TSTP Solution File: SEU355+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 13:31:13 EDT 2022
% Result : Theorem 0.44s 1.00s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n024.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sun Jun 19 10:36:32 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.44/0.99 ============================== Prover9 ===============================
% 0.44/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.99 Process 17855 was started by sandbox2 on n024.cluster.edu,
% 0.44/0.99 Sun Jun 19 10:36:33 2022
% 0.44/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17702_n024.cluster.edu".
% 0.44/0.99 ============================== end of head ===========================
% 0.44/0.99
% 0.44/0.99 ============================== INPUT =================================
% 0.44/0.99
% 0.44/0.99 % Reading from file /tmp/Prover9_17702_n024.cluster.edu
% 0.44/0.99
% 0.44/0.99 set(prolog_style_variables).
% 0.44/0.99 set(auto2).
% 0.44/0.99 % set(auto2) -> set(auto).
% 0.44/0.99 % set(auto) -> set(auto_inference).
% 0.44/0.99 % set(auto) -> set(auto_setup).
% 0.44/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.99 % set(auto) -> set(auto_limits).
% 0.44/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.99 % set(auto) -> set(auto_denials).
% 0.44/0.99 % set(auto) -> set(auto_process).
% 0.44/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.99 % set(auto2) -> assign(stats, some).
% 0.44/0.99 % set(auto2) -> clear(echo_input).
% 0.44/0.99 % set(auto2) -> set(quiet).
% 0.44/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.99 % set(auto2) -> clear(print_given).
% 0.44/0.99 assign(lrs_ticks,-1).
% 0.44/0.99 assign(sos_limit,10000).
% 0.44/0.99 assign(order,kbo).
% 0.44/0.99 set(lex_order_vars).
% 0.44/0.99 clear(print_given).
% 0.44/0.99
% 0.44/0.99 % formulas(sos). % not echoed (22 formulas)
% 0.44/0.99
% 0.44/0.99 ============================== end of input ==========================
% 0.44/0.99
% 0.44/0.99 % From the command line: assign(max_seconds, 300).
% 0.44/0.99
% 0.44/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.99
% 0.44/0.99 % Formulas that are not ordinary clauses:
% 0.44/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 3 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 4 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_set_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 5 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 6 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 7 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 8 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 9 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 10 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 11 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 12 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 13 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 14 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 15 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 16 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 17 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 18 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 19 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 20 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 21 -(all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_set_smaller(A,empty_set,B) & relstr_element_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/0.99
% 0.44/0.99 ============================== end of process non-clausal formulas ===
% 0.44/0.99
% 0.44/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/0.99
% 0.44/0.99 ============================== PREDICATE ELIMINATION =================
% 0.44/0.99 22 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(6)].
% 0.44/0.99 23 rel_str(c1) # label(existence_l1_orders_2) # label(axiom). [clausify(10)].
% 0.44/0.99 24 rel_str(c6) # label(t6_yellow_0) # label(negated_conjecture). [clausify(21)].
% 0.44/0.99 Derived: one_sorted_str(c1). [resolve(22,a,23,a)].
% 0.44/0.99 Derived: one_sorted_str(c6). [resolve(22,a,24,a)].
% 0.44/0.99 25 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | in(f1(A,C,B),C) # label(d8_lattice3) # label(axiom). [clausify(3)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | in(f1(c1,B,A),B). [resolve(25,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_element_smaller(c6,B,A) | in(f1(c6,B,A),B). [resolve(25,a,24,a)].
% 0.44/0.99 26 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | in(f2(A,C,B),C) # label(d9_lattice3) # label(axiom). [clausify(4)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_set_smaller(c1,B,A) | in(f2(c1,B,A),B). [resolve(26,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | in(f2(c6,B,A),B). [resolve(26,a,24,a)].
% 0.44/0.99 27 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | element(f1(A,C,B),the_carrier(A)) # label(d8_lattice3) # label(axiom). [clausify(3)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | element(f1(c1,B,A),the_carrier(c1)). [resolve(27,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_element_smaller(c6,B,A) | element(f1(c6,B,A),the_carrier(c6)). [resolve(27,a,24,a)].
% 0.44/0.99 28 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | -related(A,B,f1(A,C,B)) # label(d8_lattice3) # label(axiom). [clausify(3)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | -related(c1,A,f1(c1,B,A)). [resolve(28,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_element_smaller(c6,B,A) | -related(c6,A,f1(c6,B,A)). [resolve(28,a,24,a)].
% 0.44/0.99 29 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | element(f2(A,C,B),the_carrier(A)) # label(d9_lattice3) # label(axiom). [clausify(4)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_set_smaller(c1,B,A) | element(f2(c1,B,A),the_carrier(c1)). [resolve(29,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | element(f2(c6,B,A),the_carrier(c6)). [resolve(29,a,24,a)].
% 0.44/0.99 30 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | -related(A,f2(A,C,B),B) # label(d9_lattice3) # label(axiom). [clausify(4)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | relstr_set_smaller(c1,B,A) | -related(c1,f2(c1,B,A),A). [resolve(30,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | -related(c6,f2(c6,B,A),A). [resolve(30,a,24,a)].
% 0.44/0.99 31 -rel_str(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,C,B) | -element(D,the_carrier(A)) | -in(D,C) | related(A,B,D) # label(d8_lattice3) # label(axiom). [clausify(3)].
% 0.44/0.99 Derived: -element(A,the_carrier(c1)) | -relstr_element_smaller(c1,B,A) | -element(C,the_carrier(c1)) | -in(C,B) | related(c1,A,C). [resolve(31,a,23,a)].
% 0.44/0.99 Derived: -element(A,the_carrier(c6)) | -relstr_element_smaller(c6,B,A) | -element(C,the_carrier(c6)) | -in(C,B) | related(c6,A,C). [resolve(31,a,24,a)].
% 0.44/0.99 32 -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | -element(D,the_carrier(A)) | -in(D,C) | related(A,D,B) # label(d9_lattice3) # label(axiom). [clausify(4)].
% 0.44/1.00 Derived: -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | -element(C,the_carrier(c1)) | -in(C,B) | related(c1,C,A). [resolve(32,a,23,a)].
% 0.44/1.00 Derived: -element(A,the_carrier(c6)) | -relstr_set_smaller(c6,B,A) | -element(C,the_carrier(c6)) | -in(C,B) | related(c6,C,A). [resolve(32,a,24,a)].
% 0.44/1.00
% 0.44/1.00 ============================== end predicate elimination =============
% 0.44/1.00
% 0.44/1.00 Auto_denials: (non-Horn, no changes).
% 0.44/1.00
% 0.44/1.00 Term ordering decisions:
% 0.44/1.00 Function symbol KB weights: empty_set=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. the_carrier=1. f3=1. f1=1. f2=1.
% 0.44/1.00
% 0.44/1.00 ============================== end of process initial clauses ========
% 0.44/1.00
% 0.44/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.00
% 0.44/1.00 ============================== end of clauses for search =============
% 0.44/1.00
% 0.44/1.00 ============================== SEARCH ================================
% 0.44/1.00
% 0.44/1.00 % Starting search at 0.02 seconds.
% 0.44/1.00
% 0.44/1.00 ============================== PROOF =================================
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00 % SZS output start Refutation
% 0.44/1.00
% 0.44/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.00 % Length of proof is 18.
% 0.44/1.00 % Level of proof is 5.
% 0.44/1.00 % Maximum clause weight is 14.000.
% 0.44/1.00 % Given clauses 50.
% 0.44/1.00
% 0.44/1.00 3 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_set_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 19 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 21 -(all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_set_smaller(A,empty_set,B) & relstr_element_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.00 24 rel_str(c6) # label(t6_yellow_0) # label(negated_conjecture). [clausify(21)].
% 0.44/1.00 25 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | in(f1(A,C,B),C) # label(d8_lattice3) # label(axiom). [clausify(3)].
% 0.44/1.00 26 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | in(f2(A,C,B),C) # label(d9_lattice3) # label(axiom). [clausify(4)].
% 0.44/1.00 33 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 0.44/1.00 36 element(c7,the_carrier(c6)) # label(t6_yellow_0) # label(negated_conjecture). [clausify(21)].
% 0.44/1.00 39 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(19)].
% 0.44/1.00 41 -relstr_set_smaller(c6,empty_set,c7) | -relstr_element_smaller(c6,empty_set,c7) # label(t6_yellow_0) # label(negated_conjecture). [clausify(21)].
% 0.44/1.00 47 -element(A,the_carrier(c6)) | relstr_element_smaller(c6,B,A) | in(f1(c6,B,A),B). [resolve(25,a,24,a)].
% 0.44/1.00 49 -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | in(f2(c6,B,A),B). [resolve(26,a,24,a)].
% 0.44/1.00 68 -in(A,empty_set). [ur(39,b,33,a)].
% 0.44/1.00 73 relstr_element_smaller(c6,A,c7) | in(f1(c6,A,c7),A). [resolve(47,a,36,a)].
% 0.44/1.00 76 relstr_set_smaller(c6,A,c7) | in(f2(c6,A,c7),A). [resolve(49,a,36,a)].
% 0.44/1.00 96 -relstr_element_smaller(c6,empty_set,c7). [resolve(76,a,41,a),unit_del(a,68)].
% 0.44/1.00 102 $F. [resolve(96,a,73,a),unit_del(a,68)].
% 0.44/1.00
% 0.44/1.00 % SZS output end Refutation
% 0.44/1.00 ============================== end of proof ==========================
% 0.44/1.00
% 0.44/1.00 ============================== STATISTICS ============================
% 0.44/1.00
% 0.44/1.00 Given=50. Generated=86. Kept=69. proofs=1.
% 0.44/1.00 Usable=48. Sos=17. Demods=1. Limbo=1, Disabled=48. Hints=0.
% 0.44/1.00 Megabytes=0.13.
% 0.44/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of statistics =====================
% 0.44/1.00
% 0.44/1.00 ============================== end of search =========================
% 0.44/1.00
% 0.44/1.00 THEOREM PROVED
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00
% 0.44/1.00 Exiting with 1 proof.
% 0.44/1.00
% 0.44/1.00 Process 17855 exit (max_proofs) Sun Jun 19 10:36:33 2022
% 0.44/1.00 Prover9 interrupted
%------------------------------------------------------------------------------