TSTP Solution File: SEU128+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 13:29:11 EDT 2022
% Result : Theorem 1.11s 1.46s
% Output : Refutation 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 21:46:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/1.02 ============================== Prover9 ===============================
% 0.76/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.02 Process 17443 was started by sandbox on n017.cluster.edu,
% 0.76/1.02 Sun Jun 19 21:46:59 2022
% 0.76/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17100_n017.cluster.edu".
% 0.76/1.02 ============================== end of head ===========================
% 0.76/1.02
% 0.76/1.02 ============================== INPUT =================================
% 0.76/1.02
% 0.76/1.02 % Reading from file /tmp/Prover9_17100_n017.cluster.edu
% 0.76/1.02
% 0.76/1.02 set(prolog_style_variables).
% 0.76/1.02 set(auto2).
% 0.76/1.02 % set(auto2) -> set(auto).
% 0.76/1.02 % set(auto) -> set(auto_inference).
% 0.76/1.02 % set(auto) -> set(auto_setup).
% 0.76/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.02 % set(auto) -> set(auto_limits).
% 0.76/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.02 % set(auto) -> set(auto_denials).
% 0.76/1.02 % set(auto) -> set(auto_process).
% 0.76/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.02 % set(auto2) -> assign(stats, some).
% 0.76/1.02 % set(auto2) -> clear(echo_input).
% 0.76/1.02 % set(auto2) -> set(quiet).
% 0.76/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.02 % set(auto2) -> clear(print_given).
% 0.76/1.02 assign(lrs_ticks,-1).
% 0.76/1.02 assign(sos_limit,10000).
% 0.76/1.02 assign(order,kbo).
% 0.76/1.02 set(lex_order_vars).
% 0.76/1.02 clear(print_given).
% 0.76/1.02
% 0.76/1.02 % formulas(sos). % not echoed (36 formulas)
% 0.76/1.02
% 0.76/1.02 ============================== end of input ==========================
% 0.76/1.02
% 0.76/1.02 % From the command line: assign(max_seconds, 300).
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.02
% 0.76/1.02 % Formulas that are not ordinary clauses:
% 0.76/1.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 4 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 5 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 6 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 8 (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].
% 0.76/1.02 9 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 11 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 12 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 13 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 14 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 15 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 16 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 17 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 18 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 19 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 20 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 21 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 22 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 23 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 24 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 25 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 26 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 27 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 28 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 29 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 30 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 31 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 32 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 33 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 34 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.11/1.46 35 -(all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.11/1.46
% 1.11/1.46 ============================== end of process non-clausal formulas ===
% 1.11/1.46
% 1.11/1.46 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.46
% 1.11/1.46 ============================== PREDICATE ELIMINATION =================
% 1.11/1.46
% 1.11/1.46 ============================== end predicate elimination =============
% 1.11/1.46
% 1.11/1.46 Auto_denials: (non-Horn, no changes).
% 1.11/1.46
% 1.11/1.46 Term ordering decisions:
% 1.11/1.46
% 1.11/1.46 % Assigning unary symbol f1 kb_weight 0 and highest precedence (19).
% 1.11/1.46 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. set_intersection2=1. f3=1. f5=1. f6=1. f2=1. f4=1. f1=0.
% 1.11/1.46
% 1.11/1.46 ============================== end of process initial clauses ========
% 1.11/1.46
% 1.11/1.46 ============================== CLAUSES FOR SEARCH ====================
% 1.11/1.46
% 1.11/1.46 ============================== end of clauses for search =============
% 1.11/1.46
% 1.11/1.46 ============================== SEARCH ================================
% 1.11/1.46
% 1.11/1.46 % Starting search at 0.02 seconds.
% 1.11/1.46
% 1.11/1.46 ============================== PROOF =================================
% 1.11/1.46 % SZS status Theorem
% 1.11/1.46 % SZS output start Refutation
% 1.11/1.46
% 1.11/1.46 % Proof 1 at 0.42 (+ 0.03) seconds.
% 1.11/1.46 % Length of proof is 19.
% 1.11/1.46 % Level of proof is 4.
% 1.11/1.46 % Maximum clause weight is 14.000.
% 1.11/1.46 % Given clauses 419.
% 1.11/1.46
% 1.11/1.46 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.46 8 (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].
% 1.11/1.46 35 -(all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.11/1.46 40 subset(c3,c4) # label(t19_xboole_1) # label(negated_conjecture). [clausify(35)].
% 1.11/1.46 41 subset(c3,c5) # label(t19_xboole_1) # label(negated_conjecture). [clausify(35)].
% 1.11/1.46 49 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 1.11/1.46 51 subset(A,B) | in(f3(A,B),A) # label(d3_tarski) # label(axiom). [clausify(7)].
% 1.11/1.46 60 -subset(c3,set_intersection2(c4,c5)) # label(t19_xboole_1) # label(negated_conjecture). [clausify(35)].
% 1.11/1.46 73 subset(A,B) | -in(f3(A,B),B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 1.11/1.46 78 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 1.11/1.46 86 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(8)].
% 1.11/1.46 117 in(f3(c3,set_intersection2(c4,c5)),c3). [resolve(60,a,51,a)].
% 1.11/1.46 154 -in(f3(c3,set_intersection2(c4,c5)),set_intersection2(c4,c5)). [ur(73,a,60,a)].
% 1.11/1.46 174 -in(A,c3) | in(A,c5). [resolve(78,a,41,a)].
% 1.11/1.46 175 -in(A,c3) | in(A,c4). [resolve(78,a,40,a)].
% 1.11/1.46 1435 in(f3(c3,set_intersection2(c4,c5)),c4). [resolve(117,a,175,a)].
% 1.11/1.46 1436 in(f3(c3,set_intersection2(c4,c5)),c5). [resolve(117,a,174,a)].
% 1.11/1.46 5513 $F. [ur(86,b,154,a,c,1436,a,d,1435,a),rewrite([49(3)]),xx(a)].
% 1.11/1.46
% 1.11/1.46 % SZS output end Refutation
% 1.11/1.46 ============================== end of proof ==========================
% 1.11/1.46
% 1.11/1.46 ============================== STATISTICS ============================
% 1.11/1.46
% 1.11/1.46 Given=419. Generated=24637. Kept=5476. proofs=1.
% 1.11/1.46 Usable=412. Sos=4948. Demods=16. Limbo=1, Disabled=169. Hints=0.
% 1.11/1.46 Megabytes=3.58.
% 1.11/1.46 User_CPU=0.42, System_CPU=0.03, Wall_clock=1.
% 1.11/1.46
% 1.11/1.46 ============================== end of statistics =====================
% 1.11/1.46
% 1.11/1.46 ============================== end of search =========================
% 1.11/1.46
% 1.11/1.46 THEOREM PROVED
% 1.11/1.46 % SZS status Theorem
% 1.11/1.46
% 1.11/1.46 Exiting with 1 proof.
% 1.11/1.46
% 1.11/1.46 Process 17443 exit (max_proofs) Sun Jun 19 21:47:00 2022
% 1.21/1.46 Prover9 interrupted
%------------------------------------------------------------------------------