TSTP Solution File: GRP517-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:19:26 EDT 2022
% Result : Unsatisfiable 0.77s 1.07s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 21:36:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.77/1.07 ============================== Prover9 ===============================
% 0.77/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.07 Process 26488 was started by sandbox2 on n027.cluster.edu,
% 0.77/1.07 Mon Jun 13 21:36:33 2022
% 0.77/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26334_n027.cluster.edu".
% 0.77/1.07 ============================== end of head ===========================
% 0.77/1.07
% 0.77/1.07 ============================== INPUT =================================
% 0.77/1.07
% 0.77/1.07 % Reading from file /tmp/Prover9_26334_n027.cluster.edu
% 0.77/1.07
% 0.77/1.07 set(prolog_style_variables).
% 0.77/1.07 set(auto2).
% 0.77/1.07 % set(auto2) -> set(auto).
% 0.77/1.07 % set(auto) -> set(auto_inference).
% 0.77/1.07 % set(auto) -> set(auto_setup).
% 0.77/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.07 % set(auto) -> set(auto_limits).
% 0.77/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.07 % set(auto) -> set(auto_denials).
% 0.77/1.07 % set(auto) -> set(auto_process).
% 0.77/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.07 % set(auto2) -> assign(stats, some).
% 0.77/1.07 % set(auto2) -> clear(echo_input).
% 0.77/1.07 % set(auto2) -> set(quiet).
% 0.77/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.07 % set(auto2) -> clear(print_given).
% 0.77/1.07 assign(lrs_ticks,-1).
% 0.77/1.07 assign(sos_limit,10000).
% 0.77/1.07 assign(order,kbo).
% 0.77/1.07 set(lex_order_vars).
% 0.77/1.07 clear(print_given).
% 0.77/1.07
% 0.77/1.07 % formulas(sos). % not echoed (2 formulas)
% 0.77/1.07
% 0.77/1.07 ============================== end of input ==========================
% 0.77/1.07
% 0.77/1.07 % From the command line: assign(max_seconds, 300).
% 0.77/1.07
% 0.77/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.07
% 0.77/1.07 % Formulas that are not ordinary clauses:
% 0.77/1.07
% 0.77/1.07 ============================== end of process non-clausal formulas ===
% 0.77/1.07
% 0.77/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.07
% 0.77/1.07 ============================== PREDICATE ELIMINATION =================
% 0.77/1.07
% 0.77/1.07 ============================== end predicate elimination =============
% 0.77/1.07
% 0.77/1.07 Auto_denials:
% 0.77/1.07 % copying label prove_these_axioms_1 to answer in negative clause
% 0.77/1.07
% 0.77/1.07 Term ordering decisions:
% 0.77/1.07
% 0.77/1.07 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.77/1.07 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 0.77/1.07
% 0.77/1.07 ============================== end of process initial clauses ========
% 0.77/1.07
% 0.77/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.07
% 0.77/1.07 ============================== end of clauses for search =============
% 0.77/1.07
% 0.77/1.07 ============================== SEARCH ================================
% 0.77/1.07
% 0.77/1.07 % Starting search at 0.01 seconds.
% 0.77/1.07
% 0.77/1.07 ============================== PROOF =================================
% 0.77/1.07 % SZS status Unsatisfiable
% 0.77/1.07 % SZS output start Refutation
% 0.77/1.07
% 0.77/1.07 % Proof 1 at 0.05 (+ 0.00) seconds: prove_these_axioms_1.
% 0.77/1.07 % Length of proof is 23.
% 0.77/1.07 % Level of proof is 14.
% 0.77/1.07 % Maximum clause weight is 17.000.
% 0.77/1.07 % Given clauses 28.
% 0.77/1.07
% 0.77/1.07 1 multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.77/1.07 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.77/1.07 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 0.77/1.07 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))].
% 0.77/1.07 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)].
% 0.77/1.07 9 multiply(multiply(inverse(A),B),A) = B. [para(1(a,1),4(a,1,2))].
% 0.77/1.07 13 multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A). [para(1(a,1),9(a,1,1)),flip(a)].
% 0.77/1.07 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)].
% 0.77/1.07 17 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [back_rewrite(5),rewrite([13(6)])].
% 0.77/1.07 18 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(15),rewrite([17(4)])].
% 0.77/1.07 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)].
% 0.77/1.07 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)].
% 0.77/1.07 28 multiply(A,B) = multiply(B,A). [para(9(a,1),18(a,1,2))].
% 0.77/1.07 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)])].
% 0.77/1.07 44 multiply(A,multiply(B,multiply(C,inverse(multiply(A,B))))) = C. [back_rewrite(1),rewrite([28(3),28(4)])].
% 0.77/1.07 45 multiply(A,multiply(B,inverse(inverse(C)))) = multiply(A,multiply(C,B)). [back_rewrite(27),rewrite([28(3),28(5)])].
% 0.77/1.07 47 multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([28(4),28(8)])].
% 0.77/1.07 68 multiply(A,multiply(B,multiply(inverse(inverse(C)),inverse(multiply(A,C))))) = B. [para(45(a,2),44(a,1)),rewrite([28(6),17(6)])].
% 0.77/1.07 89 inverse(inverse(A)) = A. [para(68(a,1),44(a,1)),flip(a)].
% 0.77/1.07 90 multiply(A,multiply(B,inverse(multiply(A,C)))) = multiply(B,inverse(C)). [para(89(a,1),41(a,1,2,2,1,2)),rewrite([28(6)])].
% 0.77/1.07 111 multiply(A,multiply(B,inverse(multiply(C,B)))) = multiply(A,inverse(C)). [para(90(a,1),17(a,1)),rewrite([28(3)]),flip(a)].
% 0.77/1.07 141 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(111(a,1),90(a,1))].
% 0.77/1.07 142 $F # answer(prove_these_axioms_1). [resolve(141,a,47,a)].
% 0.77/1.07
% 0.77/1.07 % SZS output end Refutation
% 0.77/1.07 ============================== end of proof ==========================
% 0.77/1.07
% 0.77/1.07 ============================== STATISTICS ============================
% 0.77/1.07
% 0.77/1.07 Given=28. Generated=781. Kept=140. proofs=1.
% 0.77/1.07 Usable=13. Sos=31. Demods=47. Limbo=4, Disabled=93. Hints=0.
% 0.77/1.07 Megabytes=0.15.
% 0.77/1.07 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.77/1.07
% 0.77/1.07 ============================== end of statistics =====================
% 0.77/1.07
% 0.77/1.07 ============================== end of search =========================
% 0.77/1.07
% 0.77/1.07 THEOREM PROVED
% 0.77/1.07 % SZS status Unsatisfiable
% 0.77/1.07
% 0.77/1.07 Exiting with 1 proof.
% 0.77/1.07
% 0.77/1.07 Process 26488 exit (max_proofs) Mon Jun 13 21:36:33 2022
% 0.77/1.07 Prover9 interrupted
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