TSTP Solution File: SEU133+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 13:29:13 EDT 2022
% Result : Theorem 1.04s 1.32s
% Output : Refutation 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.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 22:39:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.77/1.03 ============================== Prover9 ===============================
% 0.77/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.03 Process 20421 was started by sandbox on n025.cluster.edu,
% 0.77/1.03 Sun Jun 19 22:39:45 2022
% 0.77/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20267_n025.cluster.edu".
% 0.77/1.03 ============================== end of head ===========================
% 0.77/1.03
% 0.77/1.03 ============================== INPUT =================================
% 0.77/1.03
% 0.77/1.03 % Reading from file /tmp/Prover9_20267_n025.cluster.edu
% 0.77/1.03
% 0.77/1.03 set(prolog_style_variables).
% 0.77/1.03 set(auto2).
% 0.77/1.03 % set(auto2) -> set(auto).
% 0.77/1.03 % set(auto) -> set(auto_inference).
% 0.77/1.03 % set(auto) -> set(auto_setup).
% 0.77/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.03 % set(auto) -> set(auto_limits).
% 0.77/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.03 % set(auto) -> set(auto_denials).
% 0.77/1.03 % set(auto) -> set(auto_process).
% 0.77/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.03 % set(auto2) -> assign(stats, some).
% 0.77/1.03 % set(auto2) -> clear(echo_input).
% 0.77/1.03 % set(auto2) -> set(quiet).
% 0.77/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.03 % set(auto2) -> clear(print_given).
% 0.77/1.03 assign(lrs_ticks,-1).
% 0.77/1.03 assign(sos_limit,10000).
% 0.77/1.03 assign(order,kbo).
% 0.77/1.03 set(lex_order_vars).
% 0.77/1.03 clear(print_given).
% 0.77/1.03
% 0.77/1.03 % formulas(sos). % not echoed (46 formulas)
% 0.77/1.03
% 0.77/1.03 ============================== end of input ==========================
% 0.77/1.03
% 0.77/1.03 % From the command line: assign(max_seconds, 300).
% 0.77/1.03
% 0.77/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.04
% 0.77/1.04 % Formulas that are not ordinary clauses:
% 0.77/1.04 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 4 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 5 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 6 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 8 (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].
% 0.77/1.04 9 (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].
% 0.77/1.04 10 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 11 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 12 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 13 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 14 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 15 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 16 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 17 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 18 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 19 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 20 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 21 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 22 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 23 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 24 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 25 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 26 (all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 27 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 28 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 29 (all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 30 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 31 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 32 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 33 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 34 (all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 35 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 36 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 37 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 38 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 39 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 40 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 41 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 42 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 43 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.04 44 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.77/1.04 45 -(all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.04
% 0.77/1.04 ============================== end of process non-clausal formulas ===
% 0.77/1.04
% 0.77/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.04
% 0.77/1.04 ============================== PREDICATE ELIMINATION =================
% 0.77/1.04
% 0.77/1.04 ============================== end predicate elimination =============
% 1.04/1.32
% 1.04/1.32 Auto_denials: (non-Horn, no changes).
% 1.04/1.32
% 1.04/1.32 Term ordering decisions:
% 1.04/1.32
% 1.04/1.32 % Assigning unary symbol f1 kb_weight 0 and highest precedence (21).
% 1.04/1.32 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_intersection2=1. set_union2=1. set_difference=1. f3=1. f6=1. f7=1. f8=1. f2=1. f4=1. f5=1. f1=0.
% 1.04/1.32
% 1.04/1.32 ============================== end of process initial clauses ========
% 1.04/1.32
% 1.04/1.32 ============================== CLAUSES FOR SEARCH ====================
% 1.04/1.32
% 1.04/1.32 ============================== end of clauses for search =============
% 1.04/1.32
% 1.04/1.32 ============================== SEARCH ================================
% 1.04/1.32
% 1.04/1.32 % Starting search at 0.02 seconds.
% 1.04/1.32
% 1.04/1.32 ============================== PROOF =================================
% 1.04/1.32 % SZS status Theorem
% 1.04/1.32 % SZS output start Refutation
% 1.04/1.32
% 1.04/1.32 % Proof 1 at 0.29 (+ 0.01) seconds.
% 1.04/1.32 % Length of proof is 10.
% 1.04/1.32 % Level of proof is 3.
% 1.04/1.32 % Maximum clause weight is 11.000.
% 1.04/1.32 % Given clauses 234.
% 1.04/1.32
% 1.04/1.32 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.32 9 (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].
% 1.04/1.32 45 -(all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.04/1.32 61 subset(A,B) | in(f3(A,B),A) # label(d3_tarski) # label(axiom). [clausify(7)].
% 1.04/1.32 72 -subset(set_difference(c3,c4),c3) # label(t36_xboole_1) # label(negated_conjecture). [clausify(45)].
% 1.04/1.32 86 subset(A,B) | -in(f3(A,B),B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 1.04/1.32 102 set_difference(A,B) != C | -in(D,C) | in(D,A) # label(d4_xboole_0) # label(axiom). [clausify(9)].
% 1.04/1.32 149 in(f3(set_difference(c3,c4),c3),set_difference(c3,c4)). [resolve(72,a,61,a)].
% 1.04/1.32 224 -in(f3(set_difference(c3,c4),c3),c3). [ur(86,a,72,a)].
% 1.04/1.32 2985 $F. [ur(102,b,149,a,c,224,a),flip(a),xx(a)].
% 1.04/1.32
% 1.04/1.32 % SZS output end Refutation
% 1.04/1.32 ============================== end of proof ==========================
% 1.04/1.32
% 1.04/1.32 ============================== STATISTICS ============================
% 1.04/1.32
% 1.04/1.32 Given=234. Generated=11392. Kept=2938. proofs=1.
% 1.04/1.32 Usable=228. Sos=2606. Demods=34. Limbo=23, Disabled=149. Hints=0.
% 1.04/1.32 Megabytes=2.41.
% 1.04/1.32 User_CPU=0.29, System_CPU=0.01, Wall_clock=0.
% 1.04/1.32
% 1.04/1.32 ============================== end of statistics =====================
% 1.04/1.32
% 1.04/1.32 ============================== end of search =========================
% 1.04/1.32
% 1.04/1.32 THEOREM PROVED
% 1.04/1.32 % SZS status Theorem
% 1.04/1.32
% 1.04/1.32 Exiting with 1 proof.
% 1.04/1.32
% 1.04/1.32 Process 20421 exit (max_proofs) Sun Jun 19 22:39:45 2022
% 1.04/1.32 Prover9 interrupted
%------------------------------------------------------------------------------