TSTP Solution File: BOO007-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 23:47:58 EDT 2022
% Result : Unsatisfiable 1.25s 1.53s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 17:45:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.25/1.53 ============================== Prover9 ===============================
% 1.25/1.53 Prover9 (32) version 2009-11A, November 2009.
% 1.25/1.53 Process 3331 was started by sandbox2 on n018.cluster.edu,
% 1.25/1.53 Wed Jun 1 17:45:30 2022
% 1.25/1.53 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3177_n018.cluster.edu".
% 1.25/1.53 ============================== end of head ===========================
% 1.25/1.53
% 1.25/1.53 ============================== INPUT =================================
% 1.25/1.53
% 1.25/1.53 % Reading from file /tmp/Prover9_3177_n018.cluster.edu
% 1.25/1.53
% 1.25/1.53 set(prolog_style_variables).
% 1.25/1.53 set(auto2).
% 1.25/1.53 % set(auto2) -> set(auto).
% 1.25/1.53 % set(auto) -> set(auto_inference).
% 1.25/1.53 % set(auto) -> set(auto_setup).
% 1.25/1.53 % set(auto_setup) -> set(predicate_elim).
% 1.25/1.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.25/1.53 % set(auto) -> set(auto_limits).
% 1.25/1.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.25/1.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.25/1.53 % set(auto) -> set(auto_denials).
% 1.25/1.53 % set(auto) -> set(auto_process).
% 1.25/1.53 % set(auto2) -> assign(new_constants, 1).
% 1.25/1.53 % set(auto2) -> assign(fold_denial_max, 3).
% 1.25/1.53 % set(auto2) -> assign(max_weight, "200.000").
% 1.25/1.53 % set(auto2) -> assign(max_hours, 1).
% 1.25/1.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.25/1.53 % set(auto2) -> assign(max_seconds, 0).
% 1.25/1.53 % set(auto2) -> assign(max_minutes, 5).
% 1.25/1.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.25/1.53 % set(auto2) -> set(sort_initial_sos).
% 1.25/1.53 % set(auto2) -> assign(sos_limit, -1).
% 1.25/1.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.25/1.53 % set(auto2) -> assign(max_megs, 400).
% 1.25/1.53 % set(auto2) -> assign(stats, some).
% 1.25/1.53 % set(auto2) -> clear(echo_input).
% 1.25/1.53 % set(auto2) -> set(quiet).
% 1.25/1.53 % set(auto2) -> clear(print_initial_clauses).
% 1.25/1.53 % set(auto2) -> clear(print_given).
% 1.25/1.53 assign(lrs_ticks,-1).
% 1.25/1.53 assign(sos_limit,10000).
% 1.25/1.53 assign(order,kbo).
% 1.25/1.53 set(lex_order_vars).
% 1.25/1.53 clear(print_given).
% 1.25/1.53
% 1.25/1.53 % formulas(sos). % not echoed (15 formulas)
% 1.25/1.53
% 1.25/1.53 ============================== end of input ==========================
% 1.25/1.53
% 1.25/1.53 % From the command line: assign(max_seconds, 300).
% 1.25/1.53
% 1.25/1.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.25/1.53
% 1.25/1.53 % Formulas that are not ordinary clauses:
% 1.25/1.53
% 1.25/1.53 ============================== end of process non-clausal formulas ===
% 1.25/1.53
% 1.25/1.53 ============================== PROCESS INITIAL CLAUSES ===============
% 1.25/1.53
% 1.25/1.53 ============================== PREDICATE ELIMINATION =================
% 1.25/1.53
% 1.25/1.53 ============================== end predicate elimination =============
% 1.25/1.53
% 1.25/1.53 Auto_denials:
% 1.25/1.53 % copying label prove_associativity to answer in negative clause
% 1.25/1.53
% 1.25/1.53 Term ordering decisions:
% 1.25/1.53
% 1.25/1.53 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.25/1.53 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 1.25/1.53
% 1.25/1.53 ============================== end of process initial clauses ========
% 1.25/1.53
% 1.25/1.53 ============================== CLAUSES FOR SEARCH ====================
% 1.25/1.53
% 1.25/1.53 ============================== end of clauses for search =============
% 1.25/1.53
% 1.25/1.53 ============================== SEARCH ================================
% 1.25/1.53
% 1.25/1.53 % Starting search at 0.01 seconds.
% 1.25/1.53
% 1.25/1.53 ============================== PROOF =================================
% 1.25/1.53 % SZS status Unsatisfiable
% 1.25/1.53 % SZS output start Refutation
% 1.25/1.53
% 1.25/1.53 % Proof 1 at 0.54 (+ 0.02) seconds: prove_associativity.
% 1.25/1.53 % Length of proof is 42.
% 1.25/1.53 % Level of proof is 16.
% 1.25/1.53 % Maximum clause weight is 23.000.
% 1.25/1.53 % Given clauses 157.
% 1.25/1.53
% 1.25/1.53 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 1.25/1.53 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 1.25/1.53 5 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 1.25/1.53 7 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 1.25/1.53 9 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 1.25/1.53 10 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 1.25/1.53 11 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 1.25/1.53 12 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(11),rewrite([9(2)]),flip(a),rewrite([9(2)])].
% 1.25/1.53 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 1.25/1.53 16 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(15),rewrite([10(2)]),flip(a),rewrite([10(2)])].
% 1.25/1.53 17 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity4) # label(axiom). [assumption].
% 1.25/1.53 18 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(17),flip(a)].
% 1.25/1.53 19 multiply(a,multiply(b,c)) != multiply(multiply(a,b),c) # label(prove_associativity) # label(negated_conjecture) # answer(prove_associativity). [assumption].
% 1.25/1.53 20 multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)) # answer(prove_associativity). [copy(19),rewrite([10(10)]),flip(a)].
% 1.25/1.53 21 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(3(a,1),12(a,1,1)),rewrite([9(2),3(2)]),flip(a)].
% 1.25/1.53 22 multiply(A,add(B,A)) = add(A,multiply(B,additive_identity)). [para(3(a,1),12(a,1,2)),rewrite([10(2)])].
% 1.25/1.53 27 multiply(multiplicative_identity,add(A,B)) = add(A,B). [para(1(a,1),16(a,1,1)),rewrite([10(2),1(2)]),flip(a)].
% 1.25/1.53 28 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(1(a,1),16(a,1,2)),rewrite([9(2)]),flip(a)].
% 1.25/1.53 29 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(7(a,1),16(a,1,1)),rewrite([10(3),21(4)]),flip(a)].
% 1.25/1.53 30 multiply(A,add(B,inverse(A))) = multiply(B,A). [para(7(a,1),16(a,1,2)),rewrite([9(3),21(3)]),flip(a)].
% 1.25/1.53 31 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [para(16(a,1),12(a,1,1)),rewrite([9(4),10(7),10(8)])].
% 1.25/1.53 48 add(additive_identity,add(A,B)) = add(A,B). [para(27(a,1),21(a,1,2)),rewrite([27(6)])].
% 1.25/1.53 50 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(5(a,1),48(a,1,2)),rewrite([5(5)])].
% 1.25/1.53 51 add(A,multiply(A,additive_identity)) = A. [para(50(a,1),16(a,2,2)),rewrite([10(2),1(4),9(3),1(5)])].
% 1.25/1.53 53 add(A,multiply(B,multiply(A,additive_identity))) = multiply(A,add(B,A)). [para(51(a,1),12(a,1,2)),rewrite([10(2)]),flip(a)].
% 1.25/1.53 55 multiply(additive_identity,additive_identity) = additive_identity. [para(51(a,1),21(a,1)),flip(a)].
% 1.25/1.53 64 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(22(a,1),16(a,1,2)),rewrite([9(6)])].
% 1.25/1.53 68 add(multiply(A,B),add(A,multiply(C,additive_identity))) = multiply(A,add(B,add(A,C))). [para(22(a,1),18(a,1,2)),rewrite([9(6)])].
% 1.25/1.53 74 multiply(A,A) = A. [para(55(a,1),12(a,2,2)),rewrite([9(2),3(2),3(2),3(3)])].
% 1.25/1.53 75 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(74(a,1),16(a,1,1)),flip(a)].
% 1.25/1.53 87 add(A,multiply(B,multiply(A,additive_identity))) = add(A,multiply(A,B)). [back_rewrite(53),rewrite([9(5),75(6)])].
% 1.25/1.53 88 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(7(a,1),28(a,2,2)),rewrite([29(4),3(6)])].
% 1.25/1.53 106 add(additive_identity,inverse(A)) = inverse(A). [para(88(a,1),21(a,1,2)),rewrite([88(6)])].
% 1.25/1.53 133 multiply(A,additive_identity) = additive_identity. [para(106(a,1),30(a,1,2)),rewrite([7(2),10(3)]),flip(a)].
% 1.25/1.53 136 add(A,multiply(A,B)) = A. [back_rewrite(87),rewrite([133(2),133(2),3(2)]),flip(a)].
% 1.25/1.53 141 multiply(A,add(B,add(A,C))) = A. [back_rewrite(68),rewrite([133(3),3(3),9(2),136(2)]),flip(a)].
% 1.25/1.53 142 add(A,multiply(B,A)) = A. [back_rewrite(64),rewrite([133(3),3(3),9(2),141(5)])].
% 1.25/1.53 169 multiply(A,multiply(B,add(C,A))) = multiply(B,A). [para(16(a,1),31(a,2)),rewrite([142(4),10(3),136(5),10(4)])].
% 1.25/1.53 179 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = add(multiply(A,multiply(B,D)),multiply(C,multiply(A,B))). [para(136(a,1),31(a,1,1,2))].
% 1.25/1.53 1005 multiply(multiply(A,B),multiply(B,C)) = multiply(C,multiply(A,B)). [para(142(a,1),169(a,1,2,2)),rewrite([10(2)])].
% 1.25/1.53 2365 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [para(16(a,1),179(a,2)),rewrite([142(5),1005(3),136(5),10(4)]),flip(a)].
% 1.25/1.53 2366 $F # answer(prove_associativity). [resolve(2365,a,20,a(flip))].
% 1.25/1.53
% 1.25/1.53 % SZS output end Refutation
% 1.25/1.53 ============================== end of proof ==========================
% 1.25/1.53
% 1.25/1.53 ============================== STATISTICS ============================
% 1.25/1.53
% 1.25/1.53 Given=157. Generated=20228. Kept=2360. proofs=1.
% 1.25/1.53 Usable=133. Sos=1644. Demods=1740. Limbo=5, Disabled=592. Hints=0.
% 1.25/1.53 Megabytes=3.17.
% 1.25/1.53 User_CPU=0.54, System_CPU=0.02, Wall_clock=0.
% 1.25/1.53
% 1.25/1.53 ============================== end of statistics =====================
% 1.25/1.53
% 1.25/1.53 ============================== end of search =========================
% 1.25/1.53
% 1.25/1.53 THEOREM PROVED
% 1.25/1.53 % SZS status Unsatisfiable
% 1.25/1.53
% 1.25/1.53 Exiting with 1 proof.
% 1.25/1.53
% 1.25/1.53 Process 3331 exit (max_proofs) Wed Jun 1 17:45:30 2022
% 1.25/1.53 Prover9 interrupted
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