TSTP Solution File: GRP002-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:16:37 EDT 2022
% Result : Unsatisfiable 0.66s 0.99s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.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 07:00:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.99 ============================== Prover9 ===============================
% 0.66/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.99 Process 17772 was started by sandbox2 on n008.cluster.edu,
% 0.66/0.99 Mon Jun 13 07:00:38 2022
% 0.66/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17618_n008.cluster.edu".
% 0.66/0.99 ============================== end of head ===========================
% 0.66/0.99
% 0.66/0.99 ============================== INPUT =================================
% 0.66/0.99
% 0.66/0.99 % Reading from file /tmp/Prover9_17618_n008.cluster.edu
% 0.66/0.99
% 0.66/0.99 set(prolog_style_variables).
% 0.66/0.99 set(auto2).
% 0.66/0.99 % set(auto2) -> set(auto).
% 0.66/0.99 % set(auto) -> set(auto_inference).
% 0.66/0.99 % set(auto) -> set(auto_setup).
% 0.66/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.99 % set(auto) -> set(auto_limits).
% 0.66/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.99 % set(auto) -> set(auto_denials).
% 0.66/0.99 % set(auto) -> set(auto_process).
% 0.66/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.99 % set(auto2) -> assign(stats, some).
% 0.66/0.99 % set(auto2) -> clear(echo_input).
% 0.66/0.99 % set(auto2) -> set(quiet).
% 0.66/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.99 % set(auto2) -> clear(print_given).
% 0.66/0.99 assign(lrs_ticks,-1).
% 0.66/0.99 assign(sos_limit,10000).
% 0.66/0.99 assign(order,kbo).
% 0.66/0.99 set(lex_order_vars).
% 0.66/0.99 clear(print_given).
% 0.66/0.99
% 0.66/0.99 % formulas(sos). % not echoed (12 formulas)
% 0.66/0.99
% 0.66/0.99 ============================== end of input ==========================
% 0.66/0.99
% 0.66/0.99 % From the command line: assign(max_seconds, 300).
% 0.66/0.99
% 0.66/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.99
% 0.66/0.99 % Formulas that are not ordinary clauses:
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% 0.66/0.99 ============================== end of process non-clausal formulas ===
% 0.66/0.99
% 0.66/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/0.99
% 0.66/0.99 ============================== PREDICATE ELIMINATION =================
% 0.66/0.99
% 0.66/0.99 ============================== end predicate elimination =============
% 0.66/0.99
% 0.66/0.99 Auto_denials:
% 0.66/0.99 % copying label prove_k_times_inverse_b_is_e to answer in negative clause
% 0.66/0.99
% 0.66/0.99 Term ordering decisions:
% 0.66/0.99
% 0.66/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.66/0.99 Function symbol KB weights: identity=1. b=1. h=1. a=1. c=1. d=1. j=1. k=1. multiply=1. inverse=0.
% 0.66/0.99
% 0.66/0.99 ============================== end of process initial clauses ========
% 0.66/0.99
% 0.66/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.66/0.99
% 0.66/0.99 ============================== end of clauses for search =============
% 0.66/0.99
% 0.66/0.99 ============================== SEARCH ================================
% 0.66/0.99
% 0.66/0.99 % Starting search at 0.01 seconds.
% 0.66/0.99
% 0.66/0.99 ============================== PROOF =================================
% 0.66/0.99 % SZS status Unsatisfiable
% 0.66/0.99 % SZS output start Refutation
% 0.66/0.99
% 0.66/0.99 % Proof 1 at 0.05 (+ 0.00) seconds: prove_k_times_inverse_b_is_e.
% 0.66/0.99 % Length of proof is 48.
% 0.66/0.99 % Level of proof is 11.
% 0.66/0.99 % Maximum clause weight is 13.000.
% 0.66/0.99 % Given clauses 115.
% 0.66/0.99
% 0.66/0.99 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.66/0.99 2 multiply(A,identity) = A # label(right_identity) # label(axiom). [assumption].
% 0.66/0.99 3 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 0.66/0.99 4 multiply(h,b) = j # label(h_times_b_is_j) # label(negated_conjecture). [assumption].
% 0.66/0.99 5 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.66/0.99 6 multiply(A,inverse(A)) = identity # label(right_inverse) # label(axiom). [assumption].
% 0.66/0.99 7 multiply(c,inverse(a)) = d # label(c_times_inverse_a_is_d) # label(negated_conjecture). [assumption].
% 0.66/0.99 8 multiply(d,inverse(b)) = h # label(d_times_inverse_b_is_h) # label(negated_conjecture). [assumption].
% 0.66/0.99 9 multiply(j,inverse(h)) = k # label(j_times_inverse_h_is_k) # label(negated_conjecture). [assumption].
% 0.66/0.99 10 multiply(A,multiply(A,A)) = identity # label(x_cubed_is_identity) # label(hypothesis). [assumption].
% 0.66/0.99 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.66/0.99 12 multiply(k,inverse(b)) != identity # label(prove_k_times_inverse_b_is_e) # label(negated_conjecture) # answer(prove_k_times_inverse_b_is_e). [assumption].
% 0.66/0.99 14 multiply(a,multiply(b,A)) = multiply(c,A). [para(3(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 16 multiply(inverse(A),multiply(A,B)) = B. [para(5(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.66/0.99 17 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(11(a,1),6(a,1))].
% 0.66/0.99 19 multiply(c,multiply(inverse(a),A)) = multiply(d,A). [para(7(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 24 multiply(inverse(a),c) = b. [para(3(a,1),16(a,1,2))].
% 0.66/0.99 26 inverse(inverse(A)) = A. [para(5(a,1),16(a,1,2)),rewrite([2(4)])].
% 0.66/0.99 27 multiply(inverse(c),d) = inverse(a). [para(7(a,1),16(a,1,2))].
% 0.66/0.99 28 multiply(inverse(d),h) = inverse(b). [para(8(a,1),16(a,1,2))].
% 0.66/0.99 30 multiply(A,A) = inverse(A). [para(10(a,1),16(a,1,2)),rewrite([2(3)]),flip(a)].
% 0.66/0.99 32 multiply(inverse(a),multiply(c,A)) = multiply(b,A). [para(24(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 34 multiply(c,inverse(b)) = a. [para(6(a,1),14(a,1,2)),rewrite([2(3)]),flip(a)].
% 0.66/0.99 35 multiply(A,multiply(A,B)) = multiply(inverse(A),B). [para(30(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 36 multiply(A,multiply(B,multiply(A,B))) = inverse(multiply(A,B)). [para(30(a,1),11(a,1)),flip(a)].
% 0.66/0.99 37 multiply(c,b) = multiply(a,inverse(b)). [para(30(a,1),14(a,1,2)),flip(a)].
% 0.66/0.99 39 multiply(inverse(c),a) = inverse(b). [para(34(a,1),16(a,1,2))].
% 0.66/0.99 40 multiply(inverse(c),multiply(d,A)) = multiply(inverse(a),A). [para(27(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 47 multiply(inverse(c),multiply(a,A)) = multiply(inverse(b),A). [para(39(a,1),11(a,1,1)),flip(a)].
% 0.66/0.99 51 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(17(a,1),16(a,1,2)),rewrite([2(3)]),flip(a)].
% 0.66/0.99 52 multiply(inverse(d),j) = identity. [para(28(a,1),17(a,1,2,2,1)),rewrite([26(6),4(5)])].
% 0.66/0.99 54 j = d. [para(52(a,1),16(a,1,2)),rewrite([26(3),2(3)]),flip(a)].
% 0.66/0.99 62 multiply(d,inverse(h)) = k. [back_rewrite(9),rewrite([54(1)])].
% 0.66/0.99 63 multiply(h,b) = d. [back_rewrite(4),rewrite([54(4)])].
% 0.66/0.99 75 multiply(b,inverse(c)) = inverse(a). [para(3(a,1),51(a,1,2,1))].
% 0.66/0.99 81 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(51(a,1),16(a,1,2)),flip(a)].
% 0.66/0.99 83 multiply(b,inverse(d)) = inverse(h). [para(63(a,1),51(a,1,2,1))].
% 0.66/0.99 87 multiply(A,multiply(B,multiply(A,B))) = multiply(inverse(B),inverse(A)). [back_rewrite(36),rewrite([81(5)])].
% 0.66/0.99 92 multiply(inverse(a),d) = multiply(b,inverse(a)). [para(7(a,1),32(a,1,2))].
% 0.66/0.99 96 multiply(c,inverse(d)) = multiply(a,inverse(h)). [para(83(a,1),14(a,1,2)),flip(a)].
% 0.66/0.99 111 multiply(inverse(c),multiply(inverse(a),A)) = multiply(c,multiply(d,A)). [para(19(a,1),35(a,1,2)),flip(a)].
% 0.66/0.99 116 multiply(inverse(b),inverse(c)) = multiply(b,inverse(a)). [para(75(a,1),35(a,1,2)),flip(a)].
% 0.66/0.99 132 multiply(inverse(c),inverse(d)) = multiply(b,inverse(a)). [para(30(a,1),40(a,1,2)),rewrite([92(9)])].
% 0.66/0.99 158 multiply(inverse(b),multiply(a,A)) = multiply(c,multiply(d,A)). [para(35(a,1),47(a,1,2)),rewrite([111(6)]),flip(a)].
% 0.66/0.99 214 multiply(inverse(c),multiply(b,inverse(a))) = multiply(a,inverse(h)). [para(132(a,1),35(a,1,2)),rewrite([26(10),96(11)])].
% 0.66/0.99 269 multiply(c,k) = multiply(a,inverse(b)). [para(116(a,1),87(a,1,2,2)),rewrite([214(9),158(7),62(5),26(6),26(7),37(6)])].
% 0.66/0.99 283 k = b. [para(269(a,1),16(a,1,2)),rewrite([47(7),30(5),26(3)]),flip(a)].
% 0.66/0.99 320 $F # answer(prove_k_times_inverse_b_is_e). [back_rewrite(12),rewrite([283(1),6(4)]),xx(a)].
% 0.66/0.99
% 0.66/0.99 % SZS output end Refutation
% 0.66/0.99 ============================== end of proof ==========================
% 0.66/0.99
% 0.66/0.99 ============================== STATISTICS ============================
% 0.66/0.99
% 0.66/0.99 Given=115. Generated=1820. Kept=319. proofs=1.
% 0.66/0.99 Usable=74. Sos=88. Demods=197. Limbo=37, Disabled=132. Hints=0.
% 0.66/0.99 Megabytes=0.23.
% 0.66/0.99 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.66/0.99
% 0.66/0.99 ============================== end of statistics =====================
% 0.66/0.99
% 0.66/0.99 ============================== end of search =========================
% 0.66/0.99
% 0.66/0.99 THEOREM PROVED
% 0.66/0.99 % SZS status Unsatisfiable
% 0.66/0.99
% 0.66/0.99 Exiting with 1 proof.
% 0.66/0.99
% 0.66/0.99 Process 17772 exit (max_proofs) Mon Jun 13 07:00:38 2022
% 0.66/0.99 Prover9 interrupted
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