TSTP Solution File: BOO013-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 23:48:00 EDT 2022
% Result : Unsatisfiable 0.82s 1.11s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.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 : Wed Jun 1 15:18:07 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.82/1.11 ============================== Prover9 ===============================
% 0.82/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.11 Process 1707 was started by sandbox on n028.cluster.edu,
% 0.82/1.11 Wed Jun 1 15:18:08 2022
% 0.82/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1550_n028.cluster.edu".
% 0.82/1.11 ============================== end of head ===========================
% 0.82/1.11
% 0.82/1.11 ============================== INPUT =================================
% 0.82/1.11
% 0.82/1.11 % Reading from file /tmp/Prover9_1550_n028.cluster.edu
% 0.82/1.11
% 0.82/1.11 set(prolog_style_variables).
% 0.82/1.11 set(auto2).
% 0.82/1.11 % set(auto2) -> set(auto).
% 0.82/1.11 % set(auto) -> set(auto_inference).
% 0.82/1.11 % set(auto) -> set(auto_setup).
% 0.82/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.11 % set(auto) -> set(auto_limits).
% 0.82/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.11 % set(auto) -> set(auto_denials).
% 0.82/1.11 % set(auto) -> set(auto_process).
% 0.82/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.11 % set(auto2) -> assign(stats, some).
% 0.82/1.11 % set(auto2) -> clear(echo_input).
% 0.82/1.11 % set(auto2) -> set(quiet).
% 0.82/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.11 % set(auto2) -> clear(print_given).
% 0.82/1.11 assign(lrs_ticks,-1).
% 0.82/1.11 assign(sos_limit,10000).
% 0.82/1.11 assign(order,kbo).
% 0.82/1.11 set(lex_order_vars).
% 0.82/1.11 clear(print_given).
% 0.82/1.11
% 0.82/1.11 % formulas(sos). % not echoed (19 formulas)
% 0.82/1.11
% 0.82/1.11 ============================== end of input ==========================
% 0.82/1.11
% 0.82/1.11 % From the command line: assign(max_seconds, 300).
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.11
% 0.82/1.11 % Formulas that are not ordinary clauses:
% 0.82/1.11
% 0.82/1.11 ============================== end of process non-clausal formulas ===
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.11
% 0.82/1.11 ============================== PREDICATE ELIMINATION =================
% 0.82/1.11
% 0.82/1.11 ============================== end predicate elimination =============
% 0.82/1.11
% 0.82/1.11 Auto_denials:
% 0.82/1.11 % copying label prove_b_is_a to answer in negative clause
% 0.82/1.11
% 0.82/1.11 Term ordering decisions:
% 0.82/1.11
% 0.82/1.11 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.82/1.11 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 0.82/1.11
% 0.82/1.11 ============================== end of process initial clauses ========
% 0.82/1.11
% 0.82/1.11 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.11
% 0.82/1.11 ============================== end of clauses for search =============
% 0.82/1.11
% 0.82/1.11 ============================== SEARCH ================================
% 0.82/1.11
% 0.82/1.11 % Starting search at 0.01 seconds.
% 0.82/1.11
% 0.82/1.11 ============================== PROOF =================================
% 0.82/1.11 % SZS status Unsatisfiable
% 0.82/1.11 % SZS output start Refutation
% 0.82/1.11
% 0.82/1.11 % Proof 1 at 0.12 (+ 0.00) seconds: prove_b_is_a.
% 0.82/1.11 % Length of proof is 56.
% 0.82/1.11 % Level of proof is 12.
% 0.82/1.11 % Maximum clause weight is 21.000.
% 0.82/1.11 % Given clauses 81.
% 0.82/1.11
% 0.82/1.11 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.82/1.11 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.82/1.11 5 add(a,b) = multiplicative_identity # label(b_and_multiplicative_identity) # label(hypothesis). [assumption].
% 0.82/1.11 6 add(a,c) = multiplicative_identity # label(c_and_multiplicative_identity) # label(hypothesis). [assumption].
% 0.82/1.11 7 multiply(a,b) = additive_identity # label(b_a_additive_identity) # label(hypothesis). [assumption].
% 0.82/1.11 8 multiply(a,c) = additive_identity # label(c_a_additive_identity) # label(hypothesis). [assumption].
% 0.82/1.11 9 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.82/1.11 11 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.82/1.11 13 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.82/1.11 14 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.82/1.11 15 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.82/1.11 16 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(15),rewrite([13(2)]),flip(a),rewrite([13(2)])].
% 0.82/1.11 17 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.82/1.11 18 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(17),flip(a)].
% 0.82/1.11 19 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 0.82/1.11 20 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(19),rewrite([14(2)]),flip(a),rewrite([14(2)])].
% 0.82/1.11 23 b != c # label(prove_b_is_a) # label(negated_conjecture) # answer(prove_b_is_a). [assumption].
% 0.82/1.11 24 c != b # answer(prove_b_is_a). [copy(23),flip(a)].
% 0.82/1.11 25 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(3(a,1),16(a,1,1)),rewrite([13(2),3(2)]),flip(a)].
% 0.82/1.11 26 multiply(A,add(B,A)) = add(A,multiply(B,additive_identity)). [para(3(a,1),16(a,1,2)),rewrite([14(2)])].
% 0.82/1.11 27 multiply(multiplicative_identity,add(A,b)) = add(b,multiply(A,a)). [para(5(a,1),16(a,1,1)),rewrite([13(3),14(7)])].
% 0.82/1.11 31 multiply(multiplicative_identity,add(A,inverse(B))) = add(inverse(B),multiply(B,A)). [para(9(a,1),16(a,1,1)),rewrite([13(3)])].
% 0.82/1.11 33 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(3(a,1),18(a,1,1)),rewrite([14(4)])].
% 0.82/1.11 35 multiply(multiplicative_identity,add(A,B)) = add(A,B). [para(1(a,1),20(a,1,1)),rewrite([14(2),1(2)]),flip(a)].
% 0.82/1.11 36 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(1(a,1),20(a,1,2)),rewrite([13(2)]),flip(a)].
% 0.82/1.11 37 multiply(b,add(A,a)) = multiply(A,b). [para(7(a,1),20(a,1,1)),rewrite([14(3),25(4),13(5)]),flip(a)].
% 0.82/1.11 41 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(11(a,1),20(a,1,1)),rewrite([14(3),25(4)]),flip(a)].
% 0.82/1.11 42 multiply(A,add(B,inverse(A))) = multiply(B,A). [para(11(a,1),20(a,1,2)),rewrite([13(3),25(3)]),flip(a)].
% 0.82/1.11 43 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [para(20(a,1),16(a,1,1)),rewrite([13(4),14(7),14(8)])].
% 0.82/1.11 53 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [back_rewrite(31),rewrite([35(4),14(4)]),flip(a)].
% 0.82/1.11 56 add(b,multiply(A,a)) = add(A,b). [back_rewrite(27),rewrite([35(4)]),flip(a)].
% 0.82/1.11 73 multiply(multiplicative_identity,b) = add(additive_identity,b). [para(5(a,1),26(a,1,2)),rewrite([14(3),14(7),56(8)])].
% 0.82/1.11 92 add(A,add(additive_identity,b)) = add(A,b). [para(73(a,1),20(a,1,2)),rewrite([1(2),35(8)])].
% 0.82/1.11 99 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(3(a,1),33(a,1,2))].
% 0.82/1.11 103 multiply(b,b) = add(additive_identity,b). [para(33(a,1),37(a,1)),rewrite([14(4),56(5)]),flip(a)].
% 0.82/1.11 115 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(11(a,1),36(a,2,2)),rewrite([41(4),3(6)])].
% 0.82/1.11 135 add(A,multiply(A,A)) = A. [para(36(a,1),33(a,1)),rewrite([14(5),1(5),3(4)])].
% 0.82/1.11 138 add(b,b) = add(additive_identity,b). [para(103(a,1),36(a,2,2)),rewrite([13(4),26(5),14(4),1(4),13(3),92(8)]),flip(a)].
% 0.82/1.11 142 inverse(multiplicative_identity) = additive_identity. [para(115(a,1),11(a,1))].
% 0.82/1.11 143 add(additive_identity,inverse(A)) = inverse(A). [para(115(a,1),25(a,1,2)),rewrite([115(6)])].
% 0.82/1.11 145 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(142(a,1),9(a,1,2)),rewrite([13(3)])].
% 0.82/1.11 149 add(A,multiply(B,multiply(A,A))) = multiply(A,add(B,A)). [para(135(a,1),16(a,1,2)),rewrite([14(2)]),flip(a)].
% 0.82/1.11 152 multiply(additive_identity,additive_identity) = additive_identity. [para(135(a,1),25(a,1)),flip(a)].
% 0.82/1.11 154 add(additive_identity,b) = b. [para(103(a,1),135(a,1,2)),rewrite([92(5),138(3)])].
% 0.82/1.11 161 multiply(A,A) = A. [back_rewrite(99),rewrite([152(4),3(3)])].
% 0.82/1.11 168 multiply(A,add(A,B)) = add(A,multiply(A,B)). [back_rewrite(149),rewrite([161(1),14(1),13(3)]),flip(a)].
% 0.82/1.11 178 multiply(b,inverse(a)) = inverse(a). [para(5(a,1),41(a,1,2)),rewrite([14(4),115(4)]),flip(a)].
% 0.82/1.11 179 multiply(c,inverse(a)) = inverse(a). [para(6(a,1),41(a,1,2)),rewrite([14(4),115(4)]),flip(a)].
% 0.82/1.11 235 add(A,multiply(B,multiply(A,additive_identity))) = add(A,multiply(A,B)). [para(145(a,1),43(a,1,1,2)),rewrite([1(2),1(2),13(1),168(2),1(4)]),flip(a)].
% 0.82/1.11 302 multiply(A,additive_identity) = additive_identity. [para(143(a,1),42(a,1,2)),rewrite([11(2),14(3)]),flip(a)].
% 0.82/1.11 311 add(A,multiply(A,B)) = A. [back_rewrite(235),rewrite([302(2),302(2),3(2)]),flip(a)].
% 0.82/1.11 418 add(b,inverse(a)) = b. [para(178(a,1),311(a,1,2))].
% 0.82/1.11 419 add(c,inverse(a)) = c. [para(179(a,1),311(a,1,2))].
% 0.82/1.11 576 inverse(a) = b. [para(418(a,1),53(a,2)),rewrite([14(5),7(5),13(4),143(4)])].
% 0.82/1.11 577 c = b. [para(419(a,1),53(a,2)),rewrite([576(2),14(4),8(4),13(3),154(3)]),flip(a)].
% 0.82/1.11 578 $F # answer(prove_b_is_a). [resolve(577,a,24,a)].
% 0.82/1.11
% 0.82/1.11 % SZS output end Refutation
% 0.82/1.11 ============================== end of proof ==========================
% 0.82/1.11
% 0.82/1.11 ============================== STATISTICS ============================
% 0.82/1.11
% 0.82/1.11 Given=81. Generated=2932. Kept=572. proofs=1.
% 0.82/1.11 Usable=68. Sos=248. Demods=329. Limbo=28, Disabled=246. Hints=0.
% 0.82/1.11 Megabytes=0.56.
% 0.82/1.11 User_CPU=0.12, System_CPU=0.00, Wall_clock=0.
% 0.82/1.11
% 0.82/1.11 ============================== end of statistics =====================
% 0.82/1.11
% 0.82/1.11 ============================== end of search =========================
% 0.82/1.11
% 0.82/1.11 THEOREM PROVED
% 0.82/1.11 % SZS status Unsatisfiable
% 0.82/1.11
% 0.82/1.11 Exiting with 1 proof.
% 0.82/1.11
% 0.82/1.11 Process 1707 exit (max_proofs) Wed Jun 1 15:18:08 2022
% 0.82/1.11 Prover9 interrupted
%------------------------------------------------------------------------------