TSTP Solution File: SEU132+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 13:29:12 EDT 2022
% Result : Theorem 2.19s 2.45s
% Output : Refutation 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 22:55:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 25290 was started by sandbox2 on n012.cluster.edu,
% 0.42/0.97 Sat Jun 18 22:55:08 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25137_n012.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_25137_n012.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (15 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 2 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 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].
% 0.42/0.97 4 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 5 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 8 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 9 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 10 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 11 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 12 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 13 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 14 -(all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97
% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials: (non-Horn, no changes).
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 2.19/2.45 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. f1=1. f2=1.
% 2.19/2.45
% 2.19/2.45 ============================== end of process initial clauses ========
% 2.19/2.45
% 2.19/2.45 ============================== CLAUSES FOR SEARCH ====================
% 2.19/2.45
% 2.19/2.45 ============================== end of clauses for search =============
% 2.19/2.45
% 2.19/2.45 ============================== SEARCH ================================
% 2.19/2.45
% 2.19/2.45 % Starting search at 0.01 seconds.
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=49.000, iters=3460
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=47.000, iters=3460
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=45.000, iters=3460
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=43.000, iters=3458
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=41.000, iters=3453
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=39.000, iters=3435
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=37.000, iters=3390
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=33.000, iters=3555
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=31.000, iters=3382
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=29.000, iters=3385
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=27.000, iters=3384
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=25.000, iters=3350
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=23.000, iters=3352
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=22.000, iters=3366
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=21.000, iters=3389
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=20.000, iters=3337
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=19.000, iters=3337
% 2.19/2.45
% 2.19/2.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 0.77 sec).
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=18.000, iters=3350
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=17.000, iters=3358
% 2.19/2.45
% 2.19/2.45 Low Water (keep): wt=16.000, iters=3333
% 2.19/2.45
% 2.19/2.45 ============================== PROOF =================================
% 2.19/2.45 % SZS status Theorem
% 2.19/2.45 % SZS output start Refutation
% 2.19/2.45
% 2.19/2.45 % Proof 1 at 1.47 (+ 0.02) seconds.
% 2.19/2.45 % Length of proof is 32.
% 2.19/2.45 % Level of proof is 7.
% 2.19/2.45 % Maximum clause weight is 23.000.
% 2.19/2.45 % Given clauses 904.
% 2.19/2.45
% 2.19/2.45 2 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.19/2.45 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].
% 2.19/2.45 9 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 2.19/2.45 14 -(all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.19/2.45 18 subset(c3,c4) # label(t33_xboole_1) # label(negated_conjecture). [clausify(14)].
% 2.19/2.45 19 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(9)].
% 2.19/2.45 21 subset(A,B) | in(f1(A,B),A) # label(d3_tarski) # label(axiom). [clausify(2)].
% 2.19/2.45 22 set_difference(A,B) = C | in(f2(A,B,C),C) | in(f2(A,B,C),A) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 2.19/2.45 26 -subset(set_difference(c3,c5),set_difference(c4,c5)) # label(t33_xboole_1) # label(negated_conjecture). [clausify(14)].
% 2.19/2.45 27 set_difference(A,B) != C | -in(D,C) | -in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 2.19/2.45 30 subset(A,B) | -in(f1(A,B),B) # label(d3_tarski) # label(axiom). [clausify(2)].
% 2.19/2.45 31 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(2)].
% 2.19/2.45 32 set_difference(A,B) != C | -in(D,C) | in(D,A) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 2.19/2.45 33 set_difference(A,B) != C | in(D,C) | -in(D,A) | in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 2.19/2.45 35 set_difference(A,B) = C | -in(f2(A,B,C),C) | -in(f2(A,B,C),A) | in(f2(A,B,C),B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 2.19/2.45 36 set_difference(A,B) = A | in(f2(A,B,A),A). [factor(22,b,c)].
% 2.19/2.45 40 set_difference(A,B) = A | -in(f2(A,B,A),A) | in(f2(A,B,A),B). [factor(35,b,c)].
% 2.19/2.45 47 in(f1(set_difference(c3,c5),set_difference(c4,c5)),set_difference(c3,c5)). [resolve(26,a,21,a)].
% 2.19/2.45 53 -in(f1(set_difference(c3,c5),set_difference(c4,c5)),set_difference(c4,c5)). [ur(30,a,26,a)].
% 2.19/2.45 55 -in(A,c3) | in(A,c4). [resolve(31,a,18,a)].
% 2.19/2.45 73 set_difference(A,B) = A | set_difference(C,A) != D | -in(f2(A,B,A),D). [resolve(36,b,27,c)].
% 2.19/2.45 83 set_difference(A,B) = A | in(f2(A,B,A),B). [resolve(40,b,36,b),merge(c)].
% 2.19/2.45 116 -in(f1(set_difference(c3,c5),set_difference(c4,c5)),set_difference(set_difference(c4,c5),A)). [ur(32,a,19,a(flip),c,53,a),rewrite([19(13)])].
% 2.19/2.45 136 set_difference(c3,c5) != set_difference(A,B) | in(f1(set_difference(c3,c5),set_difference(c4,c5)),A). [resolve(47,a,32,b),flip(a)].
% 2.19/2.45 283 -in(f1(set_difference(c3,c5),set_difference(c4,c5)),c5). [ur(27,a,xx,b,47,a)].
% 2.19/2.45 4131 set_difference(A,B) = A | set_difference(C,A) != B. [resolve(73,c,83,b),merge(c)].
% 2.19/2.45 4256 set_difference(A,set_difference(B,A)) = A. [resolve(4131,b,19,a(flip)),rewrite([19(3)])].
% 2.19/2.45 4263 set_difference(set_difference(A,B),B) = set_difference(A,B). [resolve(4256,a,4131,b)].
% 2.19/2.45 6217 in(f1(set_difference(c3,c5),set_difference(c4,c5)),c3). [xx_res(136,a)].
% 2.19/2.45 6258 in(f1(set_difference(c3,c5),set_difference(c4,c5)),c4). [resolve(6217,a,55,a)].
% 2.19/2.45 9507 set_difference(set_difference(c4,c5),A) != set_difference(c4,c5). [ur(33,b,116,a,c,6258,a,d,283,a),flip(a)].
% 2.19/2.45 9508 $F. [resolve(9507,a,4263,a)].
% 2.19/2.45
% 2.19/2.45 % SZS output end Refutation
% 2.19/2.45 ============================== end of proof ==========================
% 2.19/2.45
% 2.19/2.45 ============================== STATISTICS ============================
% 2.19/2.45
% 2.19/2.45 Given=904. Generated=57237. Kept=9493. proofs=1.
% 2.19/2.45 Usable=876. Sos=8282. Demods=9. Limbo=2, Disabled=353. Hints=0.
% 2.19/2.46 Megabytes=9.03.
% 2.19/2.46 User_CPU=1.48, System_CPU=0.02, Wall_clock=2.
% 2.19/2.46
% 2.19/2.46 ============================== end of statistics =====================
% 2.19/2.46
% 2.19/2.46 ============================== end of search =========================
% 2.19/2.46
% 2.19/2.46 THEOREM PROVED
% 2.19/2.46 % SZS status Theorem
% 2.19/2.46
% 2.19/2.46 Exiting with 1 proof.
% 2.19/2.46
% 2.19/2.46 Process 25290 exit (max_proofs) Sat Jun 18 22:55:10 2022
% 2.19/2.46 Prover9 interrupted
%------------------------------------------------------------------------------