TSTP Solution File: SEU264+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n006.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 13:30:28 EDT 2022

% Result   : Theorem 0.77s 1.02s
% Output   : Refutation 0.77s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jun 19 16:54:55 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.44/1.02  ============================== Prover9 ===============================
% 0.44/1.02  Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02  Process 6475 was started by sandbox on n006.cluster.edu,
% 0.44/1.02  Sun Jun 19 16:54:56 2022
% 0.44/1.02  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6322_n006.cluster.edu".
% 0.44/1.02  ============================== end of head ===========================
% 0.44/1.02  
% 0.44/1.02  ============================== INPUT =================================
% 0.44/1.02  
% 0.44/1.02  % Reading from file /tmp/Prover9_6322_n006.cluster.edu
% 0.44/1.02  
% 0.44/1.02  set(prolog_style_variables).
% 0.44/1.02  set(auto2).
% 0.44/1.02      % set(auto2) -> set(auto).
% 0.44/1.02      % set(auto) -> set(auto_inference).
% 0.44/1.02      % set(auto) -> set(auto_setup).
% 0.44/1.02      % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02      % set(auto) -> set(auto_limits).
% 0.44/1.02      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02      % set(auto) -> set(auto_denials).
% 0.44/1.02      % set(auto) -> set(auto_process).
% 0.44/1.02      % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02      % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02      % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02      % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02      % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02      % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02      % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02      % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02      % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02      % set(auto2) -> assign(stats, some).
% 0.44/1.02      % set(auto2) -> clear(echo_input).
% 0.44/1.02      % set(auto2) -> set(quiet).
% 0.44/1.02      % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02      % set(auto2) -> clear(print_given).
% 0.44/1.02  assign(lrs_ticks,-1).
% 0.44/1.02  assign(sos_limit,10000).
% 0.44/1.02  assign(order,kbo).
% 0.44/1.02  set(lex_order_vars).
% 0.44/1.02  clear(print_given).
% 0.44/1.02  
% 0.44/1.02  % formulas(sos).  % not echoed (18 formulas)
% 0.44/1.02  
% 0.44/1.02  ============================== end of input ==========================
% 0.44/1.02  
% 0.44/1.02  % From the command line: assign(max_seconds, 300).
% 0.44/1.02  
% 0.44/1.02  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02  
% 0.44/1.02  % Formulas that are not ordinary clauses:
% 0.44/1.02  1 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  2 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  3 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  4 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  5 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  6 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  7 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  8 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  9 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  10 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  11 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  12 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  13 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  14 (all A all B all C (relation_of2_as_subset(C,A,B) -> subset(relation_dom(C),A) & subset(relation_rng(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  15 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(relation_rng(D),B) -> relation_of2_as_subset(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.02  16 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause).  [assumption].
% 0.77/1.02  17 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.77/1.02  18 -(all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(A,B) -> relation_of2_as_subset(D,C,B)))) # label(t16_relset_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.77/1.02  
% 0.77/1.02  ============================== end of process non-clausal formulas ===
% 0.77/1.02  
% 0.77/1.02  ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.02  
% 0.77/1.02  ============================== PREDICATE ELIMINATION =================
% 0.77/1.02  19 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom).  [clausify(17)].
% 0.77/1.02  20 element(f2(A),A) # label(existence_m1_subset_1) # label(axiom).  [clausify(10)].
% 0.77/1.02  Derived: subset(f2(powerset(A)),A).  [resolve(19,a,20,a)].
% 0.77/1.02  21 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom).  [clausify(17)].
% 0.77/1.02  22 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom).  [clausify(1)].
% 0.77/1.02  Derived: relation(f2(powerset(cartesian_product2(A,B)))).  [resolve(22,a,20,a)].
% 0.77/1.02  Derived: relation(A) | -subset(A,cartesian_product2(B,C)).  [resolve(22,a,21,a)].
% 0.77/1.02  23 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom).  [clausify(8)].
% 0.77/1.02  Derived: -relation_of2_as_subset(A,B,C) | subset(A,cartesian_product2(B,C)).  [resolve(23,b,19,a)].
% 0.77/1.02  Derived: -relation_of2_as_subset(A,B,C) | relation(A).  [resolve(23,b,22,a)].
% 0.77/1.02  24 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom).  [clausify(12)].
% 0.77/1.02  25 relation_of2(f1(A,B),A,B) # label(existence_m1_relset_1) # label(axiom).  [clausify(9)].
% 0.77/1.02  26 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom).  [clausify(12)].
% 0.77/1.02  Derived: relation_of2_as_subset(f1(A,B),A,B).  [resolve(24,b,25,a)].
% 0.77/1.02  
% 0.77/1.02  ============================== end predicate elimination =============
% 0.77/1.02  
% 0.77/1.02  Auto_denials:
% 0.77/1.02    % copying label t16_relset_1 to answer in negative clause
% 0.77/1.02  
% 0.77/1.02  Term ordering decisions:
% 0.77/1.02  Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. cartesian_product2=1. f1=1. f3=1. relation_rng=1. powerset=1. relation_dom=1. f2=1.
% 0.77/1.02  
% 0.77/1.02  ============================== end of process initial clauses ========
% 0.77/1.02  
% 0.77/1.02  ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.02  
% 0.77/1.02  ============================== end of clauses for search =============
% 0.77/1.02  
% 0.77/1.02  ============================== SEARCH ================================
% 0.77/1.02  
% 0.77/1.02  % Starting search at 0.01 seconds.
% 0.77/1.02  
% 0.77/1.02  ============================== PROOF =================================
% 0.77/1.02  % SZS status Theorem
% 0.77/1.02  % SZS output start Refutation
% 0.77/1.02  
% 0.77/1.02  % Proof 1 at 0.01 (+ 0.00) seconds: t16_relset_1.
% 0.77/1.02  % Length of proof is 14.
% 0.77/1.02  % Level of proof is 4.
% 0.77/1.02  % Maximum clause weight is 12.000.
% 0.77/1.02  % Given clauses 14.
% 0.77/1.02  
% 0.77/1.02  14 (all A all B all C (relation_of2_as_subset(C,A,B) -> subset(relation_dom(C),A) & subset(relation_rng(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.77/1.02  15 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(relation_rng(D),B) -> relation_of2_as_subset(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.77/1.02  16 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause).  [assumption].
% 0.77/1.02  18 -(all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(A,B) -> relation_of2_as_subset(D,C,B)))) # label(t16_relset_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.77/1.02  28 subset(c1,c2) # label(t16_relset_1) # label(negated_conjecture).  [clausify(18)].
% 0.77/1.02  29 relation_of2_as_subset(c4,c3,c1) # label(t16_relset_1) # label(negated_conjecture).  [clausify(18)].
% 0.77/1.02  31 -relation_of2_as_subset(c4,c3,c2) # label(t16_relset_1) # label(negated_conjecture) # answer(t16_relset_1).  [clausify(18)].
% 0.77/1.02  33 -relation_of2_as_subset(A,B,C) | subset(relation_rng(A),C) # label(t12_relset_1) # label(axiom).  [clausify(14)].
% 0.77/1.02  34 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(axiom).  [clausify(16)].
% 0.77/1.02  35 -relation_of2_as_subset(A,B,C) | -subset(relation_rng(A),D) | relation_of2_as_subset(A,B,D) # label(t14_relset_1) # label(axiom).  [clausify(15)].
% 0.77/1.02  42 subset(relation_rng(c4),c1).  [ur(33,a,29,a)].
% 0.77/1.02  46 -subset(relation_rng(c4),c2) # answer(t16_relset_1).  [ur(35,a,29,a,c,31,a)].
% 0.77/1.02  63 -subset(relation_rng(c4),c1) # answer(t16_relset_1).  [ur(34,b,28,a,c,46,a)].
% 0.77/1.02  64 $F # answer(t16_relset_1).  [resolve(63,a,42,a)].
% 0.77/1.02  
% 0.77/1.02  % SZS output end Refutation
% 0.77/1.02  ============================== end of proof ==========================
% 0.77/1.02  
% 0.77/1.02  ============================== STATISTICS ============================
% 0.77/1.02  
% 0.77/1.02  Given=14. Generated=46. Kept=37. proofs=1.
% 0.77/1.02  Usable=14. Sos=17. Demods=0. Limbo=4, Disabled=24. Hints=0.
% 0.77/1.02  Megabytes=0.07.
% 0.77/1.02  User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.77/1.02  
% 0.77/1.02  ============================== end of statistics =====================
% 0.77/1.02  
% 0.77/1.02  ============================== end of search =========================
% 0.77/1.02  
% 0.77/1.02  THEOREM PROVED
% 0.77/1.02  % SZS status Theorem
% 0.77/1.02  
% 0.77/1.02  Exiting with 1 proof.
% 0.77/1.02  
% 0.77/1.02  Process 6475 exit (max_proofs) Sun Jun 19 16:54:56 2022
% 0.77/1.02  Prover9 interrupted
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