TSTP Solution File: SET600+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 04:30:36 EDT 2022
% Result : Theorem 0.81s 1.11s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 : Sat Jul 9 23:31:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.02 ============================== Prover9 ===============================
% 0.75/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.02 Process 11549 was started by sandbox on n026.cluster.edu,
% 0.75/1.02 Sat Jul 9 23:31:41 2022
% 0.75/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11182_n026.cluster.edu".
% 0.75/1.02 ============================== end of head ===========================
% 0.75/1.02
% 0.75/1.02 ============================== INPUT =================================
% 0.75/1.02
% 0.75/1.02 % Reading from file /tmp/Prover9_11182_n026.cluster.edu
% 0.75/1.02
% 0.75/1.02 set(prolog_style_variables).
% 0.75/1.02 set(auto2).
% 0.75/1.02 % set(auto2) -> set(auto).
% 0.75/1.02 % set(auto) -> set(auto_inference).
% 0.75/1.02 % set(auto) -> set(auto_setup).
% 0.75/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.02 % set(auto) -> set(auto_limits).
% 0.75/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.02 % set(auto) -> set(auto_denials).
% 0.75/1.02 % set(auto) -> set(auto_process).
% 0.75/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.02 % set(auto2) -> assign(stats, some).
% 0.75/1.02 % set(auto2) -> clear(echo_input).
% 0.75/1.02 % set(auto2) -> set(quiet).
% 0.75/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.02 % set(auto2) -> clear(print_given).
% 0.75/1.02 assign(lrs_ticks,-1).
% 0.75/1.02 assign(sos_limit,10000).
% 0.75/1.02 assign(order,kbo).
% 0.75/1.02 set(lex_order_vars).
% 0.75/1.02 clear(print_given).
% 0.75/1.02
% 0.75/1.02 % formulas(sos). % not echoed (9 formulas)
% 0.75/1.02
% 0.75/1.02 ============================== end of input ==========================
% 0.75/1.02
% 0.75/1.02 % From the command line: assign(max_seconds, 300).
% 0.75/1.02
% 0.75/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.02
% 0.75/1.02 % Formulas that are not ordinary clauses:
% 0.75/1.02 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].
% 0.75/1.02 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 3 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 5 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 6 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 7 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 9 -(all B all C (union(B,C) = empty_set <-> B = empty_set & C = empty_set)) # label(prove_th59) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.02
% 0.75/1.02 ============================== end of process non-clausal formulas ===
% 0.75/1.02
% 0.75/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.02
% 0.75/1.02 ============================== PREDICATE ELIMINATION =================
% 0.75/1.02 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.75/1.02 11 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.75/1.02 Derived: -member(A,B) | member(f2(B),B). [resolve(10,a,11,a)].
% 0.75/1.02
% 0.75/1.02 ============================== end predicate elimination =============
% 0.75/1.02
% 0.75/1.02 Auto_denials: (non-Horn, no changes).
% 0.75/1.02
% 0.75/1.02 Term ordering decisions:
% 0.75/1.02
% 0.75/1.02 % Assigning unary symbol f2 kb_weight 0 and highest precedence (10).
% 0.75/1.02 Function symbol KB weights: empty_set=1. c1=1. c2=1. union=1. f1=1. f3=1. f2=0.
% 0.75/1.02
% 0.75/1.02 ============================== end of process initial clauses ========
% 0.81/1.11
% 0.81/1.11 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.11
% 0.81/1.11 ============================== end of clauses for search =============
% 0.81/1.11
% 0.81/1.11 ============================== SEARCH ================================
% 0.81/1.11
% 0.81/1.11 % Starting search at 0.01 seconds.
% 0.81/1.11
% 0.81/1.11 ============================== PROOF =================================
% 0.81/1.11 % SZS status Theorem
% 0.81/1.11 % SZS output start Refutation
% 0.81/1.11
% 0.81/1.11 % Proof 1 at 0.09 (+ 0.00) seconds.
% 0.81/1.11 % Length of proof is 40.
% 0.81/1.11 % Level of proof is 10.
% 0.81/1.11 % Maximum clause weight is 26.000.
% 0.81/1.11 % Given clauses 108.
% 0.81/1.11
% 0.81/1.11 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].
% 0.81/1.11 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 3 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 5 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 9 -(all B all C (union(B,C) = empty_set <-> B = empty_set & C = empty_set)) # label(prove_th59) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.11 13 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(4)].
% 0.81/1.11 15 union(c1,c2) = empty_set | empty_set = c1 # label(prove_th59) # label(negated_conjecture). [clausify(9)].
% 0.81/1.11 16 union(c1,c2) = empty_set | c1 = empty_set. [copy(15),flip(b)].
% 0.81/1.11 17 union(c1,c2) = empty_set | empty_set = c2 # label(prove_th59) # label(negated_conjecture). [clausify(9)].
% 0.81/1.11 18 union(c1,c2) = empty_set | c2 = empty_set. [copy(17),flip(b)].
% 0.81/1.11 19 A = B | member(f3(B,A),B) | member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.81/1.11 20 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(2)].
% 0.81/1.11 21 union(c1,c2) != empty_set | empty_set != c1 | empty_set != c2 # label(prove_th59) # label(negated_conjecture). [clausify(9)].
% 0.81/1.11 22 union(c1,c2) != empty_set | c1 != empty_set | c2 != empty_set. [copy(21),flip(b),flip(c)].
% 0.81/1.11 23 A != B | subset(B,A) # label(equal_defn) # label(axiom). [clausify(3)].
% 0.81/1.11 25 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(1)].
% 0.81/1.11 29 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(5)].
% 0.81/1.11 32 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.81/1.11 33 A = B | -member(f3(B,A),B) | -member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.81/1.11 41 subset(union(c1,c2),empty_set) | c1 = empty_set. [resolve(23,a,16,a(flip))].
% 0.81/1.11 42 member(f3(A,B),union(B,C)) | B = A | member(f3(A,B),A). [resolve(25,b,19,c)].
% 0.81/1.11 44 member(f3(union(A,B),A),union(A,B)) | union(A,B) = A. [factor(42,a,c),flip(b)].
% 0.81/1.11 56 member(f3(union(A,B),C),A) | member(f3(union(A,B),C),B) | union(A,B) = C | member(f3(union(A,B),C),C). [resolve(32,a,19,b),flip(c)].
% 0.81/1.11 60 member(f3(union(A,A),B),A) | union(A,A) = B | member(f3(union(A,A),B),B). [factor(56,a,b)].
% 0.81/1.11 61 member(f3(union(A,B),A),A) | member(f3(union(A,B),A),B) | union(A,B) = A. [factor(56,a,d)].
% 0.81/1.11 64 member(f3(union(A,A),A),A) | union(A,A) = A. [factor(60,a,c)].
% 0.81/1.11 85 c1 = empty_set | -member(A,union(c1,c2)). [resolve(41,a,29,a),unit_del(c,20)].
% 0.81/1.11 90 c1 = A | member(f3(A,c1),A) | c1 = empty_set. [resolve(42,a,85,b)].
% 0.81/1.11 103 c1 = empty_set. [factor(90,a,c),unit_del(b,20)].
% 0.81/1.11 115 union(empty_set,c2) != empty_set | c2 != empty_set. [back_rewrite(22),rewrite([103(1),103(6)]),xx(b)].
% 0.81/1.11 116 union(empty_set,c2) = empty_set | c2 = empty_set. [back_rewrite(18),rewrite([103(1)])].
% 0.81/1.11 138 union(A,B) = A | -member(f3(union(A,B),A),A). [resolve(44,a,33,b),flip(b),merge(b)].
% 0.81/1.11 436 union(A,A) = A. [resolve(138,b,64,a),merge(b)].
% 0.81/1.11 475 member(f3(union(A,B),A),B) | union(A,B) = A. [resolve(61,a,138,b),merge(c)].
% 0.81/1.11 564 member(f3(union(A,B),B),A) | union(A,B) = B. [para(13(a,1),475(a,1,1)),rewrite([13(4)])].
% 0.81/1.11 597 c2 = empty_set | union(empty_set,c2) = c2. [para(116(a,1),564(a,1,1)),unit_del(b,20)].
% 0.81/1.11 610 c2 = empty_set. [para(597(b,1),116(a,1)),merge(b),merge(c)].
% 0.81/1.11 611 $F. [back_rewrite(115),rewrite([610(2),436(3),610(4)]),xx(a),xx(b)].
% 0.81/1.11
% 0.81/1.11 % SZS output end Refutation
% 0.81/1.11 ============================== end of proof ==========================
% 0.81/1.11
% 0.81/1.11 ============================== STATISTICS ============================
% 0.81/1.11
% 0.81/1.11 Given=108. Generated=1973. Kept=596. proofs=1.
% 0.81/1.11 Usable=70. Sos=267. Demods=5. Limbo=1, Disabled=280. Hints=0.
% 0.81/1.11 Megabytes=0.42.
% 0.81/1.11 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.81/1.11
% 0.81/1.11 ============================== end of statistics =====================
% 0.81/1.11
% 0.81/1.11 ============================== end of search =========================
% 0.81/1.11
% 0.81/1.11 THEOREM PROVED
% 0.81/1.11 % SZS status Theorem
% 0.81/1.11
% 0.81/1.11 Exiting with 1 proof.
% 0.81/1.11
% 0.81/1.11 Process 11549 exit (max_proofs) Sat Jul 9 23:31:41 2022
% 0.81/1.11 Prover9 interrupted
%------------------------------------------------------------------------------