TSTP Solution File: SET185+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 04:28:05 EDT 2022
% Result : Theorem 0.71s 0.99s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sun Jul 10 10:42:07 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.71/0.99 ============================== Prover9 ===============================
% 0.71/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.71/0.99 Process 27967 was started by sandbox2 on n005.cluster.edu,
% 0.71/0.99 Sun Jul 10 10:42:07 2022
% 0.71/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27814_n005.cluster.edu".
% 0.71/0.99 ============================== end of head ===========================
% 0.71/0.99
% 0.71/0.99 ============================== INPUT =================================
% 0.71/0.99
% 0.71/0.99 % Reading from file /tmp/Prover9_27814_n005.cluster.edu
% 0.71/0.99
% 0.71/0.99 set(prolog_style_variables).
% 0.71/0.99 set(auto2).
% 0.71/0.99 % set(auto2) -> set(auto).
% 0.71/0.99 % set(auto) -> set(auto_inference).
% 0.71/0.99 % set(auto) -> set(auto_setup).
% 0.71/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.71/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/0.99 % set(auto) -> set(auto_limits).
% 0.71/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/0.99 % set(auto) -> set(auto_denials).
% 0.71/0.99 % set(auto) -> set(auto_process).
% 0.71/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.99 % set(auto2) -> assign(stats, some).
% 0.71/0.99 % set(auto2) -> clear(echo_input).
% 0.71/0.99 % set(auto2) -> set(quiet).
% 0.71/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.99 % set(auto2) -> clear(print_given).
% 0.71/0.99 assign(lrs_ticks,-1).
% 0.71/0.99 assign(sos_limit,10000).
% 0.71/0.99 assign(order,kbo).
% 0.71/0.99 set(lex_order_vars).
% 0.71/0.99 clear(print_given).
% 0.71/0.99
% 0.71/0.99 % formulas(sos). % not echoed (7 formulas)
% 0.71/0.99
% 0.71/0.99 ============================== end of input ==========================
% 0.71/0.99
% 0.71/0.99 % From the command line: assign(max_seconds, 300).
% 0.71/0.99
% 0.71/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.99
% 0.71/0.99 % Formulas that are not ordinary clauses:
% 0.71/0.99 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].
% 0.71/0.99 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 3 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 5 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 7 -(all B all C (subset(B,C) -> union(B,C) = C)) # label(prove_subset_union) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.71/0.99
% 0.71/0.99 ============================== end of process non-clausal formulas ===
% 0.71/0.99
% 0.71/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/0.99
% 0.71/0.99 ============================== PREDICATE ELIMINATION =================
% 0.71/0.99
% 0.71/0.99 ============================== end predicate elimination =============
% 0.71/0.99
% 0.71/0.99 Auto_denials: (non-Horn, no changes).
% 0.71/0.99
% 0.71/0.99 Term ordering decisions:
% 0.71/0.99 Function symbol KB weights: c1=1. c2=1. union=1. f1=1. f2=1.
% 0.71/0.99
% 0.71/0.99 ============================== end of process initial clauses ========
% 0.71/0.99
% 0.71/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.71/0.99
% 0.71/0.99 ============================== end of clauses for search =============
% 0.71/0.99
% 0.71/0.99 ============================== SEARCH ================================
% 0.71/0.99
% 0.71/0.99 % Starting search at 0.01 seconds.
% 0.71/0.99
% 0.71/0.99 ============================== PROOF =================================
% 0.71/0.99 % SZS status Theorem
% 0.71/0.99 % SZS output start Refutation
% 0.71/0.99
% 0.71/0.99 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.71/0.99 % Length of proof is 21.
% 0.71/0.99 % Level of proof is 7.
% 0.71/0.99 % Maximum clause weight is 26.000.
% 0.71/0.99 % Given clauses 60.
% 0.71/0.99
% 0.71/0.99 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].
% 0.71/0.99 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.99 7 -(all B all C (subset(B,C) -> union(B,C) = C)) # label(prove_subset_union) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.71/0.99 9 subset(c1,c2) # label(prove_subset_union) # label(negated_conjecture). [clausify(7)].
% 0.71/0.99 10 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(4)].
% 0.71/0.99 12 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 0.71/0.99 13 union(c1,c2) != c2 # label(prove_subset_union) # label(negated_conjecture). [clausify(7)].
% 0.71/0.99 17 member(A,union(B,C)) | -member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.71/0.99 19 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.71/0.99 23 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.71/0.99 24 A = B | -member(f2(B,A),B) | -member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 0.71/0.99 31 -member(A,c1) | member(A,c2). [resolve(19,a,9,a)].
% 0.71/0.99 41 member(f2(A,union(B,C)),B) | member(f2(A,union(B,C)),C) | union(B,C) = A | member(f2(A,union(B,C)),A). [resolve(23,a,12,c)].
% 0.71/0.99 177 member(f2(A,union(B,c1)),B) | union(B,c1) = A | member(f2(A,union(B,c1)),A) | member(f2(A,union(B,c1)),c2). [resolve(41,a,31,a),rewrite([10(2),10(6),10(9),10(13)])].
% 0.71/0.99 191 member(f2(A,union(A,c1)),A) | union(A,c1) = A | member(f2(A,union(A,c1)),c2). [factor(177,a,c)].
% 0.71/0.99 223 member(f2(c2,union(c1,c2)),c2). [factor(191,a,c),rewrite([10(4),10(10)]),unit_del(b,13)].
% 0.71/0.99 231 -member(f2(c2,union(c1,c2)),union(c1,c2)). [resolve(223,a,24,b),unit_del(a,13)].
% 0.71/0.99 233 member(f2(c2,union(c1,c2)),union(A,c2)). [resolve(223,a,17,b)].
% 0.71/0.99 234 $F. [resolve(233,a,231,a)].
% 0.71/0.99
% 0.71/0.99 % SZS output end Refutation
% 0.71/0.99 ============================== end of proof ==========================
% 0.71/0.99
% 0.71/0.99 ============================== STATISTICS ============================
% 0.71/0.99
% 0.71/0.99 Given=60. Generated=537. Kept=226. proofs=1.
% 0.71/0.99 Usable=57. Sos=139. Demods=2. Limbo=3, Disabled=43. Hints=0.
% 0.71/0.99 Megabytes=0.19.
% 0.71/0.99 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.71/0.99
% 0.71/0.99 ============================== end of statistics =====================
% 0.71/0.99
% 0.71/0.99 ============================== end of search =========================
% 0.71/0.99
% 0.71/0.99 THEOREM PROVED
% 0.71/0.99 % SZS status Theorem
% 0.71/0.99
% 0.71/0.99 Exiting with 1 proof.
% 0.71/0.99
% 0.71/0.99 Process 27967 exit (max_proofs) Sun Jul 10 10:42:07 2022
% 0.71/0.99 Prover9 interrupted
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