TSTP Solution File: SET183+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 04:28:04 EDT 2022
% Result : Theorem 0.44s 1.00s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 21:59:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 24736 was started by sandbox2 on n018.cluster.edu,
% 0.44/1.00 Sun Jul 10 21:59:58 2022
% 0.44/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24582_n018.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_24582_n018.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (8 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 1 (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].
% 0.44/1.00 2 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 5 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 6 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 7 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 8 -(all B all C (subset(B,C) -> intersection(B,C) = B)) # label(prove_subset_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.00
% 0.44/1.00 ============================== end of process non-clausal formulas ===
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.00
% 0.44/1.00 ============================== PREDICATE ELIMINATION =================
% 0.44/1.00
% 0.44/1.00 ============================== end predicate elimination =============
% 0.44/1.00
% 0.44/1.00 Auto_denials: (non-Horn, no changes).
% 0.44/1.00
% 0.44/1.00 Term ordering decisions:
% 0.44/1.00 Function symbol KB weights: c1=1. c2=1. intersection=1. f1=1. f2=1.
% 0.44/1.00
% 0.44/1.00 ============================== end of process initial clauses ========
% 0.44/1.00
% 0.44/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.00
% 0.44/1.00 ============================== end of clauses for search =============
% 0.44/1.00
% 0.44/1.00 ============================== SEARCH ================================
% 0.44/1.00
% 0.44/1.00 % Starting search at 0.01 seconds.
% 0.44/1.00
% 0.44/1.00 ============================== PROOF =================================
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00 % SZS output start Refutation
% 0.44/1.00
% 0.44/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.00 % Length of proof is 19.
% 0.44/1.00 % Level of proof is 5.
% 0.44/1.00 % Maximum clause weight is 11.000.
% 0.44/1.00 % Given clauses 27.
% 0.44/1.00
% 0.44/1.00 1 (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].
% 0.44/1.00 2 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 8 -(all B all C (subset(B,C) -> intersection(B,C) = B)) # label(prove_subset_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.00 10 subset(c1,c2) # label(prove_subset_intersection) # label(negated_conjecture). [clausify(8)].
% 0.44/1.00 11 subset(intersection(A,B),A) # label(intersection_is_subset) # label(axiom). [clausify(2)].
% 0.44/1.00 13 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(3)].
% 0.44/1.00 15 intersection(c1,c2) != c1 # label(prove_subset_intersection) # label(negated_conjecture). [clausify(8)].
% 0.44/1.00 20 subset(A,B) | -member(f1(A,B),B) # label(subset_defn) # label(axiom). [clausify(3)].
% 0.44/1.00 21 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(3)].
% 0.44/1.00 22 A = B | -subset(B,A) | -subset(A,B) # label(equal_defn) # label(axiom). [clausify(4)].
% 0.44/1.00 25 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 0.44/1.00 37 -member(A,c1) | member(A,c2). [resolve(21,a,10,a)].
% 0.44/1.00 42 -subset(c1,intersection(c1,c2)). [ur(22,a,15,a,c,11,a)].
% 0.44/1.00 58 member(f1(c1,intersection(c1,c2)),c1). [resolve(42,a,13,a)].
% 0.44/1.00 59 -member(f1(c1,intersection(c1,c2)),intersection(c1,c2)). [ur(20,a,42,a)].
% 0.44/1.00 68 member(f1(c1,intersection(c1,c2)),c2). [resolve(58,a,37,a)].
% 0.44/1.00 72 $F. [ur(25,a,59,a,b,58,a),unit_del(a,68)].
% 0.44/1.00
% 0.44/1.00 % SZS output end Refutation
% 0.44/1.00 ============================== end of proof ==========================
% 0.44/1.00
% 0.44/1.00 ============================== STATISTICS ============================
% 0.44/1.00
% 0.44/1.00 Given=27. Generated=147. Kept=63. proofs=1.
% 0.44/1.00 Usable=27. Sos=32. Demods=1. Limbo=4, Disabled=18. Hints=0.
% 0.44/1.00 Megabytes=0.08.
% 0.44/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of statistics =====================
% 0.44/1.00
% 0.44/1.00 ============================== end of search =========================
% 0.44/1.00
% 0.44/1.00 THEOREM PROVED
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00
% 0.44/1.00 Exiting with 1 proof.
% 0.44/1.00
% 0.44/1.00 Process 24736 exit (max_proofs) Sun Jul 10 21:59:58 2022
% 0.44/1.00 Prover9 interrupted
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