TSTP Solution File: SET984+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 04:33:51 EDT 2022
% Result : Theorem 0.76s 1.04s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n005.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 Jul 10 06:36:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/1.01 ============================== Prover9 ===============================
% 0.47/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.01 Process 27989 was started by sandbox2 on n005.cluster.edu,
% 0.47/1.01 Sun Jul 10 06:36:37 2022
% 0.47/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27836_n005.cluster.edu".
% 0.47/1.01 ============================== end of head ===========================
% 0.47/1.01
% 0.47/1.01 ============================== INPUT =================================
% 0.47/1.01
% 0.47/1.01 % Reading from file /tmp/Prover9_27836_n005.cluster.edu
% 0.47/1.01
% 0.47/1.01 set(prolog_style_variables).
% 0.47/1.01 set(auto2).
% 0.47/1.01 % set(auto2) -> set(auto).
% 0.47/1.01 % set(auto) -> set(auto_inference).
% 0.47/1.01 % set(auto) -> set(auto_setup).
% 0.47/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.01 % set(auto) -> set(auto_limits).
% 0.47/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.01 % set(auto) -> set(auto_denials).
% 0.47/1.01 % set(auto) -> set(auto_process).
% 0.47/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.01 % set(auto2) -> assign(stats, some).
% 0.47/1.01 % set(auto2) -> clear(echo_input).
% 0.47/1.01 % set(auto2) -> set(quiet).
% 0.47/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.01 % set(auto2) -> clear(print_given).
% 0.47/1.01 assign(lrs_ticks,-1).
% 0.47/1.01 assign(sos_limit,10000).
% 0.47/1.01 assign(order,kbo).
% 0.47/1.01 set(lex_order_vars).
% 0.47/1.01 clear(print_given).
% 0.47/1.01
% 0.47/1.01 % formulas(sos). % not echoed (12 formulas)
% 0.47/1.01
% 0.47/1.01 ============================== end of input ==========================
% 0.47/1.01
% 0.47/1.01 % From the command line: assign(max_seconds, 300).
% 0.47/1.01
% 0.47/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.01
% 0.47/1.01 % Formulas that are not ordinary clauses:
% 0.47/1.01 1 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 2 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 3 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 4 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 5 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 6 (all A all B (cartesian_product2(A,B) = empty_set <-> A = empty_set | B = empty_set)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 7 (all A all B all C all D cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 8 (all A all B all C all D (cartesian_product2(A,B) = cartesian_product2(C,D) -> A = empty_set | B = empty_set | A = C & B = D)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 9 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 10 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.01 11 -(all A all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) -> cartesian_product2(A,B) = empty_set | subset(A,C) & subset(B,D))) # label(t138_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.47/1.01
% 0.47/1.01 ============================== end of process non-clausal formulas ===
% 0.47/1.01
% 0.47/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.01
% 0.47/1.01 ============================== PREDICATE ELIMINATION =================
% 0.47/1.01
% 0.47/1.01 ============================== end predicate elimination =============
% 0.76/1.04
% 0.76/1.04 Auto_denials: (non-Horn, no changes).
% 0.76/1.04
% 0.76/1.04 Term ordering decisions:
% 0.76/1.04 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cartesian_product2=1. set_intersection2=1.
% 0.76/1.04
% 0.76/1.04 ============================== end of process initial clauses ========
% 0.76/1.04
% 0.76/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.04
% 0.76/1.04 ============================== end of clauses for search =============
% 0.76/1.04
% 0.76/1.04 ============================== SEARCH ================================
% 0.76/1.04
% 0.76/1.04 % Starting search at 0.01 seconds.
% 0.76/1.04
% 0.76/1.04 ============================== PROOF =================================
% 0.76/1.04 % SZS status Theorem
% 0.76/1.04 % SZS output start Refutation
% 0.76/1.04
% 0.76/1.04 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.76/1.04 % Length of proof is 28.
% 0.76/1.04 % Level of proof is 7.
% 0.76/1.04 % Maximum clause weight is 16.000.
% 0.76/1.04 % Given clauses 46.
% 0.76/1.04
% 0.76/1.04 1 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 6 (all A all B (cartesian_product2(A,B) = empty_set <-> A = empty_set | B = empty_set)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 7 (all A all B all C all D cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 8 (all A all B all C all D (cartesian_product2(A,B) = cartesian_product2(C,D) -> A = empty_set | B = empty_set | A = C & B = D)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 9 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 10 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 11 -(all A all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) -> cartesian_product2(A,B) = empty_set | subset(A,C) & subset(B,D))) # label(t138_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.04 16 subset(set_intersection2(A,B),A) # label(t17_xboole_1) # label(axiom). [clausify(9)].
% 0.76/1.04 17 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(1)].
% 0.76/1.04 18 subset(cartesian_product2(c3,c4),cartesian_product2(c5,c6)) # label(t138_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.76/1.04 19 cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) # label(t123_zfmisc_1) # label(axiom). [clausify(7)].
% 0.76/1.04 20 set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)). [copy(19),flip(a)].
% 0.76/1.04 22 cartesian_product2(c3,c4) != empty_set # label(t138_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.76/1.04 23 -subset(c3,c5) | -subset(c4,c6) # label(t138_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.76/1.04 24 cartesian_product2(A,B) = empty_set | empty_set != A # label(t113_zfmisc_1) # label(axiom). [clausify(6)].
% 0.76/1.04 25 cartesian_product2(A,B) = empty_set | empty_set != B # label(t113_zfmisc_1) # label(axiom). [clausify(6)].
% 0.76/1.04 26 -subset(A,B) | set_intersection2(A,B) = A # label(t28_xboole_1) # label(axiom). [clausify(10)].
% 0.76/1.04 28 cartesian_product2(A,B) != cartesian_product2(C,D) | empty_set = C | empty_set = D | A = C # label(t134_zfmisc_1) # label(axiom). [clausify(8)].
% 0.76/1.04 29 cartesian_product2(A,B) != cartesian_product2(C,D) | empty_set = C | empty_set = D | B = D # label(t134_zfmisc_1) # label(axiom). [clausify(8)].
% 0.76/1.04 37 subset(set_intersection2(A,B),B). [para(17(a,1),16(a,1))].
% 0.76/1.04 40 c3 != empty_set. [ur(24,a,22,a),flip(a)].
% 0.76/1.04 42 c4 != empty_set. [ur(25,a,22,a),flip(a)].
% 0.76/1.04 43 cartesian_product2(set_intersection2(c3,c5),set_intersection2(c4,c6)) = cartesian_product2(c3,c4). [resolve(26,a,18,a),rewrite([20(7)])].
% 0.76/1.04 143 set_intersection2(c4,c6) = c4. [resolve(43,a,29,a),flip(a),flip(b),unit_del(a,40),unit_del(b,42)].
% 0.76/1.04 144 set_intersection2(c3,c5) = c3. [resolve(43,a,28,a),flip(a),flip(b),unit_del(a,40),unit_del(b,42)].
% 0.76/1.04 235 subset(c4,c6). [para(143(a,1),37(a,1))].
% 0.76/1.04 236 -subset(c3,c5). [back_unit_del(23),unit_del(b,235)].
% 0.76/1.04 237 $F. [para(144(a,1),37(a,1)),unit_del(a,236)].
% 0.76/1.04
% 0.76/1.04 % SZS output end Refutation
% 0.76/1.04 ============================== end of proof ==========================
% 0.76/1.04
% 0.76/1.04 ============================== STATISTICS ============================
% 0.76/1.04
% 0.76/1.04 Given=46. Generated=1036. Kept=224. proofs=1.
% 0.76/1.04 Usable=44. Sos=174. Demods=13. Limbo=0, Disabled=23. Hints=0.
% 0.76/1.04 Megabytes=0.20.
% 0.76/1.04 User_CPU=0.03, System_CPU=0.01, Wall_clock=0.
% 0.76/1.04
% 0.76/1.04 ============================== end of statistics =====================
% 0.76/1.04
% 0.76/1.04 ============================== end of search =========================
% 0.76/1.04
% 0.76/1.04 THEOREM PROVED
% 0.76/1.04 % SZS status Theorem
% 0.76/1.04
% 0.76/1.04 Exiting with 1 proof.
% 0.76/1.04
% 0.76/1.04 Process 27989 exit (max_proofs) Sun Jul 10 06:36:37 2022
% 0.76/1.04 Prover9 interrupted
%------------------------------------------------------------------------------