TSTP Solution File: SET627+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 04:30:57 EDT 2022
% Result : Theorem 0.41s 1.00s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n003.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 : Sun Jul 10 14:44:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.00 ============================== Prover9 ===============================
% 0.41/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.00 Process 21707 was started by sandbox2 on n003.cluster.edu,
% 0.41/1.00 Sun Jul 10 14:44:30 2022
% 0.41/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21302_n003.cluster.edu".
% 0.41/1.00 ============================== end of head ===========================
% 0.41/1.00
% 0.41/1.00 ============================== INPUT =================================
% 0.41/1.00
% 0.41/1.00 % Reading from file /tmp/Prover9_21302_n003.cluster.edu
% 0.41/1.00
% 0.41/1.00 set(prolog_style_variables).
% 0.41/1.00 set(auto2).
% 0.41/1.00 % set(auto2) -> set(auto).
% 0.41/1.00 % set(auto) -> set(auto_inference).
% 0.41/1.00 % set(auto) -> set(auto_setup).
% 0.41/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.00 % set(auto) -> set(auto_limits).
% 0.41/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.00 % set(auto) -> set(auto_denials).
% 0.41/1.00 % set(auto) -> set(auto_process).
% 0.41/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.00 % set(auto2) -> assign(stats, some).
% 0.41/1.00 % set(auto2) -> clear(echo_input).
% 0.41/1.00 % set(auto2) -> set(quiet).
% 0.41/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.00 % set(auto2) -> clear(print_given).
% 0.41/1.00 assign(lrs_ticks,-1).
% 0.41/1.00 assign(sos_limit,10000).
% 0.41/1.00 assign(order,kbo).
% 0.41/1.00 set(lex_order_vars).
% 0.41/1.00 clear(print_given).
% 0.41/1.00
% 0.41/1.00 % formulas(sos). % not echoed (6 formulas)
% 0.41/1.00
% 0.41/1.00 ============================== end of input ==========================
% 0.41/1.00
% 0.41/1.00 % From the command line: assign(max_seconds, 300).
% 0.41/1.00
% 0.41/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.00
% 0.41/1.00 % Formulas that are not ordinary clauses:
% 0.41/1.00 1 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 2 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 3 (all B all C (disjoint(B,C) <-> -intersect(B,C))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 4 (all B all C (intersect(B,C) -> intersect(C,B))) # label(symmetry_of_intersect) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 5 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 6 -(all B disjoint(B,empty_set)) # label(prove_th104) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.00
% 0.41/1.00 ============================== end of process non-clausal formulas ===
% 0.41/1.00
% 0.41/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.41/1.00 ============================== PREDICATE ELIMINATION =================
% 0.41/1.00 7 -disjoint(c1,empty_set) # label(prove_th104) # label(negated_conjecture). [clausify(6)].
% 0.41/1.00 8 disjoint(A,B) | intersect(A,B) # label(disjoint_defn) # label(axiom). [clausify(3)].
% 0.41/1.00 Derived: intersect(c1,empty_set). [resolve(7,a,8,a)].
% 0.41/1.00 9 -disjoint(A,B) | -intersect(A,B) # label(disjoint_defn) # label(axiom). [clausify(3)].
% 0.41/1.00 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(5)].
% 0.41/1.00 11 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(5)].
% 0.41/1.00 Derived: -member(A,B) | member(f2(B),B). [resolve(10,a,11,a)].
% 0.41/1.00
% 0.41/1.00 ============================== end predicate elimination =============
% 0.41/1.00
% 0.41/1.00 Auto_denials:
% 0.41/1.00 % copying label empty_set_defn to answer in negative clause
% 0.41/1.00
% 0.41/1.00 Term ordering decisions:
% 0.41/1.00
% 0.41/1.00 % Assigning unary symbol f2 kb_weight 0 and highest precedence (6).
% 0.41/1.00 Function symbol KB weights: empty_set=1. c1=1. f1=1. f2=0.
% 0.41/1.00
% 0.41/1.00 ============================== end of process initial clauses ========
% 0.41/1.00
% 0.41/1.00 ============================== CLAUSES FOR SEARCH ====================
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% 0.41/1.00 ============================== end of clauses for search =============
% 0.41/1.00
% 0.41/1.00 ============================== SEARCH ================================
% 0.41/1.00
% 0.41/1.00 % Starting search at 0.01 seconds.
% 0.41/1.00
% 0.41/1.00 ============================== PROOF =================================
% 0.41/1.00 % SZS status Theorem
% 0.41/1.00 % SZS output start Refutation
% 0.41/1.00
% 0.41/1.00 % Proof 1 at 0.01 (+ 0.00) seconds: empty_set_defn.
% 0.41/1.00 % Length of proof is 11.
% 0.41/1.00 % Level of proof is 3.
% 0.41/1.00 % Maximum clause weight is 8.000.
% 0.41/1.00 % Given clauses 4.
% 0.41/1.00
% 0.41/1.00 1 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 2 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 3 (all B all C (disjoint(B,C) <-> -intersect(B,C))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 6 -(all B disjoint(B,empty_set)) # label(prove_th104) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.00 7 -disjoint(c1,empty_set) # label(prove_th104) # label(negated_conjecture). [clausify(6)].
% 0.41/1.00 8 disjoint(A,B) | intersect(A,B) # label(disjoint_defn) # label(axiom). [clausify(3)].
% 0.41/1.00 12 -member(A,empty_set) # label(empty_set_defn) # label(axiom) # answer(empty_set_defn). [clausify(1)].
% 0.41/1.00 15 -intersect(A,B) | member(f1(A,B),B) # label(intersect_defn) # label(axiom). [clausify(2)].
% 0.41/1.00 17 intersect(c1,empty_set). [resolve(7,a,8,a)].
% 0.41/1.00 20 -intersect(A,empty_set) # answer(empty_set_defn). [resolve(15,b,12,a)].
% 0.41/1.00 21 $F # answer(empty_set_defn). [resolve(20,a,17,a)].
% 0.41/1.00
% 0.41/1.00 % SZS output end Refutation
% 0.41/1.00 ============================== end of proof ==========================
% 0.41/1.00
% 0.41/1.00 ============================== STATISTICS ============================
% 0.41/1.00
% 0.41/1.00 Given=4. Generated=10. Kept=9. proofs=1.
% 0.41/1.00 Usable=4. Sos=4. Demods=0. Limbo=0, Disabled=12. Hints=0.
% 0.41/1.00 Megabytes=0.03.
% 0.41/1.00 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.41/1.00
% 0.41/1.00 ============================== end of statistics =====================
% 0.41/1.00
% 0.41/1.00 ============================== end of search =========================
% 0.41/1.00
% 0.41/1.00 THEOREM PROVED
% 0.41/1.00 % SZS status Theorem
% 0.41/1.00
% 0.41/1.00 Exiting with 1 proof.
% 0.41/1.00
% 0.41/1.00 Process 21707 exit (max_proofs) Sun Jul 10 14:44:30 2022
% 0.41/1.00 Prover9 interrupted
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