TSTP Solution File: SEU154+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:29:25 EDT 2022
% Result : Theorem 2.46s 2.76s
% Output : Refutation 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 11:54:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.47/1.05 ============================== Prover9 ===============================
% 0.47/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.05 Process 5142 was started by sandbox2 on n011.cluster.edu,
% 0.47/1.05 Sun Jun 19 11:54:54 2022
% 0.47/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4988_n011.cluster.edu".
% 0.47/1.05 ============================== end of head ===========================
% 0.47/1.05
% 0.47/1.05 ============================== INPUT =================================
% 0.47/1.05
% 0.47/1.05 % Reading from file /tmp/Prover9_4988_n011.cluster.edu
% 0.47/1.05
% 0.47/1.05 set(prolog_style_variables).
% 0.47/1.05 set(auto2).
% 0.47/1.05 % set(auto2) -> set(auto).
% 0.47/1.05 % set(auto) -> set(auto_inference).
% 0.47/1.05 % set(auto) -> set(auto_setup).
% 0.47/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.05 % set(auto) -> set(auto_limits).
% 0.47/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.05 % set(auto) -> set(auto_denials).
% 0.47/1.05 % set(auto) -> set(auto_process).
% 0.47/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.05 % set(auto2) -> assign(stats, some).
% 0.47/1.05 % set(auto2) -> clear(echo_input).
% 0.47/1.05 % set(auto2) -> set(quiet).
% 0.47/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.05 % set(auto2) -> clear(print_given).
% 0.47/1.05 assign(lrs_ticks,-1).
% 0.47/1.05 assign(sos_limit,10000).
% 0.47/1.05 assign(order,kbo).
% 0.47/1.05 set(lex_order_vars).
% 0.47/1.05 clear(print_given).
% 0.47/1.05
% 0.47/1.05 % formulas(sos). % not echoed (18 formulas)
% 0.47/1.05
% 0.47/1.05 ============================== end of input ==========================
% 0.47/1.05
% 0.47/1.05 % From the command line: assign(max_seconds, 300).
% 0.47/1.05
% 0.47/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.05
% 0.47/1.05 % Formulas that are not ordinary clauses:
% 0.47/1.05 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 3 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 4 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 5 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 6 (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].
% 0.47/1.05 7 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 8 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 9 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 10 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 11 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 12 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 13 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 14 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 15 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 16 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.05 17 -(all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.46/2.76
% 2.46/2.76 ============================== end of process non-clausal formulas ===
% 2.46/2.76
% 2.46/2.76 ============================== PROCESS INITIAL CLAUSES ===============
% 2.46/2.76
% 2.46/2.76 ============================== PREDICATE ELIMINATION =================
% 2.46/2.76
% 2.46/2.76 ============================== end predicate elimination =============
% 2.46/2.76
% 2.46/2.76 Auto_denials: (non-Horn, no changes).
% 2.46/2.76
% 2.46/2.76 Term ordering decisions:
% 2.46/2.76
% 2.46/2.76 % Assigning unary symbol singleton kb_weight 0 and highest precedence (15).
% 2.46/2.76 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_intersection2=1. f1=1. f2=1. f3=1. singleton=0.
% 2.46/2.76
% 2.46/2.76 ============================== end of process initial clauses ========
% 2.46/2.76
% 2.46/2.76 ============================== CLAUSES FOR SEARCH ====================
% 2.46/2.76
% 2.46/2.76 ============================== end of clauses for search =============
% 2.46/2.76
% 2.46/2.76 ============================== SEARCH ================================
% 2.46/2.76
% 2.46/2.76 % Starting search at 0.01 seconds.
% 2.46/2.76
% 2.46/2.76 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 0.64 sec).
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=29.000, iters=3343
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=27.000, iters=3351
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=26.000, iters=3369
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=24.000, iters=3385
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=23.000, iters=3403
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=22.000, iters=3349
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=21.000, iters=3353
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=20.000, iters=3539
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=19.000, iters=3448
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=18.000, iters=3357
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=17.000, iters=3531
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=16.000, iters=3339
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=15.000, iters=3378
% 2.46/2.76
% 2.46/2.76 Low Water (keep): wt=14.000, iters=3333
% 2.46/2.76
% 2.46/2.76 ============================== PROOF =================================
% 2.46/2.76 % SZS status Theorem
% 2.46/2.76 % SZS output start Refutation
% 2.46/2.76
% 2.46/2.76 % Proof 1 at 1.70 (+ 0.03) seconds.
% 2.46/2.76 % Length of proof is 58.
% 2.46/2.76 % Level of proof is 15.
% 2.46/2.76 % Maximum clause weight is 28.000.
% 2.46/2.76 % Given clauses 891.
% 2.46/2.76
% 2.46/2.76 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 4 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 5 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 6 (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].
% 2.46/2.76 7 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 11 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 16 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 2.46/2.76 17 -(all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.46/2.76 21 subset(empty_set,A) # label(t2_xboole_1) # label(axiom). [clausify(16)].
% 2.46/2.76 22 set_intersection2(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(11)].
% 2.46/2.76 23 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(2)].
% 2.46/2.76 24 subset(A,B) | in(f2(A,B),A) # label(d3_tarski) # label(axiom). [clausify(5)].
% 2.46/2.76 25 singleton(A) = B | in(f1(A,B),B) | f1(A,B) = A # label(d1_tarski) # label(axiom). [clausify(4)].
% 2.46/2.76 26 set_intersection2(A,B) = C | in(f3(A,B,C),C) | in(f3(A,B,C),A) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 2.46/2.76 27 set_intersection2(A,B) = C | in(f3(A,B,C),C) | in(f3(A,B,C),B) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 2.46/2.76 29 -in(c3,c4) # label(l28_zfmisc_1) # label(negated_conjecture). [clausify(17)].
% 2.46/2.76 30 -disjoint(singleton(c3),c4) # label(l28_zfmisc_1) # label(negated_conjecture). [clausify(17)].
% 2.46/2.76 31 -in(A,B) | -in(B,A) # label(antisymmetry_r2_hidden) # label(axiom). [clausify(1)].
% 2.46/2.76 37 disjoint(A,B) | set_intersection2(A,B) != empty_set # label(d7_xboole_0) # label(axiom). [clausify(7)].
% 2.46/2.76 39 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(5)].
% 2.46/2.76 40 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(4)].
% 2.46/2.76 41 singleton(A) != B | in(C,B) | C != A # label(d1_tarski) # label(axiom). [clausify(4)].
% 2.46/2.76 43 set_intersection2(A,B) != C | -in(D,C) | in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 2.46/2.76 45 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 2.46/2.76 49 -in(A,A). [factor(31,a,b)].
% 2.46/2.76 51 A != B | in(C,B) | -in(C,A). [factor(45,c,d),rewrite([22(1)])].
% 2.46/2.76 62 set_intersection2(c4,singleton(c3)) != empty_set. [ur(37,a,30,a),rewrite([23(4)])].
% 2.46/2.76 67 -in(A,B) | in(A,C) | in(f2(B,C),B). [resolve(39,a,24,a)].
% 2.46/2.76 75 in(A,singleton(B)) | A != B. [resolve(41,a,22,a(flip)),rewrite([22(3)])].
% 2.46/2.76 105 set_intersection2(A,B) != C | in(f3(B,D,E),C) | -in(f3(B,D,E),A) | set_intersection2(B,D) = E | in(f3(B,D,E),E). [resolve(45,d,26,c)].
% 2.46/2.76 126 -in(A,set_intersection2(A,B)). [ur(43,a,23,a,c,49,a)].
% 2.46/2.76 129 -in(A,empty_set). [ur(39,a,21,a,c,49,a)].
% 2.46/2.76 134 A != B | in(f3(A,C,D),B) | set_intersection2(A,C) = D | in(f3(A,C,D),D). [resolve(51,c,26,c)].
% 2.46/2.76 148 singleton(A) = empty_set | f1(A,empty_set) = A. [resolve(129,a,25,b)].
% 2.46/2.76 150 singleton(A) != empty_set. [ur(41,b,129,a,c,22,a)].
% 2.46/2.76 151 f1(A,empty_set) = A. [back_unit_del(148),unit_del(a,150)].
% 2.46/2.76 169 in(A,singleton(A)). [resolve(75,b,151,a),rewrite([151(2)])].
% 2.46/2.76 192 -subset(singleton(A),set_intersection2(A,B)). [ur(39,b,169,a,c,126,a)].
% 2.46/2.76 194 -subset(singleton(A),A). [ur(39,b,169,a,c,49,a)].
% 2.46/2.76 225 in(f2(singleton(A),A),singleton(A)). [resolve(194,a,24,a)].
% 2.46/2.76 236 singleton(A) != singleton(B) | f2(singleton(B),B) = A. [resolve(225,a,40,b)].
% 2.46/2.76 390 in(f3(A,B,C),D) | in(f2(C,D),C) | set_intersection2(A,B) = C | in(f3(A,B,C),B). [resolve(67,a,27,b)].
% 2.46/2.76 392 in(f3(A,B,C),D) | in(f2(C,D),C) | set_intersection2(A,B) = C | in(f3(A,B,C),A). [resolve(67,a,26,b)].
% 2.46/2.76 398 in(f2(singleton(A),set_intersection2(A,B)),singleton(A)). [resolve(192,a,24,a)].
% 2.46/2.76 417 singleton(A) != singleton(B) | f2(singleton(B),set_intersection2(B,C)) = A. [resolve(398,a,40,b)].
% 2.46/2.76 723 f2(singleton(A),A) = A. [xx_res(236,a)].
% 2.46/2.76 5179 f3(c4,singleton(c3),empty_set) != c4. [ur(134,b,49,a,c,62,a,d,129,a),flip(a)].
% 2.46/2.76 5181 -in(f3(c4,singleton(c3),empty_set),singleton(c4)). [ur(40,a,723,a(flip),c,5179,a),rewrite([723(11)])].
% 2.46/2.76 5666 f2(singleton(A),set_intersection2(A,B)) = A. [xx_res(417,a)].
% 2.46/2.76 5843 -in(c3,f2(singleton(c4),set_intersection2(A,c4))). [ur(51,a,5666,a,b,29,a),rewrite([23(5)])].
% 2.46/2.76 8019 in(f3(c4,singleton(c3),empty_set),singleton(c3)). [resolve(390,a,5181,a),unit_del(a,129),unit_del(b,62)].
% 2.46/2.76 8191 singleton(c3) != singleton(A) | f3(c4,singleton(c3),empty_set) = A. [resolve(8019,a,40,b),flip(a)].
% 2.46/2.76 8457 in(f3(c4,singleton(c3),empty_set),c4). [resolve(392,a,5181,a),unit_del(a,129),unit_del(b,62)].
% 2.46/2.76 8598 c4 != A | in(f3(c4,singleton(c3),empty_set),A). [resolve(8457,a,105,c),rewrite([22(3)]),unit_del(c,62),unit_del(d,129)].
% 2.46/2.76 8781 in(f3(c4,singleton(c3),empty_set),f2(singleton(c4),set_intersection2(A,c4))). [resolve(8598,a,5666,a(flip)),rewrite([23(9)])].
% 2.46/2.76 9408 f3(c4,singleton(c3),empty_set) = c3. [xx_res(8191,a)].
% 2.46/2.76 9434 $F. [back_rewrite(8781),rewrite([9408(5)]),unit_del(a,5843)].
% 2.46/2.76
% 2.46/2.76 % SZS output end Refutation
% 2.46/2.76 ============================== end of proof ==========================
% 2.46/2.76
% 2.46/2.76 ============================== STATISTICS ============================
% 2.46/2.76
% 2.46/2.76 Given=891. Generated=61757. Kept=9416. proofs=1.
% 2.46/2.76 Usable=828. Sos=7568. Demods=23. Limbo=26, Disabled=1023. Hints=0.
% 2.46/2.76 Megabytes=8.17.
% 2.46/2.76 User_CPU=1.70, System_CPU=0.03, Wall_clock=2.
% 2.46/2.76
% 2.46/2.76 ============================== end of statistics =====================
% 2.46/2.76
% 2.46/2.76 ============================== end of search =========================
% 2.46/2.76
% 2.46/2.76 THEOREM PROVED
% 2.46/2.76 % SZS status Theorem
% 2.46/2.76
% 2.46/2.76 Exiting with 1 proof.
% 2.46/2.76
% 2.46/2.76 Process 5142 exit (max_proofs) Sun Jun 19 11:54:56 2022
% 2.46/2.76 Prover9 interrupted
%------------------------------------------------------------------------------