TSTP Solution File: SET630+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET630+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 04:30:59 EDT 2022
% Result : Theorem 0.46s 1.00s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET630+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 : n017.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 18:24:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.00 ============================== Prover9 ===============================
% 0.46/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.00 Process 9665 was started by sandbox2 on n017.cluster.edu,
% 0.46/1.00 Sun Jul 10 18:24:48 2022
% 0.46/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9296_n017.cluster.edu".
% 0.46/1.00 ============================== end of head ===========================
% 0.46/1.00
% 0.46/1.00 ============================== INPUT =================================
% 0.46/1.00
% 0.46/1.00 % Reading from file /tmp/Prover9_9296_n017.cluster.edu
% 0.46/1.00
% 0.46/1.00 set(prolog_style_variables).
% 0.46/1.00 set(auto2).
% 0.46/1.00 % set(auto2) -> set(auto).
% 0.46/1.00 % set(auto) -> set(auto_inference).
% 0.46/1.00 % set(auto) -> set(auto_setup).
% 0.46/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.00 % set(auto) -> set(auto_limits).
% 0.46/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.00 % set(auto) -> set(auto_denials).
% 0.46/1.00 % set(auto) -> set(auto_process).
% 0.46/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.00 % set(auto2) -> assign(stats, some).
% 0.46/1.00 % set(auto2) -> clear(echo_input).
% 0.46/1.00 % set(auto2) -> set(quiet).
% 0.46/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.00 % set(auto2) -> clear(print_given).
% 0.46/1.00 assign(lrs_ticks,-1).
% 0.46/1.00 assign(sos_limit,10000).
% 0.46/1.00 assign(order,kbo).
% 0.46/1.00 set(lex_order_vars).
% 0.46/1.00 clear(print_given).
% 0.46/1.00
% 0.46/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.46/1.00
% 0.46/1.00 ============================== end of input ==========================
% 0.46/1.00
% 0.46/1.00 % From the command line: assign(max_seconds, 300).
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.00
% 0.46/1.00 % Formulas that are not ordinary clauses:
% 0.46/1.00 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 2 (all B all C all D (intersect(B,union(C,D)) <-> intersect(B,C) | intersect(B,D))) # label(intersect_with_union) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 3 (all B all C disjoint(intersection(B,C),difference(B,C))) # label(intersection_and_union_disjoint) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 4 (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].
% 0.46/1.00 5 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 6 (all B all C (disjoint(B,C) <-> -intersect(B,C))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 7 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 8 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 9 (all B all C symmetric_difference(B,C) = symmetric_difference(C,B)) # label(commutativity_of_symmetric_difference) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 10 (all B all C (intersect(B,C) -> intersect(C,B))) # label(symmetry_of_intersect) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 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].
% 0.46/1.00 12 -(all B all C disjoint(intersection(B,C),symmetric_difference(B,C))) # label(prove_intersection_and_symmetric_difference_disjoint) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.00
% 0.46/1.00 ============================== end of process non-clausal formulas ===
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.00
% 0.46/1.00 ============================== PREDICATE ELIMINATION =================
% 0.46/1.00
% 0.46/1.00 ============================== end predicate elimination =============
% 0.46/1.00
% 0.46/1.00 Auto_denials: (non-Horn, no changes).
% 0.46/1.00
% 0.46/1.00 Term ordering decisions:
% 0.46/1.00 Function symbol KB weights: c1=1. c2=1. intersection=1. union=1. difference=1. symmetric_difference=1. f1=1. f2=1.
% 0.46/1.00
% 0.46/1.00 ============================== end of process initial clauses ========
% 0.46/1.00
% 0.46/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.00
% 0.46/1.00 ============================== end of clauses for search =============
% 0.46/1.00
% 0.46/1.00 ============================== SEARCH ================================
% 0.46/1.00
% 0.46/1.00 % Starting search at 0.01 seconds.
% 0.46/1.00
% 0.46/1.00 ============================== PROOF =================================
% 0.46/1.00 % SZS status Theorem
% 0.46/1.00 % SZS output start Refutation
% 0.46/1.00
% 0.46/1.00 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.46/1.00 % Length of proof is 21.
% 0.46/1.00 % Level of proof is 5.
% 0.46/1.00 % Maximum clause weight is 11.000.
% 0.46/1.00 % Given clauses 27.
% 0.46/1.00
% 0.46/1.00 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 2 (all B all C all D (intersect(B,union(C,D)) <-> intersect(B,C) | intersect(B,D))) # label(intersect_with_union) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 3 (all B all C disjoint(intersection(B,C),difference(B,C))) # label(intersection_and_union_disjoint) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 6 (all B all C (disjoint(B,C) <-> -intersect(B,C))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 8 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 12 -(all B all C disjoint(intersection(B,C),symmetric_difference(B,C))) # label(prove_intersection_and_symmetric_difference_disjoint) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.00 13 disjoint(A,B) | intersect(A,B) # label(disjoint_defn) # label(axiom). [clausify(6)].
% 0.46/1.00 14 disjoint(intersection(A,B),difference(A,B)) # label(intersection_and_union_disjoint) # label(axiom). [clausify(3)].
% 0.46/1.00 16 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(8)].
% 0.46/1.00 18 union(difference(A,B),difference(B,A)) = symmetric_difference(A,B) # label(symmetric_difference_defn) # label(axiom). [clausify(1)].
% 0.46/1.00 19 symmetric_difference(A,B) = union(difference(A,B),difference(B,A)). [copy(18),flip(a)].
% 0.46/1.00 21 -disjoint(A,B) | -intersect(A,B) # label(disjoint_defn) # label(axiom). [clausify(6)].
% 0.46/1.00 22 -disjoint(intersection(c1,c2),symmetric_difference(c1,c2)) # label(prove_intersection_and_symmetric_difference_disjoint) # label(negated_conjecture). [clausify(12)].
% 0.46/1.00 23 -disjoint(intersection(c1,c2),union(difference(c1,c2),difference(c2,c1))). [copy(22),rewrite([19(6)])].
% 0.46/1.00 34 -intersect(A,union(B,C)) | intersect(A,B) | intersect(A,C) # label(intersect_with_union) # label(axiom). [clausify(2)].
% 0.46/1.00 40 disjoint(intersection(A,B),difference(B,A)). [para(16(a,1),14(a,1))].
% 0.46/1.00 41 -intersect(intersection(A,B),difference(A,B)). [resolve(21,a,14,a)].
% 0.46/1.00 42 intersect(intersection(c1,c2),union(difference(c1,c2),difference(c2,c1))). [resolve(23,a,13,a)].
% 0.46/1.00 70 -intersect(intersection(A,B),difference(B,A)). [resolve(40,a,21,a)].
% 0.46/1.00 74 -intersect(intersection(A,B),union(difference(A,B),difference(B,A))). [ur(34,b,41,a,c,70,a)].
% 0.46/1.00 75 $F. [resolve(74,a,42,a)].
% 0.46/1.00
% 0.46/1.00 % SZS output end Refutation
% 0.46/1.00 ============================== end of proof ==========================
% 0.46/1.00
% 0.46/1.00 ============================== STATISTICS ============================
% 0.46/1.00
% 0.46/1.00 Given=27. Generated=94. Kept=60. proofs=1.
% 0.46/1.00 Usable=27. Sos=30. Demods=3. Limbo=1, Disabled=23. Hints=0.
% 0.46/1.00 Megabytes=0.09.
% 0.46/1.00 User_CPU=0.01, System_CPU=0.00, Wall_clock=1.
% 0.46/1.00
% 0.46/1.00 ============================== end of statistics =====================
% 0.46/1.00
% 0.46/1.00 ============================== end of search =========================
% 0.46/1.00
% 0.46/1.00 THEOREM PROVED
% 0.46/1.00 % SZS status Theorem
% 0.46/1.00
% 0.46/1.00 Exiting with 1 proof.
% 0.46/1.00
% 0.46/1.00 Process 9665 exit (max_proofs) Sun Jul 10 18:24:49 2022
% 0.46/1.00 Prover9 interrupted
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