TSTP Solution File: SET621+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 : Tue Jul 19 04:30:52 EDT 2022
% Result : Theorem 2.64s 2.97s
% Output : Refutation 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n022.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 : Sat Jul 9 18:53:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 1683 was started by sandbox2 on n022.cluster.edu,
% 0.43/1.00 Sat Jul 9 18:53:26 2022
% 0.43/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1526_n022.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_1526_n022.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all B all C all D difference(difference(B,C),D) = difference(B,union(C,D))) # label(difference_difference_union) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all B all C all D difference(union(B,C),D) = union(difference(B,D),difference(C,D))) # label(difference_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all B all C all D (member(D,union(B,C)) <-> member(D,B) | member(D,C))) # label(union_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 5 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 (all B all C symmetric_difference(B,C) = symmetric_difference(C,B)) # label(commutativity_of_symmetric_difference) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 -(all B all C all D difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D)))) # label(prove_th97) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 2.64/2.97
% 2.64/2.97 ============================== PREDICATE ELIMINATION =================
% 2.64/2.97
% 2.64/2.97 ============================== end predicate elimination =============
% 2.64/2.97
% 2.64/2.97 Auto_denials: (non-Horn, no changes).
% 2.64/2.97
% 2.64/2.97 Term ordering decisions:
% 2.64/2.97 Function symbol KB weights: c1=1. c2=1. c3=1. difference=1. union=1. symmetric_difference=1. f1=1. f2=1.
% 2.64/2.97
% 2.64/2.97 ============================== end of process initial clauses ========
% 2.64/2.97
% 2.64/2.97 ============================== CLAUSES FOR SEARCH ====================
% 2.64/2.97
% 2.64/2.97 ============================== end of clauses for search =============
% 2.64/2.97
% 2.64/2.97 ============================== SEARCH ================================
% 2.64/2.97
% 2.64/2.97 % Starting search at 0.01 seconds.
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=62.000, iters=3355
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=61.000, iters=3382
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=54.000, iters=3508
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=53.000, iters=3449
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=45.000, iters=3528
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=42.000, iters=3396
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=40.000, iters=3424
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=39.000, iters=3396
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=38.000, iters=3380
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=37.000, iters=3349
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=36.000, iters=3335
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=35.000, iters=3495
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=33.000, iters=3345
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=32.000, iters=3369
% 2.64/2.97
% 2.64/2.97 Low Water (keep): wt=31.000, iters=3340
% 2.64/2.97
% 2.64/2.97 ============================== PROOF =================================
% 2.64/2.97 % SZS status Theorem
% 2.64/2.97 % SZS output start Refutation
% 2.64/2.97
% 2.64/2.97 % Proof 1 at 1.95 (+ 0.03) seconds.
% 2.64/2.97 % Length of proof is 16.
% 2.64/2.97 % Level of proof is 5.
% 2.64/2.97 % Maximum clause weight is 21.000.
% 2.64/2.97 % Given clauses 438.
% 2.64/2.97
% 2.64/2.97 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 2.64/2.97 2 (all B all C all D difference(difference(B,C),D) = difference(B,union(C,D))) # label(difference_difference_union) # label(axiom) # label(non_clause). [assumption].
% 2.64/2.97 3 (all B all C all D difference(union(B,C),D) = union(difference(B,D),difference(C,D))) # label(difference_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 2.64/2.97 7 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 2.64/2.97 12 -(all B all C all D difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D)))) # label(prove_th97) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.64/2.97 14 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(7)].
% 2.64/2.97 17 union(difference(A,B),difference(B,A)) = symmetric_difference(A,B) # label(symmetric_difference_defn) # label(axiom). [clausify(1)].
% 2.64/2.97 18 symmetric_difference(A,B) = union(difference(A,B),difference(B,A)). [copy(17),flip(a)].
% 2.64/2.97 19 difference(difference(A,B),C) = difference(A,union(B,C)) # label(difference_difference_union) # label(axiom). [clausify(2)].
% 2.64/2.97 20 union(difference(A,B),difference(C,B)) = difference(union(A,C),B) # label(difference_distributes_over_union) # label(axiom). [clausify(3)].
% 2.64/2.97 23 union(difference(c1,union(c2,c3)),difference(c2,union(c1,c3))) != difference(symmetric_difference(c1,c2),c3) # label(prove_th97) # label(negated_conjecture). [clausify(12)].
% 2.64/2.97 24 union(difference(c1,union(c2,c3)),difference(c2,union(c1,c3))) != difference(union(difference(c1,c2),difference(c2,c1)),c3). [copy(23),rewrite([18(14)])].
% 2.64/2.97 40 union(difference(A,union(B,C)),difference(D,C)) = difference(union(D,difference(A,B)),C). [para(19(a,1),20(a,1,1)),rewrite([14(6)])].
% 2.64/2.97 116 union(difference(A,union(B,C)),difference(D,union(C,E))) = difference(union(difference(D,E),difference(A,B)),C). [para(19(a,1),40(a,1,2)),rewrite([14(3)])].
% 2.64/2.97 9704 union(difference(A,union(B,C)),difference(D,union(E,C))) = difference(union(difference(A,B),difference(D,E)),C). [para(116(a,1),14(a,1)),rewrite([14(5)]),flip(a)].
% 2.64/2.97 9705 $F. [resolve(9704,a,24,a)].
% 2.64/2.97
% 2.64/2.97 % SZS output end Refutation
% 2.64/2.97 ============================== end of proof ==========================
% 2.64/2.97
% 2.64/2.97 ============================== STATISTICS ============================
% 2.64/2.97
% 2.64/2.97 Given=438. Generated=58567. Kept=9690. proofs=1.
% 2.64/2.97 Usable=237. Sos=5512. Demods=930. Limbo=2, Disabled=3961. Hints=0.
% 2.64/2.97 Megabytes=8.89.
% 2.64/2.97 User_CPU=1.95, System_CPU=0.03, Wall_clock=2.
% 2.64/2.97
% 2.64/2.97 ============================== end of statistics =====================
% 2.64/2.97
% 2.64/2.97 ============================== end of search =========================
% 2.64/2.97
% 2.64/2.97 THEOREM PROVED
% 2.64/2.97 % SZS status Theorem
% 2.64/2.97
% 2.64/2.97 Exiting with 1 proof.
% 2.64/2.97
% 2.64/2.97 Process 1683 exit (max_proofs) Sat Jul 9 18:53:28 2022
% 2.64/2.97 Prover9 interrupted
%------------------------------------------------------------------------------