TSTP Solution File: SEU104+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU104+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 13:29:02 EDT 2022
% Result : Theorem 0.98s 1.28s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU104+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 08:41:39 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.45/1.05 ============================== Prover9 ===============================
% 0.45/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.05 Process 26636 was started by sandbox on n019.cluster.edu,
% 0.45/1.05 Sun Jun 19 08:41:40 2022
% 0.45/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26483_n019.cluster.edu".
% 0.45/1.05 ============================== end of head ===========================
% 0.45/1.05
% 0.45/1.05 ============================== INPUT =================================
% 0.45/1.05
% 0.45/1.05 % Reading from file /tmp/Prover9_26483_n019.cluster.edu
% 0.45/1.05
% 0.45/1.05 set(prolog_style_variables).
% 0.45/1.05 set(auto2).
% 0.45/1.05 % set(auto2) -> set(auto).
% 0.45/1.05 % set(auto) -> set(auto_inference).
% 0.45/1.05 % set(auto) -> set(auto_setup).
% 0.45/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.05 % set(auto) -> set(auto_limits).
% 0.45/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.05 % set(auto) -> set(auto_denials).
% 0.45/1.05 % set(auto) -> set(auto_process).
% 0.45/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.05 % set(auto2) -> assign(stats, some).
% 0.45/1.05 % set(auto2) -> clear(echo_input).
% 0.45/1.05 % set(auto2) -> set(quiet).
% 0.45/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.05 % set(auto2) -> clear(print_given).
% 0.45/1.05 assign(lrs_ticks,-1).
% 0.45/1.05 assign(sos_limit,10000).
% 0.45/1.05 assign(order,kbo).
% 0.45/1.05 set(lex_order_vars).
% 0.45/1.05 clear(print_given).
% 0.45/1.05
% 0.45/1.05 % formulas(sos). % not echoed (42 formulas)
% 0.45/1.05
% 0.45/1.05 ============================== end of input ==========================
% 0.45/1.05
% 0.45/1.05 % From the command line: assign(max_seconds, 300).
% 0.45/1.05
% 0.45/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.05
% 0.45/1.05 % Formulas that are not ordinary clauses:
% 0.45/1.05 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 3 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 5 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 6 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 7 (all A all B symmetric_difference(A,B) = symmetric_difference(B,A)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 8 (all A all B symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 9 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 10 (all A all B (finite(A) -> finite(set_difference(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 11 (all A all B (finite(A) & finite(B) -> finite(symmetric_difference(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 12 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 13 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 14 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 15 (all A all B (finite(A) & finite(B) -> finite(set_union2(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 16 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 17 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 18 (exists A (-empty(A) & cup_closed(A) & cap_closed(A) & diff_closed(A) & preboolean(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 19 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 20 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 21 (all A exists B (element(B,powerset(A)) & empty(B) & relation(B) & function(B) & one_to_one(B) & epsilon_transitive(B) & epsilon_connected(B) & ordinal(B) & natural(B) & finite(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 22 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 23 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 24 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 25 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 26 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 27 (all A (preboolean(A) <-> (all B all C (in(B,A) & in(C,A) -> in(set_union2(B,C),A) & in(set_difference(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 28 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 29 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 30 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 31 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 32 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 33 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 34 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 35 (all A symmetric_difference(A,empty_set) = A) # label(t5_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 36 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 37 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 38 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 39 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 40 (all A all B set_union2(A,B) = symmetric_difference(A,set_difference(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 41 -(all A (-empty(A) -> ((all B (element(B,A) -> (all C (element(C,A) -> in(symmetric_difference(B,C),A) & in(set_difference(B,C),A))))) -> preboolean(A)))) # label(t15_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.05
% 0.45/1.05 ============================== end of process non-clausal formulas ===
% 0.45/1.05
% 0.45/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.05
% 0.45/1.05 ============================== PREDICATE ELIMINATION =================
% 0.45/1.05 42 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(5)].
% 0.45/1.05 43 cup_closed(c2) # label(rc1_finsub_1) # label(axiom). [clausify(18)].
% 0.45/1.05 44 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.98/1.28 Derived: -diff_closed(c2) | preboolean(c2). [resolve(42,a,43,a)].
% 0.98/1.28 45 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(32)].
% 0.98/1.28 46 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(26)].
% 0.98/1.28 47 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(32)].
% 0.98/1.28 Derived: element(A,powerset(A)). [resolve(45,b,46,a)].
% 0.98/1.28
% 0.98/1.28 ============================== end predicate elimination =============
% 0.98/1.28
% 0.98/1.28 Auto_denials: (non-Horn, no changes).
% 0.98/1.28
% 0.98/1.28 Term ordering decisions:
% 0.98/1.28 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. set_difference=1. symmetric_difference=1. powerset=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1.
% 0.98/1.28
% 0.98/1.28 ============================== end of process initial clauses ========
% 0.98/1.28
% 0.98/1.28 ============================== CLAUSES FOR SEARCH ====================
% 0.98/1.28
% 0.98/1.28 ============================== end of clauses for search =============
% 0.98/1.28
% 0.98/1.28 ============================== SEARCH ================================
% 0.98/1.28
% 0.98/1.28 % Starting search at 0.02 seconds.
% 0.98/1.28
% 0.98/1.28 ============================== PROOF =================================
% 0.98/1.28 % SZS status Theorem
% 0.98/1.28 % SZS output start Refutation
% 0.98/1.28
% 0.98/1.28 % Proof 1 at 0.24 (+ 0.01) seconds.
% 0.98/1.28 % Length of proof is 24.
% 0.98/1.28 % Level of proof is 6.
% 0.98/1.28 % Maximum clause weight is 16.000.
% 0.98/1.28 % Given clauses 411.
% 0.98/1.28
% 0.98/1.28 6 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.28 7 (all A all B symmetric_difference(A,B) = symmetric_difference(B,A)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.28 27 (all A (preboolean(A) <-> (all B all C (in(B,A) & in(C,A) -> in(set_union2(B,C),A) & in(set_difference(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.28 29 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.28 40 (all A all B set_union2(A,B) = symmetric_difference(A,set_difference(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.28 41 -(all A (-empty(A) -> ((all B (element(B,A) -> (all C (element(C,A) -> in(symmetric_difference(B,C),A) & in(set_difference(B,C),A))))) -> preboolean(A)))) # label(t15_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.98/1.28 66 preboolean(A) | in(f7(A),A) # label(t10_finsub_1) # label(axiom). [clausify(27)].
% 0.98/1.28 67 preboolean(A) | in(f8(A),A) # label(t10_finsub_1) # label(axiom). [clausify(27)].
% 0.98/1.28 68 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(6)].
% 0.98/1.28 69 symmetric_difference(A,B) = symmetric_difference(B,A) # label(commutativity_k5_xboole_0) # label(axiom). [clausify(7)].
% 0.98/1.28 73 symmetric_difference(A,set_difference(B,A)) = set_union2(A,B) # label(t98_xboole_1) # label(axiom). [clausify(40)].
% 0.98/1.28 80 -preboolean(c5) # label(t15_finsub_1) # label(negated_conjecture). [clausify(41)].
% 0.98/1.28 94 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(29)].
% 0.98/1.28 101 -element(A,c5) | -element(B,c5) | in(symmetric_difference(A,B),c5) # label(t15_finsub_1) # label(negated_conjecture). [clausify(41)].
% 0.98/1.28 102 -element(A,c5) | -element(B,c5) | in(set_difference(A,B),c5) # label(t15_finsub_1) # label(negated_conjecture). [clausify(41)].
% 0.98/1.28 105 preboolean(A) | -in(set_union2(f7(A),f8(A)),A) | -in(set_difference(f7(A),f8(A)),A) # label(t10_finsub_1) # label(axiom). [clausify(27)].
% 0.98/1.28 157 element(f8(A),A) | preboolean(A). [resolve(94,a,67,b)].
% 0.98/1.28 158 element(f7(A),A) | preboolean(A). [resolve(94,a,66,b)].
% 0.98/1.28 256 -element(A,c5) | in(set_difference(A,f8(c5)),c5). [resolve(157,a,102,b),unit_del(a,80)].
% 0.98/1.28 258 -element(A,c5) | in(symmetric_difference(A,f8(c5)),c5). [resolve(157,a,101,b),unit_del(a,80)].
% 0.98/1.28 2670 in(set_difference(f7(c5),f8(c5)),c5). [resolve(256,a,158,a),unit_del(b,80)].
% 0.98/1.28 3238 -in(set_union2(f7(c5),f8(c5)),c5). [resolve(2670,a,105,c),unit_del(a,80)].
% 0.98/1.28 3240 element(set_difference(f7(c5),f8(c5)),c5). [resolve(2670,a,94,a)].
% 0.98/1.28 3392 $F. [resolve(3240,a,258,a),rewrite([69(8),73(8),68(5)]),unit_del(a,3238)].
% 0.98/1.28
% 0.98/1.28 % SZS output end Refutation
% 0.98/1.28 ============================== end of proof ==========================
% 0.98/1.28
% 0.98/1.28 ============================== STATISTICS ============================
% 0.98/1.28
% 0.98/1.28 Given=411. Generated=4329. Kept=3341. proofs=1.
% 0.98/1.28 Usable=400. Sos=2906. Demods=14. Limbo=2, Disabled=106. Hints=0.
% 0.98/1.28 Megabytes=2.70.
% 0.98/1.28 User_CPU=0.24, System_CPU=0.01, Wall_clock=0.
% 0.98/1.28
% 0.98/1.28 ============================== end of statistics =====================
% 0.98/1.28
% 0.98/1.28 ============================== end of search =========================
% 0.98/1.28
% 0.98/1.28 THEOREM PROVED
% 0.98/1.28 % SZS status Theorem
% 0.98/1.28
% 0.98/1.28 Exiting with 1 proof.
% 0.98/1.28
% 0.98/1.28 Process 26636 exit (max_proofs) Sun Jun 19 08:41:40 2022
% 0.98/1.28 Prover9 interrupted
%------------------------------------------------------------------------------