TSTP Solution File: SEU152+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU152+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 13:29:24 EDT 2022
% Result : Theorem 0.78s 1.16s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU152+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 14:16:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.78/1.04 ============================== Prover9 ===============================
% 0.78/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.04 Process 31337 was started by sandbox2 on n017.cluster.edu,
% 0.78/1.04 Sun Jun 19 14:16:44 2022
% 0.78/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31184_n017.cluster.edu".
% 0.78/1.04 ============================== end of head ===========================
% 0.78/1.04
% 0.78/1.04 ============================== INPUT =================================
% 0.78/1.04
% 0.78/1.04 % Reading from file /tmp/Prover9_31184_n017.cluster.edu
% 0.78/1.04
% 0.78/1.04 set(prolog_style_variables).
% 0.78/1.04 set(auto2).
% 0.78/1.04 % set(auto2) -> set(auto).
% 0.78/1.04 % set(auto) -> set(auto_inference).
% 0.78/1.04 % set(auto) -> set(auto_setup).
% 0.78/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.04 % set(auto) -> set(auto_limits).
% 0.78/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.04 % set(auto) -> set(auto_denials).
% 0.78/1.04 % set(auto) -> set(auto_process).
% 0.78/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.04 % set(auto2) -> assign(stats, some).
% 0.78/1.04 % set(auto2) -> clear(echo_input).
% 0.78/1.04 % set(auto2) -> set(quiet).
% 0.78/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.04 % set(auto2) -> clear(print_given).
% 0.78/1.04 assign(lrs_ticks,-1).
% 0.78/1.04 assign(sos_limit,10000).
% 0.78/1.04 assign(order,kbo).
% 0.78/1.04 set(lex_order_vars).
% 0.78/1.04 clear(print_given).
% 0.78/1.04
% 0.78/1.04 % formulas(sos). % not echoed (75 formulas)
% 0.78/1.04
% 0.78/1.04 ============================== end of input ==========================
% 0.78/1.04
% 0.78/1.04 % From the command line: assign(max_seconds, 300).
% 0.78/1.04
% 0.78/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.04
% 0.78/1.04 % Formulas that are not ordinary clauses:
% 0.78/1.04 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 9 (all A all B (B = powerset(A) <-> (all C (in(C,B) <-> subset(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 10 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 11 (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].
% 0.78/1.04 12 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 13 (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].
% 0.78/1.04 14 (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].
% 0.78/1.04 15 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 16 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 17 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 18 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 21 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 22 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 23 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 24 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 25 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 26 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 27 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 28 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 29 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 30 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 31 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 32 (all A all B all C (subset(A,B) -> in(C,A) | subset(A,set_difference(B,singleton(C))))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 33 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 34 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 35 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 36 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 37 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 38 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & A != C & A != D)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 39 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 40 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 41 (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].
% 0.78/1.04 42 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 43 (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].
% 0.78/1.04 44 (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].
% 0.78/1.04 45 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.04 46 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 47 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 48 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 49 (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].
% 0.78/1.05 50 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 51 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 52 (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].
% 0.78/1.05 53 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 54 (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].
% 0.78/1.05 55 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 56 (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].
% 0.78/1.05 57 (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].
% 0.78/1.05 58 (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].
% 0.78/1.05 59 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 60 (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].
% 0.78/1.05 61 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 62 (all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 63 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 64 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 65 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 66 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 67 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 68 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 69 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 70 (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].
% 0.78/1.05 71 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 72 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.05 73 -(all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.05
% 0.78/1.05 ============================== end of process non-clausal formulas ===
% 0.78/1.05
% 0.78/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.05
% 0.78/1.05 ============================== PREDICATE ELIMINATION =================
% 0.78/1.05
% 0.78/1.05 ============================== end predicate elimination =============
% 0.78/1.05
% 0.78/1.05 Auto_denials: (non-Horn, no changes).
% 0.78/1.05
% 0.78/1.05 Term ordering decisions:
% 0.78/1.05 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_difference=1. set_intersection2=1. set_union2=1. unordered_pair=1. f1=1. f3=1. f6=1. f9=1. f10=1. f11=1. singleton=1. powerset=1. f2=1. f4=1. f5=1. f7=1. f8=1.
% 0.78/1.05
% 0.78/1.05 ============================== end of process initial clauses ========
% 0.78/1.16
% 0.78/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.78/1.16
% 0.78/1.16 ============================== end of clauses for search =============
% 0.78/1.16
% 0.78/1.16 ============================== SEARCH ================================
% 0.78/1.16
% 0.78/1.16 % Starting search at 0.03 seconds.
% 0.78/1.16
% 0.78/1.16 ============================== PROOF =================================
% 0.78/1.16 % SZS status Theorem
% 0.78/1.16 % SZS output start Refutation
% 0.78/1.16
% 0.78/1.16 % Proof 1 at 0.13 (+ 0.01) seconds.
% 0.78/1.16 % Length of proof is 15.
% 0.78/1.16 % Level of proof is 4.
% 0.78/1.16 % Maximum clause weight is 8.000.
% 0.78/1.16 % Given clauses 135.
% 0.78/1.16
% 0.78/1.16 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.16 30 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.16 39 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.16 63 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.78/1.16 73 -(all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.16 77 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(4)].
% 0.78/1.16 132 subset(singleton(A),B) | -in(A,B) # label(l2_zfmisc_1) # label(lemma). [clausify(30)].
% 0.78/1.16 143 -subset(A,B) | set_union2(A,B) = B # label(t12_xboole_1) # label(lemma). [clausify(39)].
% 0.78/1.16 174 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(63)].
% 0.78/1.16 188 in(c3,c4) # label(l23_zfmisc_1) # label(negated_conjecture). [clausify(73)].
% 0.78/1.16 189 set_union2(singleton(c3),c4) != c4 # label(l23_zfmisc_1) # label(negated_conjecture). [clausify(73)].
% 0.78/1.16 190 set_union2(c4,unordered_pair(c3,c3)) != c4. [copy(189),rewrite([174(2),77(5)])].
% 0.78/1.16 231 subset(unordered_pair(A,A),B) | -in(A,B). [back_rewrite(132),rewrite([174(1)])].
% 0.78/1.16 1074 subset(unordered_pair(c3,c3),c4). [resolve(231,b,188,a)].
% 0.78/1.16 1123 $F. [resolve(1074,a,143,a),rewrite([77(5)]),unit_del(a,190)].
% 0.78/1.16
% 0.78/1.16 % SZS output end Refutation
% 0.78/1.16 ============================== end of proof ==========================
% 0.78/1.16
% 0.78/1.16 ============================== STATISTICS ============================
% 0.78/1.16
% 0.78/1.16 Given=135. Generated=1874. Kept=1040. proofs=1.
% 0.78/1.16 Usable=129. Sos=817. Demods=25. Limbo=9, Disabled=198. Hints=0.
% 0.78/1.16 Megabytes=1.03.
% 0.78/1.16 User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.78/1.16
% 0.78/1.16 ============================== end of statistics =====================
% 0.78/1.16
% 0.78/1.16 ============================== end of search =========================
% 0.78/1.16
% 0.78/1.16 THEOREM PROVED
% 0.78/1.16 % SZS status Theorem
% 0.78/1.16
% 0.78/1.16 Exiting with 1 proof.
% 0.78/1.16
% 0.78/1.16 Process 31337 exit (max_proofs) Sun Jun 19 14:16:44 2022
% 0.78/1.16 Prover9 interrupted
%------------------------------------------------------------------------------