TSTP Solution File: SEU143+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU143+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 13:29:18 EDT 2022
% Result : Theorem 0.81s 1.12s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU143+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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 13:57:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.00 ============================== Prover9 ===============================
% 0.41/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.00 Process 15138 was started by sandbox on n028.cluster.edu,
% 0.41/1.00 Mon Jun 20 13:57:47 2022
% 0.41/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14985_n028.cluster.edu".
% 0.41/1.00 ============================== end of head ===========================
% 0.41/1.00
% 0.41/1.00 ============================== INPUT =================================
% 0.41/1.00
% 0.41/1.00 % Reading from file /tmp/Prover9_14985_n028.cluster.edu
% 0.41/1.00
% 0.41/1.00 set(prolog_style_variables).
% 0.41/1.00 set(auto2).
% 0.41/1.00 % set(auto2) -> set(auto).
% 0.41/1.00 % set(auto) -> set(auto_inference).
% 0.41/1.00 % set(auto) -> set(auto_setup).
% 0.41/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.00 % set(auto) -> set(auto_limits).
% 0.41/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.00 % set(auto) -> set(auto_denials).
% 0.41/1.00 % set(auto) -> set(auto_process).
% 0.41/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.00 % set(auto2) -> assign(stats, some).
% 0.41/1.00 % set(auto2) -> clear(echo_input).
% 0.41/1.00 % set(auto2) -> set(quiet).
% 0.41/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.00 % set(auto2) -> clear(print_given).
% 0.41/1.00 assign(lrs_ticks,-1).
% 0.41/1.00 assign(sos_limit,10000).
% 0.41/1.00 assign(order,kbo).
% 0.41/1.00 set(lex_order_vars).
% 0.41/1.00 clear(print_given).
% 0.41/1.00
% 0.41/1.00 % formulas(sos). % not echoed (64 formulas)
% 0.41/1.00
% 0.41/1.00 ============================== end of input ==========================
% 0.41/1.00
% 0.41/1.00 % From the command line: assign(max_seconds, 300).
% 0.41/1.00
% 0.41/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.00
% 0.41/1.00 % Formulas that are not ordinary clauses:
% 0.41/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 9 (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].
% 0.41/1.00 10 (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].
% 0.41/1.00 11 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 12 (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].
% 0.41/1.00 13 (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].
% 0.41/1.00 14 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 15 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 16 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 17 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 18 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 19 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 20 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 21 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 22 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 23 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 24 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 25 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 26 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 27 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 28 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 29 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 30 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 31 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 32 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 33 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 34 (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].
% 0.41/1.00 35 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 36 (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].
% 0.41/1.00 37 (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].
% 0.41/1.00 38 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 39 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 40 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 41 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 42 (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].
% 0.41/1.00 43 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 44 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.00 45 (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].
% 0.41/1.00 46 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 47 (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].
% 0.41/1.00 48 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 49 (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].
% 0.81/1.12 50 (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].
% 0.81/1.12 51 (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].
% 0.81/1.12 52 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 53 (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].
% 0.81/1.12 54 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 55 (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].
% 0.81/1.12 56 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 57 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 58 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 59 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 60 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 61 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 62 (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].
% 0.81/1.12 63 -(all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.12
% 0.81/1.12 ============================== end of process non-clausal formulas ===
% 0.81/1.12
% 0.81/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.12
% 0.81/1.12 ============================== PREDICATE ELIMINATION =================
% 0.81/1.12
% 0.81/1.12 ============================== end predicate elimination =============
% 0.81/1.12
% 0.81/1.12 Auto_denials: (non-Horn, no changes).
% 0.81/1.12
% 0.81/1.12 Term ordering decisions:
% 0.81/1.12 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. set_difference=1. set_intersection2=1. set_union2=1. unordered_pair=1. f1=1. f5=1. f8=1. f9=1. f10=1. singleton=1. f2=1. f3=1. f4=1. f6=1. f7=1.
% 0.81/1.12
% 0.81/1.12 ============================== end of process initial clauses ========
% 0.81/1.12
% 0.81/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.12
% 0.81/1.12 ============================== end of clauses for search =============
% 0.81/1.12
% 0.81/1.12 ============================== SEARCH ================================
% 0.81/1.12
% 0.81/1.12 % Starting search at 0.02 seconds.
% 0.81/1.12
% 0.81/1.12 ============================== PROOF =================================
% 0.81/1.12 % SZS status Theorem
% 0.81/1.12 % SZS output start Refutation
% 0.81/1.12
% 0.81/1.12 % Proof 1 at 0.13 (+ 0.01) seconds.
% 0.81/1.12 % Length of proof is 20.
% 0.81/1.12 % Level of proof is 5.
% 0.81/1.12 % Maximum clause weight is 11.000.
% 0.81/1.12 % Given clauses 97.
% 0.81/1.12
% 0.81/1.12 9 (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].
% 0.81/1.12 24 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 28 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 56 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.12 57 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 58 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.12 63 -(all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.12 65 empty(c1) # label(rc1_xboole_0) # label(axiom). [clausify(28)].
% 0.81/1.12 68 singleton(c3) = empty_set # label(l1_zfmisc_1) # label(negated_conjecture). [clausify(63)].
% 0.81/1.12 69 empty_set = singleton(c3). [copy(68),flip(a)].
% 0.81/1.12 70 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom). [clausify(24)].
% 0.81/1.12 83 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(56)].
% 0.81/1.12 110 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(58)].
% 0.81/1.12 121 -empty(A) | empty_set = A # label(t6_boole) # label(axiom). [clausify(57)].
% 0.81/1.12 122 -empty(A) | unordered_pair(c3,c3) = A. [copy(121),rewrite([69(2),83(3)])].
% 0.81/1.12 162 unordered_pair(A,B) != C | in(D,C) | D != B # label(d2_tarski) # label(axiom). [clausify(9)].
% 0.81/1.12 237 -in(A,c1). [ur(110,b,65,a)].
% 0.81/1.12 324 unordered_pair(c3,c3) = c1. [resolve(122,a,65,a)].
% 0.81/1.12 1115 unordered_pair(A,B) != c1. [ur(162,b,237,a,c,70,a)].
% 0.81/1.12 1116 $F. [resolve(1115,a,324,a)].
% 0.81/1.12
% 0.81/1.12 % SZS output end Refutation
% 0.81/1.12 ============================== end of proof ==========================
% 0.81/1.12
% 0.81/1.12 ============================== STATISTICS ============================
% 0.81/1.12
% 0.81/1.12 Given=97. Generated=1860. Kept=1019. proofs=1.
% 0.81/1.12 Usable=89. Sos=788. Demods=25. Limbo=20, Disabled=217. Hints=0.
% 0.81/1.12 Megabytes=0.88.
% 0.81/1.12 User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.81/1.12
% 0.81/1.12 ============================== end of statistics =====================
% 0.81/1.12
% 0.81/1.12 ============================== end of search =========================
% 0.81/1.12
% 0.81/1.12 THEOREM PROVED
% 0.81/1.12 % SZS status Theorem
% 0.81/1.12
% 0.81/1.12 Exiting with 1 proof.
% 0.81/1.12
% 0.81/1.12 Process 15138 exit (max_proofs) Mon Jun 20 13:57:47 2022
% 0.81/1.12 Prover9 interrupted
%------------------------------------------------------------------------------