TSTP Solution File: GRP513-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 11:19:25 EDT 2022
% Result : Unsatisfiable 0.42s 0.98s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.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 16:33:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 4897 was started by sandbox2 on n016.cluster.edu,
% 0.42/0.98 Mon Jun 13 16:33:45 2022
% 0.42/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4744_n016.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_4744_n016.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (2 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
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% 0.42/0.98 ============================== end of process non-clausal formulas ===
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.42/0.98 ============================== PREDICATE ELIMINATION =================
% 0.42/0.98
% 0.42/0.98 ============================== end predicate elimination =============
% 0.42/0.98
% 0.42/0.98 Auto_denials:
% 0.42/0.98 % copying label prove_these_axioms_1 to answer in negative clause
% 0.42/0.98
% 0.42/0.98 Term ordering decisions:
% 0.42/0.98
% 0.42/0.98 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.42/0.98 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 0.42/0.98
% 0.42/0.98 ============================== end of process initial clauses ========
% 0.42/0.98
% 0.42/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.98
% 0.42/0.98 ============================== end of clauses for search =============
% 0.42/0.98
% 0.42/0.98 ============================== SEARCH ================================
% 0.42/0.98
% 0.42/0.98 % Starting search at 0.01 seconds.
% 0.42/0.98
% 0.42/0.98 ============================== PROOF =================================
% 0.42/0.98 % SZS status Unsatisfiable
% 0.42/0.98 % SZS output start Refutation
% 0.42/0.98
% 0.42/0.98 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_1.
% 0.42/0.98 % Length of proof is 21.
% 0.42/0.98 % Level of proof is 12.
% 0.42/0.98 % Maximum clause weight is 18.000.
% 0.42/0.98 % Given clauses 12.
% 0.42/0.98
% 0.42/0.98 1 multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.42/0.98 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.42/0.98 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 0.42/0.98 4 multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D. [para(1(a,1),1(a,1,2,1))].
% 0.42/0.98 9 multiply(A,multiply(B,inverse(B))) = A. [para(1(a,1),4(a,1,2,2,1))].
% 0.42/0.98 12 multiply(A,multiply(B,inverse(A))) = B. [para(9(a,1),1(a,1,2,1)),rewrite([9(3)])].
% 0.42/0.98 17 multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A. [para(12(a,1),4(a,1,2,2,1))].
% 0.42/0.98 19 multiply(multiply(A,B),multiply(multiply(C,multiply(D,inverse(multiply(D,B)))),inverse(A))) = C. [para(17(a,1),1(a,1,2,2,1))].
% 0.42/0.98 24 multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(C,B). [para(17(a,1),4(a,1,2,2,1))].
% 0.42/0.98 31 multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A. [back_rewrite(19),rewrite([24(8)])].
% 0.42/0.98 34 multiply(A,multiply(multiply(B,C),inverse(multiply(D,C)))) = multiply(B,multiply(A,inverse(D))). [para(1(a,1),24(a,1,1)),flip(a)].
% 0.42/0.98 38 multiply(A,multiply(B,inverse(multiply(B,multiply(C,inverse(D)))))) = multiply(D,multiply(A,inverse(C))). [para(4(a,1),24(a,1,1)),rewrite([34(8)]),flip(a)].
% 0.42/0.98 40 multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C). [para(24(a,1),17(a,1,1)),rewrite([38(7)])].
% 0.42/0.98 44 multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(C,A). [para(31(a,1),12(a,1,2)),flip(a)].
% 0.42/0.98 45 multiply(multiply(A,B),C) = multiply(multiply(A,C),B). [para(31(a,1),24(a,1,2)),rewrite([44(7)])].
% 0.42/0.98 48 multiply(A,multiply(multiply(B,inverse(A)),C)) = multiply(B,C). [para(45(a,1),12(a,1,2))].
% 0.42/0.98 53 multiply(A,inverse(multiply(A,inverse(B)))) = B. [para(48(a,1),9(a,1))].
% 0.42/0.98 59 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(48(a,1),40(a,1))].
% 0.42/0.98 61 multiply(A,B) = multiply(B,A). [back_rewrite(44),rewrite([53(4)])].
% 0.42/0.98 63 multiply(A,inverse(A)) = c_0. [new_symbol(59)].
% 0.42/0.98 81 $F # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([61(4),63(4),61(5),63(5)]),xx(a)].
% 0.42/0.98
% 0.42/0.98 % SZS output end Refutation
% 0.42/0.98 ============================== end of proof ==========================
% 0.42/0.98
% 0.42/0.98 ============================== STATISTICS ============================
% 0.42/0.98
% 0.42/0.98 Given=12. Generated=222. Kept=79. proofs=1.
% 0.42/0.98 Usable=2. Sos=9. Demods=26. Limbo=20, Disabled=50. Hints=0.
% 0.42/0.98 Megabytes=0.09.
% 0.42/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.42/0.98
% 0.42/0.98 ============================== end of statistics =====================
% 0.42/0.98
% 0.42/0.98 ============================== end of search =========================
% 0.42/0.98
% 0.42/0.98 THEOREM PROVED
% 0.42/0.98 % SZS status Unsatisfiable
% 0.42/0.98
% 0.42/0.98 Exiting with 1 proof.
% 0.42/0.98
% 0.42/0.98 Process 4897 exit (max_proofs) Mon Jun 13 16:33:45 2022
% 0.42/0.98 Prover9 interrupted
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