TSTP Solution File: SET909+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 0.74s 1.06s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 16:59:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.02 ============================== Prover9 ===============================
% 0.42/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.02 Process 11397 was started by sandbox2 on n023.cluster.edu,
% 0.42/1.02 Sun Jul 10 16:59:26 2022
% 0.42/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11099_n023.cluster.edu".
% 0.42/1.02 ============================== end of head ===========================
% 0.42/1.02
% 0.42/1.02 ============================== INPUT =================================
% 0.42/1.02
% 0.42/1.02 % Reading from file /tmp/Prover9_11099_n023.cluster.edu
% 0.42/1.02
% 0.42/1.02 set(prolog_style_variables).
% 0.42/1.02 set(auto2).
% 0.42/1.02 % set(auto2) -> set(auto).
% 0.42/1.02 % set(auto) -> set(auto_inference).
% 0.42/1.02 % set(auto) -> set(auto_setup).
% 0.42/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.02 % set(auto) -> set(auto_limits).
% 0.42/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.02 % set(auto) -> set(auto_denials).
% 0.42/1.02 % set(auto) -> set(auto_process).
% 0.42/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.02 % set(auto2) -> assign(stats, some).
% 0.42/1.02 % set(auto2) -> clear(echo_input).
% 0.42/1.02 % set(auto2) -> set(quiet).
% 0.42/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.02 % set(auto2) -> clear(print_given).
% 0.42/1.02 assign(lrs_ticks,-1).
% 0.42/1.02 assign(sos_limit,10000).
% 0.42/1.02 assign(order,kbo).
% 0.42/1.02 set(lex_order_vars).
% 0.42/1.02 clear(print_given).
% 0.42/1.02
% 0.42/1.02 % formulas(sos). % not echoed (13 formulas)
% 0.42/1.02
% 0.42/1.02 ============================== end of input ==========================
% 0.42/1.02
% 0.42/1.02 % From the command line: assign(max_seconds, 300).
% 0.42/1.02
% 0.42/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.02
% 0.42/1.02 % Formulas that are not ordinary clauses:
% 0.42/1.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 5 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 6 (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].
% 0.42/1.02 7 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 8 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 9 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 10 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 11 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 12 -(all A all B all C set_union2(unordered_pair(A,B),C) != empty_set) # label(t50_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/1.02
% 0.42/1.02 ============================== end of process non-clausal formulas ===
% 0.42/1.02
% 0.42/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.02
% 0.42/1.02 ============================== PREDICATE ELIMINATION =================
% 0.42/1.02
% 0.42/1.02 ============================== end predicate elimination =============
% 0.42/1.02
% 0.42/1.02 Auto_denials: (non-Horn, no changes).
% 0.42/1.02
% 0.42/1.02 Term ordering decisions:
% 0.42/1.02
% 0.42/1.02 % Assigning unary symbol f1 kb_weight 0 and highest precedence (14).
% 0.74/1.06 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. unordered_pair=1. f2=1. f3=1. f1=0.
% 0.74/1.06
% 0.74/1.06 ============================== end of process initial clauses ========
% 0.74/1.06
% 0.74/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.06
% 0.74/1.06 ============================== end of clauses for search =============
% 0.74/1.06
% 0.74/1.06 ============================== SEARCH ================================
% 0.74/1.06
% 0.74/1.06 % Starting search at 0.01 seconds.
% 0.74/1.06
% 0.74/1.06 ============================== PROOF =================================
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06 % SZS output start Refutation
% 0.74/1.06
% 0.74/1.06 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.74/1.06 % Length of proof is 20.
% 0.74/1.06 % Level of proof is 5.
% 0.74/1.06 % Maximum clause weight is 11.000.
% 0.74/1.06 % Given clauses 52.
% 0.74/1.06
% 0.74/1.06 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 5 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 6 (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].
% 0.74/1.06 9 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 12 -(all A all B all C set_union2(unordered_pair(A,B),C) != empty_set) # label(t50_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.06 15 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom). [clausify(9)].
% 0.74/1.06 16 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.74/1.06 17 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(3)].
% 0.74/1.06 19 set_union2(unordered_pair(c3,c4),c5) = empty_set # label(t50_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.74/1.06 20 empty_set = set_union2(c5,unordered_pair(c3,c4)). [copy(19),rewrite([17(5)]),flip(a)].
% 0.74/1.06 25 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(4)].
% 0.74/1.06 26 set_union2(c5,unordered_pair(c3,c4)) != A | -in(B,A). [copy(25),rewrite([20(1)])].
% 0.74/1.06 29 unordered_pair(A,B) != C | in(D,C) | D != A # label(d2_tarski) # label(axiom). [clausify(5)].
% 0.74/1.06 32 set_union2(A,B) != C | in(D,C) | -in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 0.74/1.06 64 -in(A,set_union2(c5,unordered_pair(c3,c4))). [ur(26,a,17,a),rewrite([17(5)])].
% 0.74/1.06 70 in(A,unordered_pair(B,C)) | A != C. [resolve(29,a,16,a)].
% 0.74/1.06 256 in(A,unordered_pair(A,B)). [resolve(70,b,15,a),rewrite([15(1),16(1)])].
% 0.74/1.06 325 $F. [ur(32,b,64,a,c,256,a),flip(a),xx(a)].
% 0.74/1.06
% 0.74/1.06 % SZS output end Refutation
% 0.74/1.06 ============================== end of proof ==========================
% 0.74/1.06
% 0.74/1.06 ============================== STATISTICS ============================
% 0.74/1.06
% 0.74/1.06 Given=52. Generated=1234. Kept=309. proofs=1.
% 0.74/1.06 Usable=50. Sos=196. Demods=5. Limbo=20, Disabled=67. Hints=0.
% 0.74/1.06 Megabytes=0.28.
% 0.74/1.06 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.74/1.06
% 0.74/1.06 ============================== end of statistics =====================
% 0.74/1.06
% 0.74/1.06 ============================== end of search =========================
% 0.74/1.06
% 0.74/1.06 THEOREM PROVED
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06
% 0.74/1.06 Exiting with 1 proof.
% 0.74/1.06
% 0.74/1.06 Process 11397 exit (max_proofs) Sun Jul 10 16:59:26 2022
% 0.74/1.06 Prover9 interrupted
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