TSTP Solution File: SEU171+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:29:37 EDT 2022
% Result : Theorem 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 : Mon Jun 20 09:06:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 23130 was started by sandbox2 on n018.cluster.edu,
% 0.44/1.01 Mon Jun 20 09:06:51 2022
% 0.44/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22887_n018.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_22887_n018.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (23 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 (all A all B ((-empty(A) -> (element(B,A) <-> in(B,A))) & (empty(A) -> (element(B,A) <-> empty(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A all B (element(B,powerset(A)) -> subset_complement(A,B) = set_difference(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 5 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 10 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 15 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 16 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 17 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 18 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 19 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 20 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 21 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 22 -(all A (A != empty_set -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.03
% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials: (non-Horn, no changes).
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. subset_complement=1. powerset=1. f2=1. f3=1. f4=1. f1=1.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.01 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Theorem
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.75/1.03 % Length of proof is 33.
% 0.75/1.03 % Level of proof is 6.
% 0.75/1.03 % Maximum clause weight is 14.000.
% 0.75/1.03 % Given clauses 114.
% 0.75/1.03
% 0.75/1.03 2 (all A all B ((-empty(A) -> (element(B,A) <-> in(B,A))) & (empty(A) -> (element(B,A) <-> empty(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 4 (all A all B (element(B,powerset(A)) -> subset_complement(A,B) = set_difference(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 7 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 12 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 17 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 19 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 22 -(all A (A != empty_set -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.04 26 element(c5,c3) # label(t50_subset_1) # label(negated_conjecture). [clausify(22)].
% 0.75/1.04 28 element(c4,powerset(c3)) # label(t50_subset_1) # label(negated_conjecture). [clausify(22)].
% 0.75/1.04 30 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(17)].
% 0.75/1.04 36 empty_set != c3 # label(t50_subset_1) # label(negated_conjecture). [clausify(22)].
% 0.75/1.04 37 c3 != empty_set. [copy(36),flip(a)].
% 0.75/1.04 38 -in(c5,c4) # label(t50_subset_1) # label(negated_conjecture). [clausify(22)].
% 0.75/1.04 40 -in(c5,subset_complement(c3,c4)) # label(t50_subset_1) # label(negated_conjecture). [clausify(22)].
% 0.75/1.04 44 -empty(A) | empty_set = A # label(t6_boole) # label(axiom). [clausify(19)].
% 0.75/1.04 48 empty(A) | -element(B,A) | in(B,A) # label(d2_subset_1) # label(axiom). [clausify(2)].
% 0.75/1.04 50 -element(A,powerset(B)) | element(subset_complement(B,A),powerset(B)) # label(dt_k3_subset_1) # label(axiom). [clausify(7)].
% 0.75/1.04 51 set_difference(A,B) != C | -in(D,C) | in(D,A) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 0.75/1.04 52 -element(A,powerset(B)) | subset_complement(B,A) = set_difference(B,A) # label(d5_subset_1) # label(axiom). [clausify(4)].
% 0.75/1.04 53 -element(A,powerset(B)) | subset_complement(B,subset_complement(B,A)) = A # label(involutiveness_k3_subset_1) # label(axiom). [clausify(12)].
% 0.75/1.04 54 set_difference(A,B) != C | in(D,C) | -in(D,A) | in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 0.75/1.04 78 -empty(c3). [ur(44,b,37,a(flip))].
% 0.75/1.04 88 in(c5,c3). [resolve(48,b,26,a),unit_del(a,78)].
% 0.75/1.04 92 element(subset_complement(c3,c4),powerset(c3)). [resolve(50,a,28,a)].
% 0.75/1.04 97 -in(c5,set_difference(c4,A)). [ur(51,a,30,a(flip),c,38,a),rewrite([30(5)])].
% 0.75/1.04 101 subset_complement(c3,c4) = set_difference(c3,c4). [resolve(52,a,28,a)].
% 0.75/1.04 104 element(set_difference(c3,c4),powerset(c3)). [back_rewrite(92),rewrite([101(3)])].
% 0.75/1.04 105 -in(c5,set_difference(c3,c4)). [back_rewrite(40),rewrite([101(4)])].
% 0.75/1.04 108 subset_complement(c3,set_difference(c3,c4)) = c4. [resolve(53,a,28,a),rewrite([101(4)])].
% 0.75/1.04 258 set_difference(c3,set_difference(c3,c4)) = c4. [resolve(104,a,52,a),rewrite([108(5)]),flip(a)].
% 0.75/1.04 377 set_difference(c4,A) != c4. [ur(54,b,97,a,c,88,a,d,105,a),rewrite([258(5)]),flip(a)].
% 0.75/1.04 378 $F. [resolve(377,a,30,a)].
% 0.75/1.04
% 0.75/1.04 % SZS output end Refutation
% 0.75/1.04 ============================== end of proof ==========================
% 0.75/1.04
% 0.75/1.04 ============================== STATISTICS ============================
% 0.75/1.04
% 0.75/1.04 Given=114. Generated=799. Kept=354. proofs=1.
% 0.75/1.04 Usable=108. Sos=219. Demods=14. Limbo=3, Disabled=56. Hints=0.
% 0.75/1.04 Megabytes=0.29.
% 0.75/1.04 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.75/1.04
% 0.75/1.04 ============================== end of statistics =====================
% 0.75/1.04
% 0.75/1.04 ============================== end of search =========================
% 0.75/1.04
% 0.75/1.04 THEOREM PROVED
% 0.75/1.04 % SZS status Theorem
% 0.75/1.04
% 0.75/1.04 Exiting with 1 proof.
% 0.75/1.04
% 0.75/1.04 Process 23130 exit (max_proofs) Mon Jun 20 09:06:51 2022
% 0.75/1.04 Prover9 interrupted
%------------------------------------------------------------------------------