TSTP Solution File: SET983+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 04:33:50 EDT 2022
% Result : Theorem 0.80s 1.08s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 15:22:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.80/1.07 ============================== Prover9 ===============================
% 0.80/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.07 Process 15870 was started by sandbox on n015.cluster.edu,
% 0.80/1.07 Sun Jul 10 15:22:39 2022
% 0.80/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15711_n015.cluster.edu".
% 0.80/1.07 ============================== end of head ===========================
% 0.80/1.07
% 0.80/1.07 ============================== INPUT =================================
% 0.80/1.07
% 0.80/1.07 % Reading from file /tmp/Prover9_15711_n015.cluster.edu
% 0.80/1.07
% 0.80/1.07 set(prolog_style_variables).
% 0.80/1.07 set(auto2).
% 0.80/1.07 % set(auto2) -> set(auto).
% 0.80/1.07 % set(auto) -> set(auto_inference).
% 0.80/1.07 % set(auto) -> set(auto_setup).
% 0.80/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.07 % set(auto) -> set(auto_limits).
% 0.80/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.07 % set(auto) -> set(auto_denials).
% 0.80/1.07 % set(auto) -> set(auto_process).
% 0.80/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.07 % set(auto2) -> assign(stats, some).
% 0.80/1.07 % set(auto2) -> clear(echo_input).
% 0.80/1.07 % set(auto2) -> set(quiet).
% 0.80/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.07 % set(auto2) -> clear(print_given).
% 0.80/1.07 assign(lrs_ticks,-1).
% 0.80/1.07 assign(sos_limit,10000).
% 0.80/1.07 assign(order,kbo).
% 0.80/1.07 set(lex_order_vars).
% 0.80/1.07 clear(print_given).
% 0.80/1.07
% 0.80/1.07 % formulas(sos). % not echoed (8 formulas)
% 0.80/1.07
% 0.80/1.07 ============================== end of input ==========================
% 0.80/1.07
% 0.80/1.07 % From the command line: assign(max_seconds, 300).
% 0.80/1.07
% 0.80/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.07
% 0.80/1.07 % Formulas that are not ordinary clauses:
% 0.80/1.07 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 3 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 4 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 5 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 6 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 8 -(all A all B all C all D all E (in(A,cartesian_product2(B,C)) & in(A,cartesian_product2(D,E)) -> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))))) # label(t137_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.07
% 0.80/1.07 ============================== end of process non-clausal formulas ===
% 0.80/1.07
% 0.80/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.07
% 0.80/1.07 ============================== PREDICATE ELIMINATION =================
% 0.80/1.07
% 0.80/1.07 ============================== end predicate elimination =============
% 0.80/1.07
% 0.80/1.07 Auto_denials: (non-Horn, no changes).
% 0.80/1.07
% 0.80/1.07 Term ordering decisions:
% 0.80/1.07 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. set_intersection2=1. cartesian_product2=1. f1=1.
% 0.80/1.07
% 0.80/1.07 ============================== end of process initial clauses ========
% 0.80/1.07
% 0.80/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.07
% 0.80/1.07 ============================== end of clauses for search =============
% 0.80/1.07
% 0.80/1.07 ============================== SEARCH ================================
% 0.80/1.08
% 0.80/1.08 % Starting search at 0.01 seconds.
% 0.80/1.08
% 0.80/1.08 ============================== PROOF =================================
% 0.80/1.08 % SZS status Theorem
% 0.80/1.08 % SZS output start Refutation
% 0.80/1.08
% 0.80/1.08 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.80/1.08 % Length of proof is 12.
% 0.80/1.08 % Level of proof is 3.
% 0.80/1.08 % Maximum clause weight is 15.000.
% 0.80/1.08 % Given clauses 14.
% 0.80/1.08
% 0.80/1.08 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.08 3 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.08 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].
% 0.80/1.08 8 -(all A all B all C all D all E (in(A,cartesian_product2(B,C)) & in(A,cartesian_product2(D,E)) -> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))))) # label(t137_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.08 11 in(c3,cartesian_product2(c4,c5)) # label(t137_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.80/1.08 12 in(c3,cartesian_product2(c6,c7)) # label(t137_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.80/1.08 13 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(2)].
% 0.80/1.08 14 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)].
% 0.80/1.08 19 -in(c3,cartesian_product2(set_intersection2(c4,c6),set_intersection2(c5,c7))) # label(t137_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.80/1.08 20 -in(c3,set_intersection2(cartesian_product2(c4,c5),cartesian_product2(c6,c7))). [copy(19),rewrite([14(8)])].
% 0.80/1.08 23 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 0.80/1.08 76 $F. [ur(23,b,20,a,c,12,a,d,11,a),rewrite([13(7)]),xx(a)].
% 0.80/1.08
% 0.80/1.08 % SZS output end Refutation
% 0.80/1.08 ============================== end of proof ==========================
% 0.80/1.08
% 0.80/1.08 ============================== STATISTICS ============================
% 0.80/1.08
% 0.80/1.08 Given=14. Generated=107. Kept=66. proofs=1.
% 0.80/1.08 Usable=14. Sos=41. Demods=5. Limbo=11, Disabled=15. Hints=0.
% 0.80/1.08 Megabytes=0.09.
% 0.80/1.08 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.80/1.08
% 0.80/1.08 ============================== end of statistics =====================
% 0.80/1.08
% 0.80/1.08 ============================== end of search =========================
% 0.80/1.08
% 0.80/1.08 THEOREM PROVED
% 0.80/1.08 % SZS status Theorem
% 0.80/1.08
% 0.80/1.08 Exiting with 1 proof.
% 0.80/1.08
% 0.80/1.08 Process 15870 exit (max_proofs) Sun Jul 10 15:22:39 2022
% 0.80/1.08 Prover9 interrupted
%------------------------------------------------------------------------------