.75/1.05 40 multiply(A,multiply(B,inverse(A))) = B. [back_rewrite(14),rewrite([28(2),28(4),28(6),28(7),17(8),17(7),24(6),17(6),28(5),33(7),17(6),17(5),28(4),17(4),28(3),17(5),33(5)])].
% 0.75/1.05 41 multiply(A,multiply(B,inverse(multiply(A,inverse(C))))) = multiply(C,B). [back_rewrite(13),rewrite([28(2),28(4),28(5),28(6)])].
% 0.75/1.05 44 multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) | multiply(a2,multiply(b2,inverse(b2))) != a2 # answer(prove_these_axioms). [back_rewrite(3),rewrite([28(4),28(8),28(13),28(15),28(22),17(22),28(21),28(31)]),xx(c),xx(d)].
% 0.75/1.05 45 multiply(A,multiply(B,multiply(C,inverse(multiply(A,B))))) = C. [back_rewrite(1),rewrite([28(3),28(4)])].
% 0.75/1.05 46 multiply(A,multiply(B,inverse(inverse(C)))) = multiply(A,multiply(C,B)). [back_rewrite(27),rewrite([28(3),28(5)])].
% 0.75/1.05 48 multiply(A,multiply(B,inverse(B))) = A. [para(40(a,1),17(a,1)),flip(a)].
% 0.75/1.05 49 multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) # answer(prove_these_axioms). [back_rewrite(44),rewrite([48(15)]),xx(b)].
% 0.75/1.05 69 multiply(A,multiply(B,multiply(inverse(inverse(C)),inverse(multiply(A,C))))) = B. [para(46(a,2),45(a,1)),rewrite([28(6),17(6)])].
% 0.75/1.05 90 inverse(inverse(A)) = A. [para(69(a,1),45(a,1)),flip(a)].
% 0.75/1.05 91 multiply(A,multiply(B,inverse(multiply(A,C)))) = multiply(B,inverse(C)). [para(90(a,1),41(a,1,2,2,1,2)),rewrite([28(6)])].
% 0.75/1.05 112 multiply(A,multiply(B,inverse(multiply(C,B)))) = multiply(A,inverse(C)). [para(91(a,1),17(a,1)),rewrite([28(3)]),flip(a)].
% 0.75/1.05 142 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(112(a,1),91(a,1))].
% 0.75/1.05 143 $F # answer(prove_these_axioms). [resolve(142,a,49,a)].
% 0.75/1.05
% 0.75/1.05 % SZS output end Refutation
% 0.75/1.05 ============================== end of proof ==========================
% 0.75/1.05
% 0.75/1.05 ============================== STATISTICS ============================
% 0.75/1.05
% 0.75/1.05 Given=29. Generated=785. Kept=141. proofs=1.
% 0.75/1.05 Usable=13. Sos=31. Demods=47. Limbo=4, Disabled=94. Hints=0.
% 0.75/1.05 Megabytes=0.17.
% 0.75/1.05 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of statistics =====================
% 0.75/1.05
% 0.75/1.05 ============================== end of search =========================
% 0.75/1.05
% 0.75/1.05 THEOREM PROVED
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05
% 0.75/1.05 Exiting with 1 proof.
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% 0.75/1.05 Process 17790 exit (max_proofs) Mon Jun 13 08:12:50 2022
% 0.75/1.05 Prover9 interrupted
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