TSTP Solution File: BOO022-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 23:48:03 EDT 2022
% Result : Unsatisfiable 1.94s 2.26s
% Output : Refutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jun 1 22:52:30 EDT 2022
% 0.11/0.31 % CPUTime :
% 1.94/2.26 ============================== Prover9 ===============================
% 1.94/2.26 Prover9 (32) version 2009-11A, November 2009.
% 1.94/2.26 Process 7597 was started by sandbox on n032.cluster.edu,
% 1.94/2.26 Wed Jun 1 22:52:30 2022
% 1.94/2.26 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7444_n032.cluster.edu".
% 1.94/2.26 ============================== end of head ===========================
% 1.94/2.26
% 1.94/2.26 ============================== INPUT =================================
% 1.94/2.26
% 1.94/2.26 % Reading from file /tmp/Prover9_7444_n032.cluster.edu
% 1.94/2.26
% 1.94/2.26 set(prolog_style_variables).
% 1.94/2.26 set(auto2).
% 1.94/2.26 % set(auto2) -> set(auto).
% 1.94/2.26 % set(auto) -> set(auto_inference).
% 1.94/2.26 % set(auto) -> set(auto_setup).
% 1.94/2.26 % set(auto_setup) -> set(predicate_elim).
% 1.94/2.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.94/2.26 % set(auto) -> set(auto_limits).
% 1.94/2.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.94/2.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.94/2.26 % set(auto) -> set(auto_denials).
% 1.94/2.26 % set(auto) -> set(auto_process).
% 1.94/2.26 % set(auto2) -> assign(new_constants, 1).
% 1.94/2.26 % set(auto2) -> assign(fold_denial_max, 3).
% 1.94/2.26 % set(auto2) -> assign(max_weight, "200.000").
% 1.94/2.26 % set(auto2) -> assign(max_hours, 1).
% 1.94/2.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.94/2.26 % set(auto2) -> assign(max_seconds, 0).
% 1.94/2.26 % set(auto2) -> assign(max_minutes, 5).
% 1.94/2.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.94/2.26 % set(auto2) -> set(sort_initial_sos).
% 1.94/2.26 % set(auto2) -> assign(sos_limit, -1).
% 1.94/2.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.94/2.26 % set(auto2) -> assign(max_megs, 400).
% 1.94/2.26 % set(auto2) -> assign(stats, some).
% 1.94/2.26 % set(auto2) -> clear(echo_input).
% 1.94/2.26 % set(auto2) -> set(quiet).
% 1.94/2.26 % set(auto2) -> clear(print_initial_clauses).
% 1.94/2.26 % set(auto2) -> clear(print_given).
% 1.94/2.26 assign(lrs_ticks,-1).
% 1.94/2.26 assign(sos_limit,10000).
% 1.94/2.26 assign(order,kbo).
% 1.94/2.26 set(lex_order_vars).
% 1.94/2.26 clear(print_given).
% 1.94/2.26
% 1.94/2.26 % formulas(sos). % not echoed (7 formulas)
% 1.94/2.26
% 1.94/2.26 ============================== end of input ==========================
% 1.94/2.26
% 1.94/2.26 % From the command line: assign(max_seconds, 300).
% 1.94/2.26
% 1.94/2.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.94/2.26
% 1.94/2.26 % Formulas that are not ordinary clauses:
% 1.94/2.26
% 1.94/2.26 ============================== end of process non-clausal formulas ===
% 1.94/2.26
% 1.94/2.26 ============================== PROCESS INITIAL CLAUSES ===============
% 1.94/2.26
% 1.94/2.26 ============================== PREDICATE ELIMINATION =================
% 1.94/2.26
% 1.94/2.26 ============================== end predicate elimination =============
% 1.94/2.26
% 1.94/2.26 Auto_denials:
% 1.94/2.26 % copying label prove_associativity_of_multiply to answer in negative clause
% 1.94/2.26
% 1.94/2.26 Term ordering decisions:
% 1.94/2.26
% 1.94/2.26 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.94/2.26 Function symbol KB weights: n0=1. n1=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 1.94/2.26
% 1.94/2.26 ============================== end of process initial clauses ========
% 1.94/2.26
% 1.94/2.26 ============================== CLAUSES FOR SEARCH ====================
% 1.94/2.26
% 1.94/2.26 ============================== end of clauses for search =============
% 1.94/2.26
% 1.94/2.26 ============================== SEARCH ================================
% 1.94/2.26
% 1.94/2.26 % Starting search at 0.01 seconds.
% 1.94/2.26
% 1.94/2.26 ============================== PROOF =================================
% 1.94/2.26 % SZS status Unsatisfiable
% 1.94/2.26 % SZS output start Refutation
% 1.94/2.26
% 1.94/2.26 % Proof 1 at 1.40 (+ 0.04) seconds: prove_associativity_of_multiply.
% 1.94/2.26 % Length of proof is 32.
% 1.94/2.26 % Level of proof is 9.
% 1.94/2.26 % Maximum clause weight is 23.000.
% 1.94/2.26 % Given clauses 279.
% 1.94/2.26
% 1.94/2.26 3 multiply(add(A,B),B) = B # label(multiply_add) # label(axiom). [assumption].
% 1.94/2.26 4 add(multiply(A,B),B) = B # label(add_multiply) # label(axiom). [assumption].
% 1.94/2.26 5 multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)) # label(multiply_add_property) # label(axiom). [assumption].
% 1.94/2.26 6 add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)). [copy(5),flip(a)].
% 1.94/2.26 7 add(A,multiply(B,C)) = multiply(add(B,A),add(C,A)) # label(add_multiply_property) # label(axiom). [assumption].
% 1.94/2.26 8 multiply(add(A,B),add(C,B)) = add(B,multiply(A,C)). [copy(7),flip(a)].
% 1.94/2.26 9 multiply(multiply(a,b),c) != multiply(a,multiply(b,c)) # label(prove_associativity_of_multiply) # label(negated_conjecture) # answer(prove_associativity_of_multiply). [assumption].
% 1.94/2.26 12 multiply(A,A) = A. [para(4(a,1),3(a,1,1))].
% 1.94/2.26 13 add(A,A) = A. [para(3(a,1),4(a,1,1))].
% 1.94/2.26 16 multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A). [para(6(a,1),3(a,1,1))].
% 1.94/2.26 28 multiply(multiply(A,add(B,C)),add(D,multiply(C,A))) = add(multiply(C,A),multiply(multiply(B,A),D)). [para(6(a,1),8(a,1,1))].
% 1.94/2.26 35 multiply(A,add(A,B)) = add(A,multiply(B,A)). [para(12(a,1),6(a,1,1)),flip(a)].
% 1.94/2.26 36 multiply(A,add(B,A)) = A. [para(12(a,1),6(a,1,2)),rewrite([4(2)]),flip(a)].
% 1.94/2.26 38 add(A,B) = add(B,A). [para(12(a,1),8(a,1)),rewrite([12(2)])].
% 1.94/2.26 41 add(A,multiply(B,A)) = A. [back_rewrite(36),rewrite([38(1),35(2)])].
% 1.94/2.26 49 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [back_rewrite(8),rewrite([38(2)])].
% 1.94/2.26 53 multiply(A,B) = multiply(B,A). [para(13(a,1),6(a,1)),rewrite([13(2)])].
% 1.94/2.26 58 add(A,multiply(A,B)) = A. [back_rewrite(41),rewrite([53(1)])].
% 1.94/2.26 60 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [back_rewrite(28),rewrite([53(3),53(6),53(7),53(8)])].
% 1.94/2.26 62 multiply(multiply(A,B),multiply(A,add(C,B))) = multiply(A,B). [back_rewrite(16),rewrite([53(3),53(4),53(5)])].
% 1.94/2.26 63 multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)) # answer(prove_associativity_of_multiply). [back_rewrite(9),rewrite([53(5)])].
% 1.94/2.26 64 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [back_rewrite(6),rewrite([53(2)])].
% 1.94/2.26 65 multiply(A,add(B,A)) = A. [back_rewrite(3),rewrite([53(2)])].
% 1.94/2.26 139 add(A,multiply(B,A)) = A. [para(13(a,1),49(a,1,2)),rewrite([53(2),65(2)]),flip(a)].
% 1.94/2.26 308 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = add(multiply(A,multiply(B,D)),multiply(C,multiply(A,B))). [para(58(a,1),60(a,1,1,2))].
% 1.94/2.26 315 multiply(A,multiply(B,add(C,A))) = multiply(B,A). [para(139(a,1),60(a,1,2)),rewrite([53(3),64(7),58(5),53(4)])].
% 1.94/2.26 392 multiply(multiply(A,B),multiply(A,multiply(C,B))) = multiply(A,multiply(C,B)). [para(139(a,1),62(a,1,2,2)),rewrite([53(4)])].
% 1.94/2.26 1536 multiply(multiply(A,B),multiply(A,C)) = multiply(C,multiply(A,B)). [para(58(a,1),315(a,1,2,2)),rewrite([53(2)])].
% 1.94/2.26 1537 multiply(multiply(A,B),multiply(B,C)) = multiply(C,multiply(A,B)). [para(139(a,1),315(a,1,2,2)),rewrite([53(2)])].
% 1.94/2.27 1575 multiply(multiply(A,B),multiply(C,A)) = multiply(C,multiply(A,B)). [back_rewrite(392),rewrite([53(2),1536(4),53(4)])].
% 1.94/2.27 5432 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [para(139(a,1),308(a,1,2)),rewrite([1537(3),1575(7),13(7)]),flip(a)].
% 1.94/2.27 5433 $F # answer(prove_associativity_of_multiply). [resolve(5432,a,63,a(flip))].
% 1.94/2.27
% 1.94/2.27 % SZS output end Refutation
% 1.94/2.27 ============================== end of proof ==========================
% 1.94/2.27
% 1.94/2.27 ============================== STATISTICS ============================
% 1.94/2.27
% 1.94/2.27 Given=279. Generated=59069. Kept=5430. proofs=1.
% 1.94/2.27 Usable=222. Sos=3887. Demods=4062. Limbo=3, Disabled=1324. Hints=0.
% 1.94/2.27 Megabytes=6.66.
% 1.94/2.27 User_CPU=1.40, System_CPU=0.04, Wall_clock=2.
% 1.94/2.27
% 1.94/2.27 ============================== end of statistics =====================
% 1.94/2.27
% 1.94/2.27 ============================== end of search =========================
% 1.94/2.27
% 1.94/2.27 THEOREM PROVED
% 1.94/2.27 % SZS status Unsatisfiable
% 1.94/2.27
% 1.94/2.27 Exiting with 1 proof.
% 1.94/2.27
% 1.94/2.27 Process 7597 exit (max_proofs) Wed Jun 1 22:52:32 2022
% 1.94/2.27 Prover9 interrupted
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