TSTP Solution File: SET638+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET638+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 04:31:03 EDT 2022
% Result : Theorem 0.42s 0.98s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % 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 : Sun Jul 10 23:49:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 25723 was started by sandbox2 on n005.cluster.edu,
% 0.42/0.97 Sun Jul 10 23:49:52 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25570_n005.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_25570_n005.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (15 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 2 (all B all C (subset(B,C) -> intersection(B,C) = B)) # label(subset_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 3 (all B union(B,empty_set) = B) # label(union_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 4 (all B all C all D intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D))) # label(intersection_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 5 (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].
% 0.42/0.97 6 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 7 (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].
% 0.42/0.97 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].
% 0.42/0.97 9 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 10 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 11 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 12 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 13 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 14 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 15 -(all B all C all D (subset(B,union(C,D)) & intersection(B,D) = empty_set -> subset(B,C))) # label(prove_th120) # 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 16 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(13)].
% 0.42/0.98 17 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(13)].
% 0.42/0.98 Derived: -member(A,B) | member(f2(B),B). [resolve(16,a,17,a)].
% 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
% 0.42/0.98 % Assigning unary symbol f2 kb_weight 0 and highest precedence (12).
% 0.42/0.98 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. intersection=1. union=1. f1=1. f3=1. f2=0.
% 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 ================================
% 0.42/0.98
% 0.42/0.98 % Starting search at 0.01 seconds.
% 0.42/0.98
% 0.42/0.98 ============================== PROOF =================================
% 0.42/0.98 % SZS status Theorem
% 0.42/0.98 % SZS output start Refutation
% 0.42/0.98
% 0.42/0.98 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.42/0.98 % Length of proof is 21.
% 0.42/0.98 % Level of proof is 6.
% 0.42/0.98 % Maximum clause weight is 13.000.
% 0.42/0.98 % Given clauses 38.
% 0.42/0.98
% 0.42/0.98 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 2 (all B all C (subset(B,C) -> intersection(B,C) = B)) # label(subset_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all B union(B,empty_set) = B) # label(union_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all B all C all D intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D))) # label(intersection_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 15 -(all B all C all D (subset(B,union(C,D)) & intersection(B,D) = empty_set -> subset(B,C))) # label(prove_th120) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.98 19 subset(intersection(A,B),A) # label(intersection_is_subset) # label(axiom). [clausify(1)].
% 0.42/0.98 20 union(A,empty_set) = A # label(union_empty_set) # label(axiom). [clausify(3)].
% 0.42/0.98 21 subset(c1,union(c2,c3)) # label(prove_th120) # label(negated_conjecture). [clausify(15)].
% 0.42/0.98 22 intersection(c1,c3) = empty_set # label(prove_th120) # label(negated_conjecture). [clausify(15)].
% 0.42/0.98 23 empty_set = intersection(c1,c3). [copy(22),flip(a)].
% 0.42/0.98 25 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(11)].
% 0.42/0.98 27 union(intersection(A,B),intersection(A,C)) = intersection(A,union(B,C)) # label(intersection_distributes_over_union) # label(axiom). [clausify(4)].
% 0.42/0.98 31 -subset(c1,c2) # label(prove_th120) # label(negated_conjecture). [clausify(15)].
% 0.42/0.98 34 -subset(A,B) | intersection(A,B) = A # label(subset_intersection) # label(axiom). [clausify(2)].
% 0.42/0.98 48 union(A,intersection(c1,c3)) = A. [back_rewrite(20),rewrite([23(1)])].
% 0.42/0.98 51 subset(intersection(A,B),B). [para(25(a,1),19(a,1))].
% 0.42/0.98 58 intersection(c1,union(c2,c3)) = c1. [resolve(34,a,21,a)].
% 0.42/0.98 103 intersection(c1,union(A,c3)) = intersection(A,c1). [para(48(a,1),27(a,1)),rewrite([25(2)]),flip(a)].
% 0.42/0.98 104 intersection(c1,c2) = c1. [back_rewrite(58),rewrite([103(5),25(3)])].
% 0.42/0.98 139 $F. [para(104(a,1),51(a,1)),unit_del(a,31)].
% 0.42/0.98
% 0.42/0.98 % SZS output end Refutation
% 0.42/0.98 ============================== end of proof ==========================
% 0.42/0.98
% 0.42/0.98 ============================== STATISTICS ============================
% 0.42/0.98
% 0.42/0.98 Given=38. Generated=325. Kept=119. proofs=1.
% 0.42/0.98 Usable=38. Sos=76. Demods=14. Limbo=2, Disabled=33. Hints=0.
% 0.42/0.98 Megabytes=0.14.
% 0.42/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.42/0.98
% 0.42/0.98 ============================== end of statistics =====================
% 0.42/0.98
% 0.42/0.98 ============================== end of search =========================
% 0.42/0.98
% 0.42/0.98 THEOREM PROVED
% 0.42/0.98 % SZS status Theorem
% 0.42/0.98
% 0.42/0.98 Exiting with 1 proof.
% 0.42/0.98
% 0.42/0.98 Process 25723 exit (max_proofs) Sun Jul 10 23:49:52 2022
% 0.42/0.98 Prover9 interrupted
%------------------------------------------------------------------------------