TSTP Solution File: ALG003-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG003-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 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 17:53:33 EDT 2022
% Result : Unsatisfiable 1.44s 1.72s
% Output : Refutation 1.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG003-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.12/0.12 % 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 : Wed Jun 8 01:42:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.44/1.72 ============================== Prover9 ===============================
% 1.44/1.72 Prover9 (32) version 2009-11A, November 2009.
% 1.44/1.72 Process 4079 was started by sandbox2 on n027.cluster.edu,
% 1.44/1.72 Wed Jun 8 01:42:11 2022
% 1.44/1.72 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3925_n027.cluster.edu".
% 1.44/1.72 ============================== end of head ===========================
% 1.44/1.72
% 1.44/1.72 ============================== INPUT =================================
% 1.44/1.72
% 1.44/1.72 % Reading from file /tmp/Prover9_3925_n027.cluster.edu
% 1.44/1.72
% 1.44/1.72 set(prolog_style_variables).
% 1.44/1.72 set(auto2).
% 1.44/1.72 % set(auto2) -> set(auto).
% 1.44/1.72 % set(auto) -> set(auto_inference).
% 1.44/1.72 % set(auto) -> set(auto_setup).
% 1.44/1.72 % set(auto_setup) -> set(predicate_elim).
% 1.44/1.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.44/1.72 % set(auto) -> set(auto_limits).
% 1.44/1.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.44/1.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.44/1.72 % set(auto) -> set(auto_denials).
% 1.44/1.72 % set(auto) -> set(auto_process).
% 1.44/1.72 % set(auto2) -> assign(new_constants, 1).
% 1.44/1.72 % set(auto2) -> assign(fold_denial_max, 3).
% 1.44/1.72 % set(auto2) -> assign(max_weight, "200.000").
% 1.44/1.72 % set(auto2) -> assign(max_hours, 1).
% 1.44/1.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.44/1.72 % set(auto2) -> assign(max_seconds, 0).
% 1.44/1.72 % set(auto2) -> assign(max_minutes, 5).
% 1.44/1.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.44/1.72 % set(auto2) -> set(sort_initial_sos).
% 1.44/1.72 % set(auto2) -> assign(sos_limit, -1).
% 1.44/1.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.44/1.72 % set(auto2) -> assign(max_megs, 400).
% 1.44/1.72 % set(auto2) -> assign(stats, some).
% 1.44/1.72 % set(auto2) -> clear(echo_input).
% 1.44/1.72 % set(auto2) -> set(quiet).
% 1.44/1.72 % set(auto2) -> clear(print_initial_clauses).
% 1.44/1.72 % set(auto2) -> clear(print_given).
% 1.44/1.72 assign(lrs_ticks,-1).
% 1.44/1.72 assign(sos_limit,10000).
% 1.44/1.72 assign(order,kbo).
% 1.44/1.72 set(lex_order_vars).
% 1.44/1.72 clear(print_given).
% 1.44/1.72
% 1.44/1.72 % formulas(sos). % not echoed (5 formulas)
% 1.44/1.72
% 1.44/1.72 ============================== end of input ==========================
% 1.44/1.72
% 1.44/1.72 % From the command line: assign(max_seconds, 300).
% 1.44/1.72
% 1.44/1.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.44/1.72
% 1.44/1.72 % Formulas that are not ordinary clauses:
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% 1.44/1.72 ============================== end of process non-clausal formulas ===
% 1.44/1.72
% 1.44/1.72 ============================== PROCESS INITIAL CLAUSES ===============
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% 1.44/1.72 ============================== PREDICATE ELIMINATION =================
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% 1.44/1.72 ============================== end predicate elimination =============
% 1.44/1.72
% 1.44/1.72 Auto_denials:
% 1.44/1.72 % copying label prove_this to answer in negative clause
% 1.44/1.72
% 1.44/1.72 Term ordering decisions:
% 1.44/1.72 Function symbol KB weights: an_element=1. a=1. b=1. c=1. d=1. e=1. f=1. multiply=1.
% 1.44/1.72
% 1.44/1.72 ============================== end of process initial clauses ========
% 1.44/1.72
% 1.44/1.72 ============================== CLAUSES FOR SEARCH ====================
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% 1.44/1.72 ============================== end of clauses for search =============
% 1.44/1.72
% 1.44/1.72 ============================== SEARCH ================================
% 1.44/1.72
% 1.44/1.72 % Starting search at 0.01 seconds.
% 1.44/1.72
% 1.44/1.72 ============================== PROOF =================================
% 1.44/1.72 % SZS status Unsatisfiable
% 1.44/1.72 % SZS output start Refutation
% 1.44/1.72
% 1.44/1.72 % Proof 1 at 0.74 (+ 0.01) seconds: prove_this.
% 1.44/1.72 % Length of proof is 13.
% 1.44/1.72 % Level of proof is 4.
% 1.44/1.72 % Maximum clause weight is 43.000.
% 1.44/1.72 % Given clauses 60.
% 1.44/1.72
% 1.44/1.72 1 multiply(an_element,an_element) = an_element # label(idempotent_element) # label(hypothesis). [assumption].
% 1.44/1.72 2 multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)) # label(medial_law) # label(axiom). [assumption].
% 1.44/1.72 3 multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)) # label(prove_this) # label(negated_conjecture) # answer(prove_this). [assumption].
% 1.44/1.72 5 multiply(A,B) != C | multiply(A,D) != C | B = D # label(right_cancellation) # label(axiom). [assumption].
% 1.44/1.72 6 multiply(multiply(an_element,A),multiply(an_element,B)) = multiply(an_element,multiply(A,B)). [para(1(a,1),2(a,1,1)),flip(a)].
% 1.44/1.72 8 multiply(multiply(multiply(A,B),multiply(C,D)),multiply(E,F)) = multiply(multiply(multiply(A,C),E),multiply(multiply(B,D),F)). [para(2(a,1),2(a,1,1))].
% 1.44/1.72 9 multiply(multiply(A,multiply(B,C)),multiply(D,multiply(E,F))) = multiply(multiply(A,D),multiply(multiply(B,E),multiply(C,F))). [para(2(a,1),2(a,1,2)),flip(a)].
% 1.44/1.72 11 multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),f)) != multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) # answer(prove_this). [para(2(a,1),3(a,2)),flip(a)].
% 1.44/1.72 23 multiply(multiply(multiply(an_element,A),B),multiply(multiply(an_element,C),D)) = multiply(multiply(an_element,multiply(A,C)),multiply(B,D)). [para(6(a,1),2(a,1,1)),flip(a)].
% 1.44/1.72 39 multiply(multiply(A,multiply(a,multiply(d,e))),multiply(B,multiply(multiply(b,c),f))) != multiply(multiply(A,B),multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f))) # answer(prove_this). [ur(5,a,2,a,c,11,a),flip(a)].
% 1.44/1.72 1228 multiply(multiply(A,multiply(multiply(B,C),multiply(D,E))),multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f))) != multiply(multiply(A,multiply(a,multiply(d,e))),multiply(multiply(multiply(B,D),multiply(b,c)),multiply(multiply(C,E),f))) # answer(prove_this). [para(8(a,1),39(a,1,2)),flip(a)].
% 1.44/1.72 1823 multiply(multiply(an_element,multiply(multiply(A,B),C)),multiply(multiply(D,multiply(E,F)),V6)) = multiply(multiply(an_element,multiply(D,C)),multiply(multiply(multiply(A,E),multiply(B,F)),V6)). [para(9(a,1),23(a,1,1)),rewrite([23(10)]),flip(a)].
% 1.44/1.72 1824 $F # answer(prove_this). [resolve(1823,a,1228,a)].
% 1.44/1.72
% 1.44/1.72 % SZS output end Refutation
% 1.44/1.72 ============================== end of proof ==========================
% 1.44/1.72
% 1.44/1.72 ============================== STATISTICS ============================
% 1.44/1.72
% 1.44/1.72 Given=60. Generated=8316. Kept=1823. proofs=1.
% 1.44/1.72 Usable=58. Sos=1592. Demods=80. Limbo=27, Disabled=150. Hints=0.
% 1.44/1.72 Megabytes=2.98.
% 1.44/1.72 User_CPU=0.74, System_CPU=0.01, Wall_clock=1.
% 1.44/1.72
% 1.44/1.72 ============================== end of statistics =====================
% 1.44/1.72
% 1.44/1.72 ============================== end of search =========================
% 1.44/1.72
% 1.44/1.72 THEOREM PROVED
% 1.44/1.72 % SZS status Unsatisfiable
% 1.44/1.72
% 1.44/1.72 Exiting with 1 proof.
% 1.44/1.72
% 1.44/1.72 Process 4079 exit (max_proofs) Wed Jun 8 01:42:12 2022
% 1.44/1.72 Prover9 interrupted
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