TSTP Solution File: SET173+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 04:27:59 EDT 2022
% Result : Theorem 0.72s 1.03s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.32 % Computer : n028.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 11 09:58:58 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 3966 was started by sandbox2 on n028.cluster.edu,
% 0.42/0.98 Mon Jul 11 09:58:59 2022
% 0.42/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3813_n028.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_3813_n028.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (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].
% 0.42/0.98 2 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 5 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 6 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 -(all B all C intersection(B,union(B,C)) = B) # label(prove_absorbtion_for_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.98
% 0.42/0.98 ============================== end of process non-clausal formulas ===
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.98
% 0.42/0.98 ============================== PREDICATE ELIMINATION =================
% 0.42/0.98
% 0.42/0.98 ============================== end predicate elimination =============
% 0.42/0.98
% 0.42/0.98 Auto_denials: (non-Horn, no changes).
% 0.42/0.98
% 0.42/0.98 Term ordering decisions:
% 0.42/0.98 Function symbol KB weights: c1=1. c2=1. intersection=1. union=1. f1=1. f2=1.
% 0.42/0.98
% 0.42/0.98 ============================== end of process initial clauses ========
% 0.42/0.98
% 0.42/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.98
% 0.42/0.98 ============================== end of clauses for search =============
% 0.42/0.98
% 0.42/0.98 ============================== SEARCH ================================
% 0.72/1.03
% 0.72/1.03 % Starting search at 0.01 seconds.
% 0.72/1.03
% 0.72/1.03 ============================== PROOF =================================
% 0.72/1.03 % SZS status Theorem
% 0.72/1.03 % SZS output start Refutation
% 0.72/1.03
% 0.72/1.03 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.72/1.03 % Length of proof is 27.
% 0.72/1.03 % Level of proof is 9.
% 0.72/1.03 % Maximum clause weight is 26.000.
% 0.72/1.03 % Given clauses 82.
% 0.72/1.03
% 0.72/1.03 1 (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].
% 0.72/1.03 2 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 9 -(all B all C intersection(B,union(B,C)) = B) # label(prove_absorbtion_for_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.03 14 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.72/1.03 15 intersection(c1,union(c1,c2)) != c1 # label(prove_absorbtion_for_intersection) # label(negated_conjecture). [clausify(9)].
% 0.72/1.03 18 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(1)].
% 0.72/1.03 20 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(2)].
% 0.72/1.03 27 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.72/1.03 28 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(2)].
% 0.72/1.03 29 A = B | -member(f2(B,A),B) | -member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.72/1.03 32 member(f2(A,B),union(B,C)) | B = A | member(f2(A,B),A). [resolve(18,b,14,c)].
% 0.72/1.03 33 member(f2(A,B),union(A,C)) | B = A | member(f2(A,B),B). [resolve(18,b,14,b)].
% 0.72/1.03 34 member(f2(union(A,B),A),union(A,B)) | union(A,B) = A. [factor(32,a,c),flip(b)].
% 0.72/1.03 36 member(f2(A,intersection(B,C)),B) | intersection(B,C) = A | member(f2(A,intersection(B,C)),A). [resolve(20,a,14,c)].
% 0.72/1.03 38 member(f2(A,intersection(A,B)),A) | intersection(A,B) = A. [factor(36,a,c)].
% 0.72/1.03 53 member(f2(union(A,B),C),A) | member(f2(union(A,B),C),B) | union(A,B) = C | member(f2(union(A,B),C),C). [resolve(27,a,14,b),flip(c)].
% 0.72/1.03 56 member(f2(union(A,A),B),A) | union(A,A) = B | member(f2(union(A,A),B),B). [factor(53,a,b)].
% 0.72/1.03 60 member(f2(union(A,A),A),A) | union(A,A) = A. [factor(56,a,c)].
% 0.72/1.03 126 intersection(A,B) = A | -member(f2(A,intersection(A,B)),intersection(A,B)). [resolve(38,a,29,b),merge(b)].
% 0.72/1.03 154 union(A,B) = A | -member(f2(union(A,B),A),A). [resolve(34,a,29,b),flip(b),merge(b)].
% 0.72/1.03 181 union(A,A) = A. [resolve(154,b,60,a),merge(b)].
% 0.72/1.03 184 member(f2(A,B),A) | A = B | member(f2(A,B),B). [back_rewrite(56),rewrite([181(1),181(3),181(4)])].
% 0.72/1.03 434 -member(f2(c1,intersection(c1,union(c1,c2))),intersection(c1,union(c1,c2))). [ur(126,a,15,a)].
% 0.72/1.03 436 member(f2(c1,intersection(c1,union(c1,c2))),c1). [resolve(434,a,184,c),flip(b),unit_del(b,15)].
% 0.72/1.03 457 -member(f2(c1,intersection(c1,union(c1,c2))),union(c1,c2)). [ur(28,a,434,a,b,436,a)].
% 0.72/1.03 496 $F. [resolve(457,a,33,a),unit_del(a,15),unit_del(b,434)].
% 0.72/1.03
% 0.72/1.03 % SZS output end Refutation
% 0.72/1.03 ============================== end of proof ==========================
% 0.72/1.03
% 0.72/1.03 ============================== STATISTICS ============================
% 0.72/1.03
% 0.72/1.03 Given=82. Generated=1208. Kept=486. proofs=1.
% 0.72/1.03 Usable=76. Sos=323. Demods=4. Limbo=0, Disabled=107. Hints=0.
% 0.72/1.03 Megabytes=0.38.
% 0.72/1.03 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.72/1.03
% 0.72/1.03 ============================== end of statistics =====================
% 0.72/1.03
% 0.72/1.03 ============================== end of search =========================
% 0.72/1.03
% 0.72/1.03 THEOREM PROVED
% 0.72/1.03 % SZS status Theorem
% 0.72/1.03
% 0.72/1.03 Exiting with 1 proof.
% 0.72/1.03
% 0.72/1.03 Process 3966 exit (max_proofs) Mon Jul 11 09:58:59 2022
% 0.72/1.03 Prover9 interrupted
%------------------------------------------------------------------------------