TSTP Solution File: SET908+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 04:33:19 EDT 2022
% Result : Theorem 0.76s 1.05s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Sun Jul 10 19:14:22 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 29137 was started by sandbox2 on n021.cluster.edu,
% 0.76/1.03 Sun Jul 10 19:14:23 2022
% 0.76/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28984_n021.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_28984_n021.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (12 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 6 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 7 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 9 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 10 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 11 -(all A all B set_union2(singleton(A),B) != empty_set) # label(t49_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03
% 0.76/1.03 ============================== end of process non-clausal formulas ===
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03
% 0.76/1.03 ============================== PREDICATE ELIMINATION =================
% 0.76/1.03
% 0.76/1.03 ============================== end predicate elimination =============
% 0.76/1.03
% 0.76/1.03 Auto_denials: (non-Horn, no changes).
% 0.76/1.03
% 0.76/1.03 Term ordering decisions:
% 0.76/1.03 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_union2=1. f1=1. singleton=1. f2=1. f3=1.
% 0.76/1.03
% 0.76/1.03 ============================== end of process initial clauses ========
% 0.76/1.03
% 0.76/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.05
% 0.76/1.05 ============================== end of clauses for search =============
% 0.76/1.05
% 0.76/1.05 ============================== SEARCH ================================
% 0.76/1.05
% 0.76/1.05 % Starting search at 0.01 seconds.
% 0.76/1.05
% 0.76/1.05 ============================== PROOF =================================
% 0.76/1.05 % SZS status Theorem
% 0.76/1.05 % SZS output start Refutation
% 0.76/1.05
% 0.76/1.05 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.76/1.05 % Length of proof is 18.
% 0.76/1.05 % Level of proof is 5.
% 0.76/1.05 % Maximum clause weight is 11.000.
% 0.76/1.05 % Given clauses 41.
% 0.76/1.05
% 0.76/1.05 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.05 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.05 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.05 5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.05 8 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.05 11 -(all A all B set_union2(singleton(A),B) != empty_set) # label(t49_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.05 14 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom). [clausify(8)].
% 0.76/1.05 15 set_union2(singleton(c3),c4) = empty_set # label(t49_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.76/1.05 16 empty_set = set_union2(singleton(c3),c4). [copy(15),flip(a)].
% 0.76/1.05 17 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(2)].
% 0.76/1.05 24 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(4)].
% 0.76/1.05 25 set_union2(c4,singleton(c3)) != A | -in(B,A). [copy(24),rewrite([16(1),17(4)])].
% 0.76/1.05 29 singleton(A) != B | in(C,B) | C != A # label(d1_tarski) # label(axiom). [clausify(3)].
% 0.76/1.05 31 set_union2(A,B) != C | in(D,C) | -in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(5)].
% 0.76/1.05 58 -in(A,set_union2(c4,singleton(c3))). [ur(25,a,17,a),rewrite([17(4)])].
% 0.76/1.05 71 in(A,singleton(B)) | A != B. [resolve(29,a,14,a(flip)),rewrite([14(3)])].
% 0.76/1.05 211 in(A,singleton(A)). [resolve(71,b,14,a),rewrite([14(1)])].
% 0.76/1.05 250 $F. [ur(31,b,58,a,c,211,a),flip(a),xx(a)].
% 0.76/1.05
% 0.76/1.05 % SZS output end Refutation
% 0.76/1.05 ============================== end of proof ==========================
% 0.76/1.05
% 0.76/1.05 ============================== STATISTICS ============================
% 0.76/1.05
% 0.76/1.05 Given=41. Generated=773. Kept=234. proofs=1.
% 0.76/1.05 Usable=39. Sos=146. Demods=4. Limbo=16, Disabled=54. Hints=0.
% 0.76/1.05 Megabytes=0.21.
% 0.76/1.05 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.76/1.05
% 0.76/1.05 ============================== end of statistics =====================
% 0.76/1.05
% 0.76/1.05 ============================== end of search =========================
% 0.76/1.05
% 0.76/1.05 THEOREM PROVED
% 0.76/1.05 % SZS status Theorem
% 0.76/1.05
% 0.76/1.05 Exiting with 1 proof.
% 0.76/1.05
% 0.76/1.05 Process 29137 exit (max_proofs) Sun Jul 10 19:14:23 2022
% 0.76/1.05 Prover9 interrupted
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