TSTP Solution File: BOO008-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO008-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 1.94s 2.29s
% Output : Refutation 1.94s
% 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 : BOO008-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.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 17:13:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.94/2.29 ============================== Prover9 ===============================
% 1.94/2.29 Prover9 (32) version 2009-11A, November 2009.
% 1.94/2.29 Process 30520 was started by sandbox2 on n025.cluster.edu,
% 1.94/2.29 Wed Jun 1 17:13:59 2022
% 1.94/2.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30366_n025.cluster.edu".
% 1.94/2.29 ============================== end of head ===========================
% 1.94/2.29
% 1.94/2.29 ============================== INPUT =================================
% 1.94/2.29
% 1.94/2.29 % Reading from file /tmp/Prover9_30366_n025.cluster.edu
% 1.94/2.29
% 1.94/2.29 set(prolog_style_variables).
% 1.94/2.29 set(auto2).
% 1.94/2.29 % set(auto2) -> set(auto).
% 1.94/2.29 % set(auto) -> set(auto_inference).
% 1.94/2.29 % set(auto) -> set(auto_setup).
% 1.94/2.29 % set(auto_setup) -> set(predicate_elim).
% 1.94/2.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.94/2.29 % set(auto) -> set(auto_limits).
% 1.94/2.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.94/2.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.94/2.29 % set(auto) -> set(auto_denials).
% 1.94/2.29 % set(auto) -> set(auto_process).
% 1.94/2.29 % set(auto2) -> assign(new_constants, 1).
% 1.94/2.29 % set(auto2) -> assign(fold_denial_max, 3).
% 1.94/2.29 % set(auto2) -> assign(max_weight, "200.000").
% 1.94/2.29 % set(auto2) -> assign(max_hours, 1).
% 1.94/2.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.94/2.29 % set(auto2) -> assign(max_seconds, 0).
% 1.94/2.29 % set(auto2) -> assign(max_minutes, 5).
% 1.94/2.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.94/2.29 % set(auto2) -> set(sort_initial_sos).
% 1.94/2.29 % set(auto2) -> assign(sos_limit, -1).
% 1.94/2.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.94/2.29 % set(auto2) -> assign(max_megs, 400).
% 1.94/2.29 % set(auto2) -> assign(stats, some).
% 1.94/2.29 % set(auto2) -> clear(echo_input).
% 1.94/2.29 % set(auto2) -> set(quiet).
% 1.94/2.29 % set(auto2) -> clear(print_initial_clauses).
% 1.94/2.29 % set(auto2) -> clear(print_given).
% 1.94/2.29 assign(lrs_ticks,-1).
% 1.94/2.29 assign(sos_limit,10000).
% 1.94/2.29 assign(order,kbo).
% 1.94/2.29 set(lex_order_vars).
% 1.94/2.29 clear(print_given).
% 1.94/2.29
% 1.94/2.29 % formulas(sos). % not echoed (15 formulas)
% 1.94/2.29
% 1.94/2.29 ============================== end of input ==========================
% 1.94/2.29
% 1.94/2.29 % From the command line: assign(max_seconds, 300).
% 1.94/2.29
% 1.94/2.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.94/2.29
% 1.94/2.29 % Formulas that are not ordinary clauses:
% 1.94/2.29
% 1.94/2.29 ============================== end of process non-clausal formulas ===
% 1.94/2.29
% 1.94/2.29 ============================== PROCESS INITIAL CLAUSES ===============
% 1.94/2.29
% 1.94/2.29 ============================== PREDICATE ELIMINATION =================
% 1.94/2.29
% 1.94/2.29 ============================== end predicate elimination =============
% 1.94/2.29
% 1.94/2.29 Auto_denials:
% 1.94/2.29 % copying label prove_associativity to answer in negative clause
% 1.94/2.29
% 1.94/2.29 Term ordering decisions:
% 1.94/2.29
% 1.94/2.29 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.94/2.29 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 1.94/2.29
% 1.94/2.29 ============================== end of process initial clauses ========
% 1.94/2.29
% 1.94/2.29 ============================== CLAUSES FOR SEARCH ====================
% 1.94/2.29
% 1.94/2.29 ============================== end of clauses for search =============
% 1.94/2.29
% 1.94/2.29 ============================== SEARCH ================================
% 1.94/2.29
% 1.94/2.29 % Starting search at 0.01 seconds.
% 1.94/2.29
% 1.94/2.29 ============================== PROOF =================================
% 1.94/2.29 % SZS status Unsatisfiable
% 1.94/2.29 % SZS output start Refutation
% 1.94/2.29
% 1.94/2.29 % Proof 1 at 1.26 (+ 0.03) seconds: prove_associativity.
% 1.94/2.29 % Length of proof is 37.
% 1.94/2.29 % Level of proof is 15.
% 1.94/2.29 % Maximum clause weight is 21.000.
% 1.94/2.29 % Given clauses 248.
% 1.94/2.29
% 1.94/2.29 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 1.94/2.29 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 1.94/2.29 5 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 1.94/2.29 7 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 1.94/2.29 9 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 1.94/2.29 10 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 1.94/2.29 11 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 1.94/2.29 12 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(11),rewrite([9(2)]),flip(a),rewrite([9(2)])].
% 1.94/2.29 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 1.94/2.29 16 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(15),rewrite([10(2)]),flip(a),rewrite([10(2)])].
% 1.94/2.29 19 add(a,add(b,c)) != add(add(a,b),c) # label(prove_associativity) # label(negated_conjecture) # answer(prove_associativity). [assumption].
% 1.94/2.29 20 add(c,add(a,b)) != add(a,add(b,c)) # answer(prove_associativity). [copy(19),rewrite([9(10)]),flip(a)].
% 1.94/2.29 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)].
% 1.94/2.29 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)].
% 1.94/2.29 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)].
% 1.94/2.29 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)].
% 1.94/2.29 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)].
% 1.94/2.29 34 add(add(A,multiply(B,C)),multiply(D,add(A,C))) = multiply(add(A,C),add(D,add(A,B))). [para(12(a,1),16(a,1,1)),rewrite([10(4),9(7),9(8)])].
% 1.94/2.29 48 add(additive_identity,add(A,B)) = add(A,B). [para(27(a,1),21(a,1,2)),rewrite([27(6)])].
% 1.94/2.29 50 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(5(a,1),48(a,1,2)),rewrite([5(5)])].
% 1.94/2.29 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)])].
% 1.94/2.29 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)].
% 1.94/2.29 55 multiply(additive_identity,additive_identity) = additive_identity. [para(51(a,1),21(a,1)),flip(a)].
% 1.94/2.29 74 multiply(A,A) = A. [para(55(a,1),12(a,2,2)),rewrite([9(2),3(2),3(2),3(3)])].
% 1.94/2.29 75 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(74(a,1),16(a,1,1)),flip(a)].
% 1.94/2.29 87 add(A,multiply(B,multiply(A,additive_identity))) = add(A,multiply(A,B)). [back_rewrite(53),rewrite([9(5),75(6)])].
% 1.94/2.29 88 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(7(a,1),28(a,2,2)),rewrite([29(4),3(6)])].
% 1.94/2.29 106 add(additive_identity,inverse(A)) = inverse(A). [para(88(a,1),21(a,1,2)),rewrite([88(6)])].
% 1.94/2.29 133 multiply(A,additive_identity) = additive_identity. [para(106(a,1),30(a,1,2)),rewrite([7(2),10(3)]),flip(a)].
% 1.94/2.29 136 add(A,multiply(A,B)) = A. [back_rewrite(87),rewrite([133(2),133(2),3(2)]),flip(a)].
% 1.94/2.29 145 multiply(A,add(A,B)) = A. [back_rewrite(75),rewrite([136(4)])].
% 1.94/2.29 151 multiply(A,add(B,A)) = A. [para(133(a,1),12(a,2,2)),rewrite([3(3),10(2),3(4)])].
% 1.94/2.29 227 add(A,add(B,multiply(C,A))) = add(B,A). [para(12(a,1),34(a,2)),rewrite([151(4),9(3),145(5),9(4)])].
% 1.94/2.29 1147 add(add(A,B),add(A,C)) = add(C,add(A,B)). [para(145(a,1),227(a,1,2,2)),rewrite([9(2)])].
% 1.94/2.29 1148 add(add(A,B),add(B,C)) = add(C,add(A,B)). [para(151(a,1),227(a,1,2,2)),rewrite([9(2)])].
% 1.94/2.29 5718 add(A,add(B,C)) = add(C,add(A,B)). [para(1147(a,1),9(a,1)),rewrite([9(3),1148(5)])].
% 1.94/2.29 5719 $F # answer(prove_associativity). [resolve(5718,a,20,a(flip))].
% 1.94/2.29
% 1.94/2.29 % SZS output end Refutation
% 1.94/2.29 ============================== end of proof ==========================
% 1.94/2.29
% 1.94/2.29 ============================== STATISTICS ============================
% 1.94/2.29
% 1.94/2.29 Given=248. Generated=43158. Kept=5713. proofs=1.
% 1.94/2.29 Usable=146. Sos=1950. Demods=1987. Limbo=0, Disabled=3631. Hints=0.
% 1.94/2.29 Megabytes=6.00.
% 1.94/2.29 User_CPU=1.26, System_CPU=0.03, Wall_clock=2.
% 1.94/2.29
% 1.94/2.29 ============================== end of statistics =====================
% 1.94/2.29
% 1.94/2.29 ============================== end of search =========================
% 1.94/2.29
% 1.94/2.29 THEOREM PROVED
% 1.94/2.29 % SZS status Unsatisfiable
% 1.94/2.29
% 1.94/2.29 Exiting with 1 proof.
% 1.94/2.29
% 1.94/2.29 Process 30520 exit (max_proofs) Wed Jun 1 17:14:01 2022
% 1.94/2.29 Prover9 interrupted
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