TSTP Solution File: SET877+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 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 04:33:07 EDT 2022
% Result : Theorem 0.78s 1.03s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 19:47:20 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.78/1.03 ============================== Prover9 ===============================
% 0.78/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.03 Process 16934 was started by sandbox2 on n006.cluster.edu,
% 0.78/1.03 Sun Jul 10 19:47:21 2022
% 0.78/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16781_n006.cluster.edu".
% 0.78/1.03 ============================== end of head ===========================
% 0.78/1.03
% 0.78/1.03 ============================== INPUT =================================
% 0.78/1.03
% 0.78/1.03 % Reading from file /tmp/Prover9_16781_n006.cluster.edu
% 0.78/1.03
% 0.78/1.03 set(prolog_style_variables).
% 0.78/1.03 set(auto2).
% 0.78/1.03 % set(auto2) -> set(auto).
% 0.78/1.03 % set(auto) -> set(auto_inference).
% 0.78/1.03 % set(auto) -> set(auto_setup).
% 0.78/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.03 % set(auto) -> set(auto_limits).
% 0.78/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.03 % set(auto) -> set(auto_denials).
% 0.78/1.03 % set(auto) -> set(auto_process).
% 0.78/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.03 % set(auto2) -> assign(stats, some).
% 0.78/1.03 % set(auto2) -> clear(echo_input).
% 0.78/1.03 % set(auto2) -> set(quiet).
% 0.78/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.03 % set(auto2) -> clear(print_given).
% 0.78/1.03 assign(lrs_ticks,-1).
% 0.78/1.03 assign(sos_limit,10000).
% 0.78/1.03 assign(order,kbo).
% 0.78/1.03 set(lex_order_vars).
% 0.78/1.03 clear(print_given).
% 0.78/1.03
% 0.78/1.03 % formulas(sos). % not echoed (8 formulas)
% 0.78/1.03
% 0.78/1.03 ============================== end of input ==========================
% 0.78/1.03
% 0.78/1.03 % From the command line: assign(max_seconds, 300).
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.03
% 0.78/1.03 % Formulas that are not ordinary clauses:
% 0.78/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 4 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 5 (all A all B (set_intersection2(A,singleton(B)) = singleton(B) -> in(B,A))) # label(l30_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 8 -(all A all B (set_intersection2(singleton(A),singleton(B)) = singleton(A) -> A = B)) # label(t18_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.03
% 0.78/1.03 ============================== end of process non-clausal formulas ===
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.03
% 0.78/1.03 ============================== PREDICATE ELIMINATION =================
% 0.78/1.03
% 0.78/1.03 ============================== end predicate elimination =============
% 0.78/1.03
% 0.78/1.03 Auto_denials: (non-Horn, no changes).
% 0.78/1.03
% 0.78/1.03 Term ordering decisions:
% 0.78/1.03
% 0.78/1.03 % Assigning unary symbol singleton kb_weight 0 and highest precedence (10).
% 0.78/1.03 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. set_intersection2=1. f1=1. singleton=0.
% 0.78/1.03
% 0.78/1.03 ============================== end of process initial clauses ========
% 0.78/1.03
% 0.78/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.78/1.03
% 0.78/1.03 ============================== end of clauses for search =============
% 0.78/1.03
% 0.78/1.03 ============================== SEARCH ================================
% 0.78/1.03
% 0.78/1.03 % Starting search at 0.01 seconds.
% 0.78/1.03
% 0.78/1.03 ============================== PROOF =================================
% 0.78/1.03 % SZS status Theorem
% 0.78/1.03 % SZS output start Refutation
% 0.78/1.03
% 0.78/1.03 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.78/1.03 % Length of proof is 15.
% 0.78/1.03 % Level of proof is 3.
% 0.78/1.03 % Maximum clause weight is 10.000.
% 0.78/1.03 % Given clauses 16.
% 0.78/1.03
% 0.78/1.03 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 4 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 5 (all A all B (set_intersection2(A,singleton(B)) = singleton(B) -> in(B,A))) # label(l30_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 8 -(all A all B (set_intersection2(singleton(A),singleton(B)) = singleton(A) -> A = B)) # label(t18_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.03 10 set_intersection2(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(4)].
% 0.78/1.03 11 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(2)].
% 0.78/1.03 12 singleton(c3) = set_intersection2(singleton(c3),singleton(c4)) # label(t18_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.78/1.03 13 set_intersection2(singleton(c3),singleton(c4)) = singleton(c3). [copy(12),flip(a)].
% 0.78/1.03 16 c4 != c3 # label(t18_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.78/1.03 18 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(3)].
% 0.78/1.03 20 singleton(A) != set_intersection2(B,singleton(A)) | in(A,B) # label(l30_zfmisc_1) # label(axiom). [clausify(5)].
% 0.78/1.03 21 set_intersection2(A,singleton(B)) != singleton(B) | in(B,A). [copy(20),flip(a)].
% 0.78/1.03 28 -in(c3,singleton(c4)). [ur(18,a,10,a(flip),c,16,a(flip)),rewrite([10(6)])].
% 0.78/1.03 40 $F. [ur(21,b,28,a),rewrite([11(5),13(5)]),xx(a)].
% 0.78/1.03
% 0.78/1.03 % SZS output end Refutation
% 0.78/1.03 ============================== end of proof ==========================
% 0.78/1.03
% 0.78/1.03 ============================== STATISTICS ============================
% 0.78/1.03
% 0.78/1.03 Given=16. Generated=63. Kept=29. proofs=1.
% 0.78/1.03 Usable=16. Sos=8. Demods=3. Limbo=0, Disabled=17. Hints=0.
% 0.78/1.03 Megabytes=0.05.
% 0.78/1.03 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.78/1.03
% 0.78/1.03 ============================== end of statistics =====================
% 0.78/1.03
% 0.78/1.03 ============================== end of search =========================
% 0.78/1.03
% 0.78/1.03 THEOREM PROVED
% 0.78/1.03 % SZS status Theorem
% 0.78/1.03
% 0.78/1.03 Exiting with 1 proof.
% 0.78/1.03
% 0.78/1.03 Process 16934 exit (max_proofs) Sun Jul 10 19:47:21 2022
% 0.78/1.03 Prover9 interrupted
%------------------------------------------------------------------------------