TSTP Solution File: ALG006-1 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : ALG006-1 : 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 17:53:34 EDT 2022
% Result : Unsatisfiable 0.62s 0.95s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 9 06:25:37 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.62/0.95 ============================== Prover9 ===============================
% 0.62/0.95 Prover9 (32) version 2009-11A, November 2009.
% 0.62/0.95 Process 21203 was started by sandbox2 on n032.cluster.edu,
% 0.62/0.95 Thu Jun 9 06:25:38 2022
% 0.62/0.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21050_n032.cluster.edu".
% 0.62/0.95 ============================== end of head ===========================
% 0.62/0.95
% 0.62/0.95 ============================== INPUT =================================
% 0.62/0.95
% 0.62/0.95 % Reading from file /tmp/Prover9_21050_n032.cluster.edu
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% 0.62/0.95 set(prolog_style_variables).
% 0.62/0.95 set(auto2).
% 0.62/0.95 % set(auto2) -> set(auto).
% 0.62/0.95 % set(auto) -> set(auto_inference).
% 0.62/0.95 % set(auto) -> set(auto_setup).
% 0.62/0.95 % set(auto_setup) -> set(predicate_elim).
% 0.62/0.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.62/0.95 % set(auto) -> set(auto_limits).
% 0.62/0.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.62/0.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.62/0.95 % set(auto) -> set(auto_denials).
% 0.62/0.95 % set(auto) -> set(auto_process).
% 0.62/0.95 % set(auto2) -> assign(new_constants, 1).
% 0.62/0.95 % set(auto2) -> assign(fold_denial_max, 3).
% 0.62/0.95 % set(auto2) -> assign(max_weight, "200.000").
% 0.62/0.95 % set(auto2) -> assign(max_hours, 1).
% 0.62/0.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.62/0.95 % set(auto2) -> assign(max_seconds, 0).
% 0.62/0.95 % set(auto2) -> assign(max_minutes, 5).
% 0.62/0.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.62/0.95 % set(auto2) -> set(sort_initial_sos).
% 0.62/0.95 % set(auto2) -> assign(sos_limit, -1).
% 0.62/0.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.62/0.95 % set(auto2) -> assign(max_megs, 400).
% 0.62/0.95 % set(auto2) -> assign(stats, some).
% 0.62/0.95 % set(auto2) -> clear(echo_input).
% 0.62/0.95 % set(auto2) -> set(quiet).
% 0.62/0.95 % set(auto2) -> clear(print_initial_clauses).
% 0.62/0.95 % set(auto2) -> clear(print_given).
% 0.62/0.95 assign(lrs_ticks,-1).
% 0.62/0.95 assign(sos_limit,10000).
% 0.62/0.95 assign(order,kbo).
% 0.62/0.95 set(lex_order_vars).
% 0.62/0.95 clear(print_given).
% 0.62/0.95
% 0.62/0.95 % formulas(sos). % not echoed (4 formulas)
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% 0.62/0.95 ============================== end of input ==========================
% 0.62/0.95
% 0.62/0.95 % From the command line: assign(max_seconds, 300).
% 0.62/0.95
% 0.62/0.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.62/0.95
% 0.62/0.95 % Formulas that are not ordinary clauses:
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% 0.62/0.95 ============================== end of process non-clausal formulas ===
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% 0.62/0.95 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.62/0.95 ============================== PREDICATE ELIMINATION =================
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% 0.62/0.95 ============================== end predicate elimination =============
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% 0.62/0.95 Auto_denials:
% 0.62/0.95 % copying label prove_set_difference_3_simplified to answer in negative clause
% 0.62/0.95
% 0.62/0.95 Term ordering decisions:
% 0.62/0.95 Function symbol KB weights: a=1. b=1. c=1. difference=1.
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% 0.62/0.95 ============================== end of process initial clauses ========
% 0.62/0.95
% 0.62/0.95 ============================== CLAUSES FOR SEARCH ====================
% 0.62/0.95
% 0.62/0.95 ============================== end of clauses for search =============
% 0.62/0.95
% 0.62/0.95 ============================== SEARCH ================================
% 0.62/0.95
% 0.62/0.95 % Starting search at 0.01 seconds.
% 0.62/0.95
% 0.62/0.95 ============================== PROOF =================================
% 0.62/0.95 % SZS status Unsatisfiable
% 0.62/0.95 % SZS output start Refutation
% 0.62/0.95
% 0.62/0.95 % Proof 1 at 0.02 (+ 0.00) seconds: prove_set_difference_3_simplified.
% 0.62/0.95 % Length of proof is 26.
% 0.62/0.95 % Level of proof is 13.
% 0.62/0.95 % Maximum clause weight is 23.000.
% 0.62/0.95 % Given clauses 21.
% 0.62/0.95
% 0.62/0.95 1 difference(A,difference(B,A)) = A # label(set_difference_1) # label(axiom). [assumption].
% 0.62/0.95 2 difference(A,difference(A,B)) = difference(B,difference(B,A)) # label(set_difference_2) # label(axiom). [assumption].
% 0.62/0.95 3 difference(difference(A,B),C) = difference(difference(A,C),difference(B,C)) # label(set_difference_3) # label(axiom). [assumption].
% 0.62/0.95 4 difference(difference(A,B),difference(C,B)) = difference(difference(A,C),B). [copy(3),flip(a)].
% 0.62/0.95 5 difference(difference(a,c),b) != difference(difference(a,b),c) # label(prove_set_difference_3_simplified) # label(negated_conjecture) # answer(prove_set_difference_3_simplified). [assumption].
% 0.62/0.95 6 difference(difference(A,B),B) = difference(A,B). [para(1(a,1),1(a,1,2))].
% 0.62/0.95 8 difference(difference(A,A),B) = difference(B,B). [para(1(a,1),2(a,1,2)),rewrite([6(4),4(4)]),flip(a)].
% 0.62/0.95 10 difference(difference(A,B),difference(C,A)) = difference(A,difference(B,difference(C,A))). [para(1(a,1),4(a,1,1)),flip(a)].
% 0.62/0.95 19 difference(difference(A,A),difference(B,B)) = difference(B,B). [para(8(a,1),1(a,1)),rewrite([4(5)])].
% 0.62/0.95 21 difference(difference(difference(A,A),B),C) = difference(C,C). [para(8(a,1),4(a,1,1)),rewrite([10(3),1(2)]),flip(a)].
% 0.62/0.95 23 difference(difference(A,B),A) = difference(difference(B,B),A). [para(8(a,1),4(a,1)),rewrite([4(3)]),flip(a)].
% 0.62/0.95 24 difference(difference(difference(A,A),B),C) = difference(difference(B,B),C). [para(8(a,1),4(a,2,1)),rewrite([4(4)])].
% 0.62/0.95 28 difference(A,A) = difference(B,B). [para(19(a,1),2(a,1,2)),rewrite([19(3),19(5),19(4)])].
% 0.62/0.95 31 difference(A,A) = c_0. [new_symbol(28)].
% 0.62/0.95 36 difference(difference(c_0,A),B) = difference(c_0,B). [back_rewrite(24),rewrite([31(1),31(4)])].
% 0.62/0.95 37 difference(difference(A,B),A) = difference(c_0,A). [back_rewrite(23),rewrite([31(3)])].
% 0.62/0.95 39 difference(c_0,A) = c_0. [back_rewrite(21),rewrite([31(1),36(3),31(3)])].
% 0.62/0.95 41 difference(difference(A,B),A) = c_0. [back_rewrite(37),rewrite([39(4)])].
% 0.62/0.95 42 difference(A,c_0) = A. [para(31(a,1),1(a,1,2))].
% 0.62/0.95 45 difference(A,difference(A,difference(A,B))) = difference(A,B). [para(41(a,1),2(a,1,2)),rewrite([42(3)]),flip(a)].
% 0.62/0.95 47 difference(difference(A,difference(B,C)),B) = difference(A,B). [para(41(a,1),4(a,1,2)),rewrite([42(3)]),flip(a)].
% 0.62/0.95 69 difference(difference(A,B),difference(difference(A,B),difference(A,difference(B,difference(C,A))))) = difference(A,difference(B,difference(C,A))). [para(10(a,1),45(a,1,2,2)),rewrite([10(10)])].
% 0.62/0.95 77 difference(difference(A,B),difference(A,difference(B,C))) = c_0. [para(47(a,1),41(a,1,1))].
% 0.62/0.95 82 difference(A,difference(B,difference(C,A))) = difference(A,B). [back_rewrite(69),rewrite([77(6),42(3)]),flip(a)].
% 0.62/0.95 127 difference(difference(A,B),C) = difference(difference(A,C),B). [para(1(a,1),82(a,1,2,2)),rewrite([4(3)])].
% 0.62/0.95 128 $F # answer(prove_set_difference_3_simplified). [resolve(127,a,5,a)].
% 0.62/0.95
% 0.62/0.95 % SZS output end Refutation
% 0.62/0.95 ============================== end of proof ==========================
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% 0.62/0.95 ============================== STATISTICS ============================
% 0.62/0.95
% 0.62/0.95 Given=21. Generated=782. Kept=126. proofs=1.
% 0.62/0.95 Usable=16. Sos=57. Demods=69. Limbo=0, Disabled=56. Hints=0.
% 0.62/0.95 Megabytes=0.11.
% 0.62/0.95 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
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% 0.62/0.95 ============================== end of statistics =====================
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% 0.62/0.95 ============================== end of search =========================
% 0.62/0.95
% 0.62/0.95 THEOREM PROVED
% 0.62/0.95 % SZS status Unsatisfiable
% 0.62/0.95
% 0.62/0.95 Exiting with 1 proof.
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% 0.62/0.95 Process 21203 exit (max_proofs) Thu Jun 9 06:25:38 2022
% 0.62/0.95 Prover9 interrupted
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