TSTP Solution File: BOO029-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 23:48:04 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
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Thu Jun 2 00:25:49 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 6335 was started by sandbox2 on n027.cluster.edu,
% 0.66/0.99 Thu Jun 2 00:25:49 2022
% 0.66/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6182_n027.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_6182_n027.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 (11 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_equal_inverse 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 (6).
% 0.66/0.99 Function symbol KB weights: a=1. b=1. add=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 0.03 (+ 0.00) seconds: prove_equal_inverse.
% 0.66/0.99 % Length of proof is 34.
% 0.66/0.99 % Level of proof is 13.
% 0.66/0.99 % Maximum clause weight is 14.000.
% 0.66/0.99 % Given clauses 33.
% 0.66/0.99
% 0.66/0.99 1 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.66/0.99 2 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.66/0.99 3 add(A,multiply(B,multiply(A,C))) = A # label(l1) # label(axiom). [assumption].
% 0.66/0.99 4 multiply(A,add(B,add(A,C))) = A # label(l2) # label(axiom). [assumption].
% 0.66/0.99 5 multiply(add(A,B),add(A,inverse(B))) = A # label(b1) # label(axiom). [assumption].
% 0.66/0.99 6 add(multiply(A,B),multiply(A,inverse(B))) = A # label(b2) # label(axiom). [assumption].
% 0.66/0.99 9 multiply(multiply(add(A,B),add(B,C)),B) = B # label(l4) # label(axiom). [assumption].
% 0.66/0.99 10 multiply(A,multiply(add(A,B),add(A,C))) = A. [copy(9),rewrite([2(4)]),rewrite([1(1)])].
% 0.66/0.99 11 add(add(A,B),C) = add(A,add(B,C)) # label(associativity_of_add) # label(axiom). [assumption].
% 0.66/0.99 12 add(A,add(B,C)) = add(C,add(A,B)). [copy(11),rewrite([1(2)]),flip(a)].
% 0.66/0.99 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 0.66/0.99 14 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [copy(13),rewrite([2(2)]),flip(a)].
% 0.66/0.99 15 add(b,inverse(b)) != add(a,inverse(a)) # label(prove_equal_inverse) # label(negated_conjecture) # answer(prove_equal_inverse). [assumption].
% 0.66/0.99 16 multiply(A,add(A,add(B,C))) = A. [back_rewrite(4),rewrite([12(2,R),1(1)])].
% 0.66/0.99 17 add(A,multiply(A,multiply(B,C))) = A. [back_rewrite(3),rewrite([14(2,R),2(1)])].
% 0.66/0.99 18 multiply(add(A,B),add(B,inverse(A))) = B. [para(1(a,1),5(a,1,1))].
% 0.66/0.99 19 add(multiply(A,B),multiply(B,inverse(A))) = B. [para(2(a,1),6(a,1,1))].
% 0.66/0.99 25 multiply(A,A) = A. [para(5(a,1),10(a,1,2))].
% 0.66/0.99 37 multiply(A,add(A,B)) = A. [para(6(a,1),16(a,1,2,2))].
% 0.66/0.99 39 add(A,multiply(A,B)) = A. [para(5(a,1),17(a,1,2,2))].
% 0.66/0.99 50 multiply(A,multiply(B,add(A,C))) = multiply(A,B). [para(37(a,1),14(a,2,2)),rewrite([2(2),2(4)])].
% 0.66/0.99 52 multiply(A,add(inverse(A),multiply(A,B))) = multiply(A,B). [para(39(a,1),18(a,1,1)),rewrite([1(3)])].
% 0.66/1.00 89 multiply(A,multiply(B,inverse(A))) = multiply(A,inverse(A)). [para(52(a,1),50(a,1,2)),rewrite([14(3),2(2),14(3,R),2(2),2(5)])].
% 0.66/1.00 92 multiply(A,multiply(B,inverse(B))) = multiply(B,inverse(B)). [para(89(a,1),14(a,2)),rewrite([2(2)])].
% 0.66/1.00 93 add(multiply(A,inverse(A)),multiply(B,inverse(A))) = multiply(B,inverse(A)). [para(89(a,1),19(a,1,1)),rewrite([2(6),14(6,R),25(5)])].
% 0.66/1.00 103 add(multiply(A,inverse(A)),multiply(B,inverse(multiply(A,inverse(A))))) = B. [para(92(a,1),6(a,1,1))].
% 0.66/1.00 104 add(A,multiply(B,inverse(B))) = A. [para(92(a,1),39(a,1,2))].
% 0.66/1.00 106 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(92(a,1),52(a,1,2,2)),rewrite([104(4),92(5)])].
% 0.66/1.00 107 multiply(A,inverse(A)) = c_0. [new_symbol(106)].
% 0.66/1.00 110 add(c_0,multiply(A,inverse(c_0))) = A. [back_rewrite(103),rewrite([107(2),107(3)])].
% 0.66/1.00 112 add(c_0,multiply(A,inverse(B))) = multiply(A,inverse(B)). [back_rewrite(93),rewrite([107(2)])].
% 0.66/1.00 117 multiply(A,inverse(c_0)) = A. [back_rewrite(110),rewrite([112(5)])].
% 0.66/1.00 132 add(A,inverse(A)) = inverse(c_0). [para(117(a,1),19(a,1,1)),rewrite([2(4),117(4)])].
% 0.66/1.00 134 $F # answer(prove_equal_inverse). [back_rewrite(15),rewrite([132(4),132(6)]),xx(a)].
% 0.66/1.00
% 0.66/1.00 % SZS output end Refutation
% 0.66/1.00 ============================== end of proof ==========================
% 0.66/1.00
% 0.66/1.00 ============================== STATISTICS ============================
% 0.66/1.00
% 0.66/1.00 Given=33. Generated=745. Kept=129. proofs=1.
% 0.66/1.00 Usable=26. Sos=62. Demods=90. Limbo=2, Disabled=50. Hints=0.
% 0.66/1.00 Megabytes=0.16.
% 0.66/1.00 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.66/1.00
% 0.66/1.00 ============================== end of statistics =====================
% 0.66/1.00
% 0.66/1.00 ============================== end of search =========================
% 0.66/1.00
% 0.66/1.00 THEOREM PROVED
% 0.66/1.00 % SZS status Unsatisfiable
% 0.66/1.00
% 0.66/1.00 Exiting with 1 proof.
% 0.66/1.00
% 0.66/1.00 Process 6335 exit (max_proofs) Thu Jun 2 00:25:49 2022
% 0.66/1.00 Prover9 interrupted
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