TSTP Solution File: SEU129+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU129+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:29:11 EDT 2022
% Result : Theorem 0.89s 1.16s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU129+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 20:29:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.05 ============================== Prover9 ===============================
% 0.46/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.05 Process 13099 was started by sandbox on n013.cluster.edu,
% 0.46/1.05 Sun Jun 19 20:29:14 2022
% 0.46/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12946_n013.cluster.edu".
% 0.46/1.05 ============================== end of head ===========================
% 0.46/1.05
% 0.46/1.05 ============================== INPUT =================================
% 0.46/1.05
% 0.46/1.05 % Reading from file /tmp/Prover9_12946_n013.cluster.edu
% 0.46/1.05
% 0.46/1.05 set(prolog_style_variables).
% 0.46/1.05 set(auto2).
% 0.46/1.05 % set(auto2) -> set(auto).
% 0.46/1.05 % set(auto) -> set(auto_inference).
% 0.46/1.05 % set(auto) -> set(auto_setup).
% 0.46/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.05 % set(auto) -> set(auto_limits).
% 0.46/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.05 % set(auto) -> set(auto_denials).
% 0.46/1.05 % set(auto) -> set(auto_process).
% 0.46/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.05 % set(auto2) -> assign(stats, some).
% 0.46/1.05 % set(auto2) -> clear(echo_input).
% 0.46/1.05 % set(auto2) -> set(quiet).
% 0.46/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.05 % set(auto2) -> clear(print_given).
% 0.46/1.05 assign(lrs_ticks,-1).
% 0.46/1.05 assign(sos_limit,10000).
% 0.46/1.05 assign(order,kbo).
% 0.46/1.05 set(lex_order_vars).
% 0.46/1.05 clear(print_given).
% 0.46/1.05
% 0.46/1.05 % formulas(sos). % not echoed (37 formulas)
% 0.46/1.05
% 0.46/1.05 ============================== end of input ==========================
% 0.46/1.05
% 0.46/1.05 % From the command line: assign(max_seconds, 300).
% 0.46/1.05
% 0.46/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.05
% 0.46/1.05 % Formulas that are not ordinary clauses:
% 0.46/1.05 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 4 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 5 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 9 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 11 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 12 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 13 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 14 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 15 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 16 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 17 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 18 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 19 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 20 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 21 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 22 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 23 (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].
% 0.89/1.16 24 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 25 (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].
% 0.89/1.16 26 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 27 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 28 (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].
% 0.89/1.16 29 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 30 (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].
% 0.89/1.16 31 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 32 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 33 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 34 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 35 (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].
% 0.89/1.16 36 -(all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.16
% 0.89/1.16 ============================== end of process non-clausal formulas ===
% 0.89/1.16
% 0.89/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.16
% 0.89/1.16 ============================== PREDICATE ELIMINATION =================
% 0.89/1.16
% 0.89/1.16 ============================== end predicate elimination =============
% 0.89/1.16
% 0.89/1.16 Auto_denials: (non-Horn, no changes).
% 0.89/1.16
% 0.89/1.16 Term ordering decisions:
% 0.89/1.16
% 0.89/1.16 % Assigning unary symbol f1 kb_weight 0 and highest precedence (19).
% 0.89/1.16 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_intersection2=1. set_union2=1. f3=1. f5=1. f6=1. f2=1. f4=1. f1=0.
% 0.89/1.16
% 0.89/1.16 ============================== end of process initial clauses ========
% 0.89/1.16
% 0.89/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.16
% 0.89/1.16 ============================== end of clauses for search =============
% 0.89/1.16
% 0.89/1.16 ============================== SEARCH ================================
% 0.89/1.16
% 0.89/1.16 % Starting search at 0.02 seconds.
% 0.89/1.16
% 0.89/1.16 ============================== PROOF =================================
% 0.89/1.16 % SZS status Theorem
% 0.89/1.16 % SZS output start Refutation
% 0.89/1.16
% 0.89/1.16 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.89/1.16 % Length of proof is 15.
% 0.89/1.16 % Level of proof is 4.
% 0.89/1.16 % Maximum clause weight is 11.000.
% 0.89/1.16 % Given clauses 141.
% 0.89/1.16
% 0.89/1.16 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.16 22 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.89/1.16 23 (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].
% 0.89/1.16 25 (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].
% 0.89/1.16 36 -(all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.16 41 subset(c3,c4) # label(t26_xboole_1) # label(negated_conjecture). [clausify(36)].
% 0.89/1.16 44 subset(set_intersection2(A,B),A) # label(t17_xboole_1) # label(lemma). [clausify(22)].
% 0.89/1.16 49 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 0.89/1.16 62 -subset(set_intersection2(c3,c5),set_intersection2(c4,c5)) # label(t26_xboole_1) # label(negated_conjecture). [clausify(36)].
% 0.89/1.16 79 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(25)].
% 0.89/1.16 84 -subset(A,B) | -subset(A,C) | subset(A,set_intersection2(B,C)) # label(t19_xboole_1) # label(lemma). [clausify(23)].
% 0.89/1.16 105 subset(set_intersection2(A,B),B). [para(49(a,1),44(a,1))].
% 0.89/1.16 181 -subset(A,c3) | subset(A,c4). [resolve(79,b,41,a)].
% 0.89/1.16 525 -subset(set_intersection2(c3,c5),c4). [ur(84,b,105,a,c,62,a)].
% 0.89/1.16 1044 $F. [ur(181,b,525,a),unit_del(a,44)].
% 0.89/1.16
% 0.89/1.16 % SZS output end Refutation
% 0.89/1.16 ============================== end of proof ==========================
% 0.89/1.16
% 0.89/1.16 ============================== STATISTICS ============================
% 0.89/1.16
% 0.89/1.16 Given=141. Generated=3215. Kept=1006. proofs=1.
% 0.89/1.16 Usable=134. Sos=830. Demods=13. Limbo=1, Disabled=95. Hints=0.
% 0.89/1.16 Megabytes=0.75.
% 0.89/1.16 User_CPU=0.12, System_CPU=0.01, Wall_clock=1.
% 0.89/1.16
% 0.89/1.16 ============================== end of statistics =====================
% 0.89/1.16
% 0.89/1.16 ============================== end of search =========================
% 0.89/1.16
% 0.89/1.16 THEOREM PROVED
% 0.89/1.16 % SZS status Theorem
% 0.89/1.16
% 0.89/1.16 Exiting with 1 proof.
% 0.89/1.16
% 0.89/1.16 Process 13099 exit (max_proofs) Sun Jun 19 20:29:15 2022
% 0.89/1.16 Prover9 interrupted
%------------------------------------------------------------------------------