TSTP Solution File: SET605+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET605+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 04:30:40 EDT 2022
% Result : Theorem 0.41s 0.98s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n005.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 : Mon Jul 11 02:03:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.98 ============================== Prover9 ===============================
% 0.41/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.98 Process 20834 was started by sandbox on n005.cluster.edu,
% 0.41/0.98 Mon Jul 11 02:03:37 2022
% 0.41/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20507_n005.cluster.edu".
% 0.41/0.98 ============================== end of head ===========================
% 0.41/0.98
% 0.41/0.98 ============================== INPUT =================================
% 0.41/0.98
% 0.41/0.98 % Reading from file /tmp/Prover9_20507_n005.cluster.edu
% 0.41/0.98
% 0.41/0.98 set(prolog_style_variables).
% 0.41/0.98 set(auto2).
% 0.41/0.98 % set(auto2) -> set(auto).
% 0.41/0.98 % set(auto) -> set(auto_inference).
% 0.41/0.98 % set(auto) -> set(auto_setup).
% 0.41/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.98 % set(auto) -> set(auto_limits).
% 0.41/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.98 % set(auto) -> set(auto_denials).
% 0.41/0.98 % set(auto) -> set(auto_process).
% 0.41/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.98 % set(auto2) -> assign(stats, some).
% 0.41/0.98 % set(auto2) -> clear(echo_input).
% 0.41/0.98 % set(auto2) -> set(quiet).
% 0.41/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.98 % set(auto2) -> clear(print_given).
% 0.41/0.98 assign(lrs_ticks,-1).
% 0.41/0.98 assign(sos_limit,10000).
% 0.41/0.98 assign(order,kbo).
% 0.41/0.98 set(lex_order_vars).
% 0.41/0.98 clear(print_given).
% 0.41/0.98
% 0.41/0.98 % formulas(sos). % not echoed (12 formulas)
% 0.41/0.98
% 0.41/0.98 ============================== end of input ==========================
% 0.41/0.98
% 0.41/0.98 % From the command line: assign(max_seconds, 300).
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98
% 0.41/0.98 % Formulas that are not ordinary clauses:
% 0.41/0.98 1 (all B all C subset(B,union(B,C))) # label(subset_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 2 (all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(difference_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 3 (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].
% 0.41/0.98 4 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 6 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 7 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 8 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 9 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 10 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 11 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 12 -(all B all C difference(B,union(B,C)) = empty_set) # label(prove_th76) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.98
% 0.41/0.98 ============================== end of process non-clausal formulas ===
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.98
% 0.41/0.98 ============================== PREDICATE ELIMINATION =================
% 0.41/0.98 13 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(10)].
% 0.41/0.98 14 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(10)].
% 0.41/0.98 Derived: -member(A,B) | member(f2(B),B). [resolve(13,a,14,a)].
% 0.41/0.98
% 0.41/0.98 ============================== end predicate elimination =============
% 0.41/0.98
% 0.41/0.98 Auto_denials: (non-Horn, no changes).
% 0.41/0.98
% 0.41/0.98 Term ordering decisions:
% 0.41/0.98
% 0.41/0.98 % Assigning unary symbol f2 kb_weight 0 and highest precedence (11).
% 0.41/0.98 Function symbol KB weights: empty_set=1. c1=1. c2=1. union=1. difference=1. f1=1. f3=1. f2=0.
% 0.41/0.98
% 0.41/0.98 ============================== end of process initial clauses ========
% 0.41/0.98
% 0.41/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.98
% 0.41/0.98 ============================== end of clauses for search =============
% 0.41/0.98
% 0.41/0.98 ============================== SEARCH ================================
% 0.41/0.98
% 0.41/0.98 % Starting search at 0.01 seconds.
% 0.41/0.98
% 0.41/0.98 ============================== PROOF =================================
% 0.41/0.98 % SZS status Theorem
% 0.41/0.98 % SZS output start Refutation
% 0.41/0.98
% 0.41/0.98 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.41/0.98 % Length of proof is 8.
% 0.41/0.98 % Level of proof is 3.
% 0.41/0.98 % Maximum clause weight is 8.000.
% 0.41/0.98 % Given clauses 12.
% 0.41/0.98
% 0.41/0.98 1 (all B all C subset(B,union(B,C))) # label(subset_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 2 (all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(difference_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 12 -(all B all C difference(B,union(B,C)) = empty_set) # label(prove_th76) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.98 16 subset(A,union(A,B)) # label(subset_of_union) # label(axiom). [clausify(1)].
% 0.41/0.98 21 difference(c1,union(c1,c2)) != empty_set # label(prove_th76) # label(negated_conjecture). [clausify(12)].
% 0.41/0.98 26 difference(A,B) = empty_set | -subset(A,B) # label(difference_empty_set) # label(axiom). [clausify(2)].
% 0.41/0.98 45 difference(A,union(A,B)) = empty_set. [resolve(26,b,16,a)].
% 0.41/0.98 46 $F. [resolve(45,a,21,a)].
% 0.41/0.98
% 0.41/0.98 % SZS output end Refutation
% 0.41/0.98 ============================== end of proof ==========================
% 0.41/0.98
% 0.41/0.98 ============================== STATISTICS ============================
% 0.41/0.98
% 0.41/0.98 Given=12. Generated=45. Kept=31. proofs=1.
% 0.41/0.98 Usable=12. Sos=17. Demods=1. Limbo=1, Disabled=26. Hints=0.
% 0.41/0.98 Megabytes=0.06.
% 0.41/0.98 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.41/0.98
% 0.41/0.98 ============================== end of statistics =====================
% 0.41/0.98
% 0.41/0.98 ============================== end of search =========================
% 0.41/0.98
% 0.41/0.98 THEOREM PROVED
% 0.41/0.98 % SZS status Theorem
% 0.41/0.98
% 0.41/0.98 Exiting with 1 proof.
% 0.41/0.98
% 0.41/0.98 Process 20834 exit (max_proofs) Mon Jul 11 02:03:37 2022
% 0.41/0.98 Prover9 interrupted
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