TSTP Solution File: SET874+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET874+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 04:33:06 EDT 2022
% Result : Theorem 0.43s 1.01s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET874+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.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 : Mon Jul 11 07:11:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 12923 was started by sandbox2 on n023.cluster.edu,
% 0.43/1.00 Mon Jul 11 07:11:10 2022
% 0.43/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12769_n023.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_12769_n023.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (11 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (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].
% 0.43/1.00 5 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 -(all A all B set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B)) # label(t14_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00
% 0.43/1.00 ============================== end predicate elimination =============
% 0.43/1.00
% 0.43/1.00 Auto_denials: (non-Horn, no changes).
% 0.43/1.00
% 0.43/1.00 Term ordering decisions:
% 0.43/1.00
% 0.43/1.00 % Assigning unary symbol singleton kb_weight 0 and highest precedence (11).
% 0.43/1.00 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. unordered_pair=1. set_union2=1. f1=1. singleton=0.
% 0.43/1.01
% 0.43/1.01 ============================== end of process initial clauses ========
% 0.43/1.01
% 0.43/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.01
% 0.43/1.01 ============================== end of clauses for search =============
% 0.43/1.01
% 0.43/1.01 ============================== SEARCH ================================
% 0.43/1.01
% 0.43/1.01 % Starting search at 0.01 seconds.
% 0.43/1.01
% 0.43/1.01 ============================== PROOF =================================
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01 % SZS output start Refutation
% 0.43/1.01
% 0.43/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.43/1.01 % Length of proof is 17.
% 0.43/1.01 % Level of proof is 5.
% 0.43/1.01 % Maximum clause weight is 11.000.
% 0.43/1.01 % Given clauses 25.
% 0.43/1.01
% 0.43/1.01 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (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].
% 0.43/1.01 7 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 -(all A all B set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B)) # label(t14_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01 13 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom). [clausify(7)].
% 0.43/1.01 14 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.43/1.01 15 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(3)].
% 0.43/1.01 19 set_union2(singleton(c3),unordered_pair(c3,c4)) != unordered_pair(c3,c4) # label(t14_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 22 -in(A,B) | set_union2(singleton(A),B) = B # label(l23_zfmisc_1) # label(axiom). [clausify(8)].
% 0.43/1.01 23 -in(A,B) | set_union2(B,singleton(A)) = B. [copy(22),rewrite([15(3)])].
% 0.43/1.01 24 unordered_pair(A,B) != C | in(D,C) | D != A # label(d2_tarski) # label(axiom). [clausify(4)].
% 0.43/1.01 39 in(A,unordered_pair(B,C)) | A != C. [resolve(24,a,14,a)].
% 0.43/1.01 78 in(A,unordered_pair(A,B)). [resolve(39,b,13,a),rewrite([13(1),14(1)])].
% 0.43/1.01 81 set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B). [resolve(78,a,23,a),rewrite([15(3)])].
% 0.43/1.01 82 $F. [resolve(81,a,19,a)].
% 0.43/1.01
% 0.43/1.01 % SZS output end Refutation
% 0.43/1.01 ============================== end of proof ==========================
% 0.43/1.01
% 0.43/1.01 ============================== STATISTICS ============================
% 0.43/1.01
% 0.43/1.01 Given=25. Generated=324. Kept=68. proofs=1.
% 0.43/1.01 Usable=25. Sos=33. Demods=3. Limbo=2, Disabled=23. Hints=0.
% 0.43/1.01 Megabytes=0.10.
% 0.43/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.43/1.01
% 0.43/1.01 ============================== end of statistics =====================
% 0.43/1.01
% 0.43/1.01 ============================== end of search =========================
% 0.43/1.01
% 0.43/1.01 THEOREM PROVED
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01
% 0.43/1.01 Exiting with 1 proof.
% 0.43/1.01
% 0.43/1.01 Process 12923 exit (max_proofs) Mon Jul 11 07:11:10 2022
% 0.43/1.01 Prover9 interrupted
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