TSTP Solution File: SEU140+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU140+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 13:29:16 EDT 2022
% Result : Theorem 0.75s 1.15s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU140+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 10:00:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 21700 was started by sandbox2 on n029.cluster.edu,
% 0.43/1.02 Mon Jun 20 10:00:46 2022
% 0.43/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21547_n029.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_21547_n029.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (56 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 4 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 5 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 6 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 7 (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].
% 0.43/1.02 8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 9 (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].
% 0.43/1.02 10 (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].
% 0.43/1.02 11 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 12 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 13 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 14 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 15 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 16 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 17 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 18 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 19 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 20 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 21 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 22 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 23 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 24 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 25 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 27 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 28 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 29 (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].
% 0.43/1.02 30 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 31 (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].
% 0.43/1.02 32 (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].
% 0.43/1.02 33 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 34 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 35 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 36 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 37 (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].
% 0.43/1.02 38 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 39 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 40 (all A all B set_union2(A,set_difference(B,A)) = set_union2(A,B)) # label(t39_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 41 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 42 (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].
% 0.43/1.02 43 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 44 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 45 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 46 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.02 47 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 48 (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].
% 0.75/1.15 49 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.15 50 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 51 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 52 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.15 53 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 54 (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].
% 0.75/1.15 55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.15
% 0.75/1.15 ============================== end of process non-clausal formulas ===
% 0.75/1.15
% 0.75/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.15
% 0.75/1.15 ============================== PREDICATE ELIMINATION =================
% 0.75/1.15
% 0.75/1.15 ============================== end predicate elimination =============
% 0.75/1.15
% 0.75/1.15 Auto_denials: (non-Horn, no changes).
% 0.75/1.15
% 0.75/1.15 Term ordering decisions:
% 0.75/1.15
% 0.75/1.15 % Assigning unary symbol f1 kb_weight 0 and highest precedence (23).
% 0.75/1.15 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. set_intersection2=1. set_union2=1. f3=1. f6=1. f7=1. f8=1. f2=1. f4=1. f5=1. f1=0.
% 0.75/1.15
% 0.75/1.15 ============================== end of process initial clauses ========
% 0.75/1.15
% 0.75/1.15 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.15
% 0.75/1.15 ============================== end of clauses for search =============
% 0.75/1.15
% 0.75/1.15 ============================== SEARCH ================================
% 0.75/1.15
% 0.75/1.15 % Starting search at 0.02 seconds.
% 0.75/1.15
% 0.75/1.15 ============================== PROOF =================================
% 0.75/1.15 % SZS status Theorem
% 0.75/1.15 % SZS output start Refutation
% 0.75/1.15
% 0.75/1.15 % Proof 1 at 0.15 (+ 0.00) seconds.
% 0.75/1.15 % Length of proof is 18.
% 0.75/1.15 % Level of proof is 5.
% 0.75/1.15 % Maximum clause weight is 9.000.
% 0.75/1.15 % Given clauses 139.
% 0.75/1.15
% 0.75/1.15 8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.15 42 (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].
% 0.75/1.15 55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.15 60 subset(c3,c4) # label(t63_xboole_1) # label(negated_conjecture). [clausify(55)].
% 0.75/1.15 61 disjoint(c4,c5) # label(t63_xboole_1) # label(negated_conjecture). [clausify(55)].
% 0.75/1.15 75 disjoint(A,B) | in(f7(A,B),A) # label(t3_xboole_0) # label(lemma). [clausify(42)].
% 0.75/1.15 76 disjoint(A,B) | in(f7(A,B),B) # label(t3_xboole_0) # label(lemma). [clausify(42)].
% 0.75/1.15 92 -disjoint(c3,c5) # label(t63_xboole_1) # label(negated_conjecture). [clausify(55)].
% 0.75/1.15 101 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma). [clausify(42)].
% 0.75/1.15 109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom). [clausify(26)].
% 0.75/1.15 123 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(8)].
% 0.75/1.15 273 -disjoint(c5,c3). [ur(109,b,92,a)].
% 0.75/1.15 300 -in(A,c3) | in(A,c4). [resolve(123,a,60,a)].
% 0.75/1.15 959 in(f7(c5,c3),c3). [resolve(273,a,76,a)].
% 0.75/1.15 960 in(f7(c5,c3),c5). [resolve(273,a,75,a)].
% 0.75/1.15 1084 -in(f7(c5,c3),c4). [ur(101,b,960,a,c,61,a)].
% 0.75/1.15 1292 $F. [resolve(300,a,959,a),unit_del(a,1084)].
% 0.75/1.15
% 0.75/1.15 % SZS output end Refutation
% 0.75/1.15 ============================== end of proof ==========================
% 0.75/1.15
% 0.75/1.15 ============================== STATISTICS ============================
% 0.75/1.15
% 0.75/1.15 Given=139. Generated=3023. Kept=1220. proofs=1.
% 0.75/1.15 Usable=133. Sos=1012. Demods=28. Limbo=3, Disabled=155. Hints=0.
% 0.75/1.15 Megabytes=0.98.
% 0.75/1.15 User_CPU=0.15, System_CPU=0.00, Wall_clock=0.
% 0.75/1.15
% 0.75/1.15 ============================== end of statistics =====================
% 0.75/1.15
% 0.75/1.15 ============================== end of search =========================
% 0.75/1.15
% 0.75/1.15 THEOREM PROVED
% 0.75/1.15 % SZS status Theorem
% 0.75/1.15
% 0.75/1.15 Exiting with 1 proof.
% 0.75/1.15
% 0.75/1.15 Process 21700 exit (max_proofs) Mon Jun 20 10:00:46 2022
% 0.75/1.15 Prover9 interrupted
%------------------------------------------------------------------------------