TSTP Solution File: ALG007-1 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 17:53:35 EDT 2022
% Result : Unsatisfiable 0.96s 1.24s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.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 12:49:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.96/1.24 ============================== Prover9 ===============================
% 0.96/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.24 Process 17091 was started by sandbox2 on n021.cluster.edu,
% 0.96/1.24 Wed Jun 8 12:49:23 2022
% 0.96/1.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16937_n021.cluster.edu".
% 0.96/1.24 ============================== end of head ===========================
% 0.96/1.24
% 0.96/1.24 ============================== INPUT =================================
% 0.96/1.24
% 0.96/1.24 % Reading from file /tmp/Prover9_16937_n021.cluster.edu
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% 0.96/1.24 set(prolog_style_variables).
% 0.96/1.24 set(auto2).
% 0.96/1.24 % set(auto2) -> set(auto).
% 0.96/1.24 % set(auto) -> set(auto_inference).
% 0.96/1.24 % set(auto) -> set(auto_setup).
% 0.96/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.24 % set(auto) -> set(auto_limits).
% 0.96/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.24 % set(auto) -> set(auto_denials).
% 0.96/1.24 % set(auto) -> set(auto_process).
% 0.96/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.24 % set(auto2) -> assign(stats, some).
% 0.96/1.24 % set(auto2) -> clear(echo_input).
% 0.96/1.24 % set(auto2) -> set(quiet).
% 0.96/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.24 % set(auto2) -> clear(print_given).
% 0.96/1.24 assign(lrs_ticks,-1).
% 0.96/1.24 assign(sos_limit,10000).
% 0.96/1.24 assign(order,kbo).
% 0.96/1.24 set(lex_order_vars).
% 0.96/1.24 clear(print_given).
% 0.96/1.24
% 0.96/1.24 % formulas(sos). % not echoed (4 formulas)
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% 0.96/1.24 ============================== end of input ==========================
% 0.96/1.24
% 0.96/1.24 % From the command line: assign(max_seconds, 300).
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% 0.96/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.24
% 0.96/1.24 % Formulas that are not ordinary clauses:
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% 0.96/1.24 ============================== end of process non-clausal formulas ===
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% 0.96/1.24 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.96/1.24 ============================== PREDICATE ELIMINATION =================
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% 0.96/1.24 ============================== end predicate elimination =============
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% 0.96/1.24 Auto_denials:
% 0.96/1.24 % copying label prove_set_difference_3 to answer in negative clause
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% 0.96/1.24 Term ordering decisions:
% 0.96/1.24 Function symbol KB weights: a=1. b=1. c=1. difference=1.
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% 0.96/1.24 ============================== end of process initial clauses ========
% 0.96/1.24
% 0.96/1.24 ============================== CLAUSES FOR SEARCH ====================
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% 0.96/1.24 ============================== end of clauses for search =============
% 0.96/1.24
% 0.96/1.24 ============================== SEARCH ================================
% 0.96/1.24
% 0.96/1.24 % Starting search at 0.01 seconds.
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% 0.96/1.24 ============================== PROOF =================================
% 0.96/1.24 % SZS status Unsatisfiable
% 0.96/1.24 % SZS output start Refutation
% 0.96/1.24
% 0.96/1.24 % Proof 1 at 0.28 (+ 0.01) seconds: prove_set_difference_3.
% 0.96/1.24 % Length of proof is 25.
% 0.96/1.24 % Level of proof is 11.
% 0.96/1.24 % Maximum clause weight is 17.000.
% 0.96/1.24 % Given clauses 54.
% 0.96/1.24
% 0.96/1.24 1 difference(A,difference(B,A)) = A # label(set_difference_1) # label(axiom). [assumption].
% 0.96/1.24 2 difference(A,difference(A,B)) = difference(B,difference(B,A)) # label(set_difference_2) # label(axiom). [assumption].
% 0.96/1.24 3 difference(difference(A,B),C) = difference(difference(A,C),B) # label(set_difference_3_simplified) # label(axiom). [assumption].
% 0.96/1.24 4 difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)) # label(prove_set_difference_3) # label(negated_conjecture) # answer(prove_set_difference_3). [assumption].
% 0.96/1.24 5 difference(difference(a,c),difference(b,c)) != difference(difference(a,b),c) # answer(prove_set_difference_3). [copy(4),flip(a)].
% 0.96/1.24 6 difference(difference(A,B),B) = difference(A,B). [para(1(a,1),1(a,1,2))].
% 0.96/1.24 8 difference(difference(A,B),difference(A,B)) = difference(B,B). [para(1(a,1),2(a,1,2)),rewrite([6(4)]),flip(a)].
% 0.96/1.24 10 difference(A,difference(difference(B,A),C)) = A. [para(3(a,1),1(a,1,2))].
% 0.96/1.24 11 difference(difference(A,B),difference(C,A)) = difference(A,B). [para(1(a,1),3(a,1,1)),flip(a)].
% 0.96/1.24 12 difference(difference(A,B),difference(difference(A,C),B)) = difference(C,difference(C,difference(A,B))). [para(3(a,1),2(a,1,2))].
% 0.96/1.24 13 difference(difference(A,difference(A,B)),C) = difference(difference(B,C),difference(B,A)). [para(2(a,1),3(a,1,1))].
% 0.96/1.24 15 difference(difference(difference(A,B),C),B) = difference(difference(A,B),C). [para(6(a,1),3(a,1,1)),flip(a)].
% 0.96/1.24 17 difference(A,A) = difference(B,B). [para(10(a,1),2(a,1,2)),rewrite([15(6),8(6)])].
% 0.96/1.24 23 difference(A,A) = c_0. [new_symbol(17)].
% 0.96/1.24 24 difference(A,c_0) = A. [para(23(a,1),1(a,1,2))].
% 0.96/1.24 25 difference(difference(A,B),A) = difference(c_0,B). [para(23(a,1),3(a,1,1)),flip(a)].
% 0.96/1.24 26 difference(c_0,A) = c_0. [para(23(a,1),6(a,1,1)),rewrite([23(3)])].
% 0.96/1.24 27 difference(difference(A,B),A) = c_0. [back_rewrite(25),rewrite([26(4)])].
% 0.96/1.24 44 difference(difference(difference(A,B),C),A) = c_0. [para(27(a,1),3(a,1,1)),rewrite([26(2)]),flip(a)].
% 0.96/1.24 48 difference(difference(A,B),difference(A,difference(B,C))) = c_0. [para(2(a,1),44(a,1,1)),rewrite([3(4)])].
% 0.96/1.24 132 difference(difference(difference(A,difference(A,B)),C),difference(B,C)) = c_0. [para(13(a,2),27(a,1,1))].
% 0.96/1.24 613 difference(difference(A,difference(A,B)),difference(B,difference(C,A))) = c_0. [para(11(a,1),132(a,1,1))].
% 0.96/1.24 1199 difference(A,difference(B,difference(C,A))) = difference(A,B). [para(613(a,1),12(a,1,2)),rewrite([24(5),48(9),24(6)])].
% 0.96/1.24 1236 difference(difference(A,B),difference(C,B)) = difference(difference(A,B),C). [para(1(a,1),1199(a,1,2,2))].
% 0.96/1.24 1372 $F # answer(prove_set_difference_3). [back_rewrite(5),rewrite([1236(7),3(5)]),xx(a)].
% 0.96/1.24
% 0.96/1.24 % SZS output end Refutation
% 0.96/1.24 ============================== end of proof ==========================
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% 0.96/1.24 ============================== STATISTICS ============================
% 0.96/1.24
% 0.96/1.24 Given=54. Generated=10383. Kept=1370. proofs=1.
% 0.96/1.24 Usable=44. Sos=805. Demods=860. Limbo=136, Disabled=389. Hints=0.
% 0.96/1.24 Megabytes=1.26.
% 0.96/1.24 User_CPU=0.29, System_CPU=0.01, Wall_clock=0.
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% 0.96/1.24 ============================== end of statistics =====================
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% 0.96/1.24 ============================== end of search =========================
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% 0.96/1.24 THEOREM PROVED
% 0.96/1.24 % SZS status Unsatisfiable
% 0.96/1.24
% 0.96/1.24 Exiting with 1 proof.
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% 0.96/1.24 Process 17091 exit (max_proofs) Wed Jun 8 12:49:23 2022
% 0.96/1.24 Prover9 interrupted
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