TSTP Solution File: SET949+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 04:33:38 EDT 2022
% Result : Theorem 0.40s 1.00s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.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 : Sun Jul 10 13:15:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/0.99 ============================== Prover9 ===============================
% 0.40/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.99 Process 30182 was started by sandbox on n013.cluster.edu,
% 0.40/0.99 Sun Jul 10 13:15:45 2022
% 0.40/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30029_n013.cluster.edu".
% 0.40/0.99 ============================== end of head ===========================
% 0.40/0.99
% 0.40/0.99 ============================== INPUT =================================
% 0.40/0.99
% 0.40/0.99 % Reading from file /tmp/Prover9_30029_n013.cluster.edu
% 0.40/0.99
% 0.40/0.99 set(prolog_style_variables).
% 0.40/0.99 set(auto2).
% 0.40/0.99 % set(auto2) -> set(auto).
% 0.40/0.99 % set(auto) -> set(auto_inference).
% 0.40/0.99 % set(auto) -> set(auto_setup).
% 0.40/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.99 % set(auto) -> set(auto_limits).
% 0.40/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.99 % set(auto) -> set(auto_denials).
% 0.40/0.99 % set(auto) -> set(auto_process).
% 0.40/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.99 % set(auto2) -> assign(stats, some).
% 0.40/0.99 % set(auto2) -> clear(echo_input).
% 0.40/0.99 % set(auto2) -> set(quiet).
% 0.40/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.99 % set(auto2) -> clear(print_given).
% 0.40/0.99 assign(lrs_ticks,-1).
% 0.40/0.99 assign(sos_limit,10000).
% 0.40/0.99 assign(order,kbo).
% 0.40/0.99 set(lex_order_vars).
% 0.40/0.99 clear(print_given).
% 0.40/0.99
% 0.40/0.99 % formulas(sos). % not echoed (8 formulas)
% 0.40/0.99
% 0.40/0.99 ============================== end of input ==========================
% 0.40/0.99
% 0.40/0.99 % From the command line: assign(max_seconds, 300).
% 0.40/0.99
% 0.40/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.99
% 0.40/0.99 % Formulas that are not ordinary clauses:
% 0.40/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 3 (all A all B all C (C = cartesian_product2(A,B) <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 4 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 5 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.99 8 -(all A all B all C -(in(A,cartesian_product2(B,C)) & (all D all E ordered_pair(D,E) != A))) # label(t102_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/0.99
% 0.40/0.99 ============================== end of process non-clausal formulas ===
% 0.40/0.99
% 0.40/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.40/0.99
% 0.40/0.99 ============================== PREDICATE ELIMINATION =================
% 0.40/0.99
% 0.40/0.99 ============================== end predicate elimination =============
% 0.40/0.99
% 0.40/0.99 Auto_denials: (non-Horn, no changes).
% 0.40/0.99
% 0.40/0.99 Term ordering decisions:
% 0.40/0.99
% 0.40/0.99 % Assigning unary symbol singleton kb_weight 0 and highest precedence (17).
% 0.40/0.99 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. f3=1. f4=1. f5=1. f1=1. f2=1. singleton=0.
% 0.40/0.99
% 0.40/0.99 ============================== end of process initial clauses ========
% 0.40/0.99
% 0.40/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.40/0.99
% 0.40/0.99 ============================== end of clauses for search =============
% 0.40/0.99
% 0.40/0.99 ============================== SEARCH ================================
% 0.40/1.00
% 0.40/1.00 % Starting search at 0.01 seconds.
% 0.40/1.00
% 0.40/1.00 ============================== PROOF =================================
% 0.40/1.00 % SZS status Theorem
% 0.40/1.00 % SZS output start Refutation
% 0.40/1.00
% 0.40/1.00 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.40/1.00 % Length of proof is 13.
% 0.40/1.00 % Level of proof is 4.
% 0.40/1.00 % Maximum clause weight is 28.000.
% 0.40/1.00 % Given clauses 15.
% 0.40/1.00
% 0.40/1.00 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 3 (all A all B all C (C = cartesian_product2(A,B) <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 4 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 8 -(all A all B all C -(in(A,cartesian_product2(B,C)) & (all D all E ordered_pair(D,E) != A))) # label(t102_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/1.00 10 in(c3,cartesian_product2(c4,c5)) # label(t102_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.40/1.00 11 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.40/1.00 12 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(4)].
% 0.40/1.00 13 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(12),rewrite([11(4)])].
% 0.40/1.00 21 ordered_pair(A,B) != c3 # label(t102_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.40/1.00 22 unordered_pair(singleton(A),unordered_pair(A,B)) != c3. [copy(21),rewrite([13(1)])].
% 0.40/1.00 28 cartesian_product2(A,B) != C | -in(D,C) | ordered_pair(f1(A,B,C,D),f2(A,B,C,D)) = D # label(d2_zfmisc_1) # label(axiom). [clausify(3)].
% 0.40/1.00 29 cartesian_product2(A,B) != C | -in(D,C) | unordered_pair(singleton(f1(A,B,C,D)),unordered_pair(f1(A,B,C,D),f2(A,B,C,D))) = D. [copy(28),rewrite([13(6)])].
% 0.40/1.00 82 $F. [ur(29,b,10,a,c,22,a),flip(a),xx(a)].
% 0.40/1.00
% 0.40/1.00 % SZS output end Refutation
% 0.40/1.00 ============================== end of proof ==========================
% 0.40/1.00
% 0.40/1.00 ============================== STATISTICS ============================
% 0.40/1.00
% 0.40/1.00 Given=15. Generated=87. Kept=66. proofs=1.
% 0.40/1.00 Usable=15. Sos=45. Demods=2. Limbo=6, Disabled=16. Hints=0.
% 0.40/1.00 Megabytes=0.14.
% 0.40/1.00 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.40/1.00
% 0.40/1.00 ============================== end of statistics =====================
% 0.40/1.00
% 0.40/1.00 ============================== end of search =========================
% 0.40/1.00
% 0.40/1.00 THEOREM PROVED
% 0.40/1.00 % SZS status Theorem
% 0.40/1.00
% 0.40/1.00 Exiting with 1 proof.
% 0.40/1.00
% 0.40/1.00 Process 30182 exit (max_proofs) Sun Jul 10 13:15:45 2022
% 0.40/1.00 Prover9 interrupted
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