0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n014.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 : 1200 0.13/0.34 % DateTime : Tue Jul 13 16:56:19 EDT 2021 0.13/0.34 % CPUTime : 0.46/1.08 ============================== Prover9 =============================== 0.46/1.08 Prover9 (32) version 2009-11A, November 2009. 0.46/1.08 Process 6022 was started by sandbox2 on n014.cluster.edu, 0.46/1.08 Tue Jul 13 16:56:20 2021 0.46/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_5670_n014.cluster.edu". 0.46/1.08 ============================== end of head =========================== 0.46/1.08 0.46/1.08 ============================== INPUT ================================= 0.46/1.08 0.46/1.08 % Reading from file /tmp/Prover9_5670_n014.cluster.edu 0.46/1.08 0.46/1.08 set(prolog_style_variables). 0.46/1.08 set(auto2). 0.46/1.08 % set(auto2) -> set(auto). 0.46/1.08 % set(auto) -> set(auto_inference). 0.46/1.08 % set(auto) -> set(auto_setup). 0.46/1.08 % set(auto_setup) -> set(predicate_elim). 0.46/1.08 % set(auto_setup) -> assign(eq_defs, unfold). 0.46/1.08 % set(auto) -> set(auto_limits). 0.46/1.08 % set(auto_limits) -> assign(max_weight, "100.000"). 0.46/1.08 % set(auto_limits) -> assign(sos_limit, 20000). 0.46/1.08 % set(auto) -> set(auto_denials). 0.46/1.08 % set(auto) -> set(auto_process). 0.46/1.08 % set(auto2) -> assign(new_constants, 1). 0.46/1.08 % set(auto2) -> assign(fold_denial_max, 3). 0.46/1.08 % set(auto2) -> assign(max_weight, "200.000"). 0.46/1.08 % set(auto2) -> assign(max_hours, 1). 0.46/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.46/1.08 % set(auto2) -> assign(max_seconds, 0). 0.46/1.08 % set(auto2) -> assign(max_minutes, 5). 0.46/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.46/1.08 % set(auto2) -> set(sort_initial_sos). 0.46/1.08 % set(auto2) -> assign(sos_limit, -1). 0.46/1.08 % set(auto2) -> assign(lrs_ticks, 3000). 0.46/1.08 % set(auto2) -> assign(max_megs, 400). 0.46/1.08 % set(auto2) -> assign(stats, some). 0.46/1.08 % set(auto2) -> clear(echo_input). 0.46/1.08 % set(auto2) -> set(quiet). 0.46/1.08 % set(auto2) -> clear(print_initial_clauses). 0.46/1.08 % set(auto2) -> clear(print_given). 0.46/1.08 assign(lrs_ticks,-1). 0.46/1.08 assign(sos_limit,10000). 0.46/1.08 assign(order,kbo). 0.46/1.08 set(lex_order_vars). 0.46/1.08 clear(print_given). 0.46/1.08 0.46/1.08 % formulas(sos). % not echoed (12 formulas) 0.46/1.08 0.46/1.08 ============================== end of input ========================== 0.46/1.08 0.46/1.08 % From the command line: assign(max_seconds, 1200). 0.46/1.08 0.46/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.46/1.08 0.46/1.08 % Formulas that are not ordinary clauses: 0.46/1.08 1 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 2 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 3 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 4 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 5 (all A all B all C (singleton(A) = unordered_pair(B,C) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 6 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 8 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 9 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 10 (all A all B all C all D -(A != C & A != D & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 11 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.46/1.08 12 -(all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.46/1.08 0.46/1.08 ============================== end of process non-clausal formulas === 0.46/1.08 0.46/1.08 ============================== PROCESS INITIAL CLAUSES =============== 0.46/1.08 0.46/1.08 ============================== PREDICATE ELIMINATION ================= 0.46/1.08 0.46/1.08 ============================== end predicate elimination ============= 0.46/1.08 0.46/1.08 Auto_denials: (non-Horn, no changes). 0.46/1.08 0.46/1.08 Term ordering decisions: 0.46/1.08 0.46/1.08 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12). 0.81/1.15 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. unordered_pair=1. ordered_pair=1. singleton=0. 0.81/1.15 0.81/1.15 ============================== end of process initial clauses ======== 0.81/1.15 0.81/1.15 ============================== CLAUSES FOR SEARCH ==================== 0.81/1.15 0.81/1.15 ============================== end of clauses for search ============= 0.81/1.15 0.81/1.15 ============================== SEARCH ================================ 0.81/1.15 0.81/1.15 % Starting search at 0.01 seconds. 0.81/1.15 0.81/1.15 ============================== PROOF ================================= 0.81/1.15 % SZS status Theorem 0.81/1.15 % SZS output start Refutation 0.81/1.15 0.81/1.15 % Proof 1 at 0.08 (+ 0.00) seconds. 0.81/1.15 % Length of proof is 42. 0.81/1.15 % Level of proof is 14. 0.81/1.15 % Maximum clause weight is 21.000. 0.81/1.15 % Given clauses 63. 0.81/1.15 0.81/1.15 2 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 4 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 5 (all A all B all C (singleton(A) = unordered_pair(B,C) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 6 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 8 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 10 (all A all B all C all D -(A != C & A != D & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 12 -(all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.81/1.15 15 unordered_pair(A,A) = singleton(A) # label(t69_enumset1) # label(axiom). [clausify(8)]. 0.81/1.15 16 singleton(A) = unordered_pair(A,A). [copy(15),flip(a)]. 0.81/1.15 17 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(6)]. 0.81/1.15 18 ordered_pair(c5,c6) = ordered_pair(c3,c4) # label(t33_zfmisc_1) # label(negated_conjecture). [clausify(12)]. 0.81/1.15 19 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(4)]. 0.81/1.15 20 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),unordered_pair(A,A)). [copy(19),rewrite([16(3)])]. 0.81/1.15 24 c5 != c3 | c6 != c4 # label(t33_zfmisc_1) # label(negated_conjecture). [clausify(12)]. 0.81/1.15 27 unordered_pair(A,B) != singleton(C) | A = C # label(t8_zfmisc_1) # label(axiom). [clausify(2)]. 0.81/1.15 28 unordered_pair(A,B) != unordered_pair(C,C) | A = C. [copy(27),rewrite([16(2)])]. 0.81/1.15 29 unordered_pair(A,B) != singleton(C) | B = A # label(t9_zfmisc_1) # label(axiom). [clausify(5)]. 0.81/1.15 30 unordered_pair(A,B) != unordered_pair(C,C) | B = A. [copy(29),rewrite([16(2)])]. 0.81/1.15 31 A = B | C = B | unordered_pair(A,C) != unordered_pair(B,D) # label(t10_zfmisc_1) # label(axiom). [clausify(10)]. 0.81/1.15 32 unordered_pair(unordered_pair(c5,c5),unordered_pair(c5,c6)) = unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)). [back_rewrite(18),rewrite([20(3),17(7),20(10),17(14)])]. 0.81/1.15 36 unordered_pair(A,B) != unordered_pair(C,C) | B = C. [para(17(a,1),28(a,1))]. 0.81/1.15 37 unordered_pair(A,B) != unordered_pair(C,C) | A = B. [para(17(a,1),30(a,1))]. 0.81/1.15 38 unordered_pair(c5,c5) = unordered_pair(c3,c3) | unordered_pair(c5,c6) = unordered_pair(c3,c3). [resolve(32,a,31,c)]. 0.81/1.15 43 unordered_pair(c5,c5) = A | unordered_pair(c5,c6) = A | unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)) != unordered_pair(A,B). [para(32(a,1),31(c,1))]. 0.81/1.15 47 unordered_pair(c5,c5) = unordered_pair(c3,c3) | c6 = c5. [resolve(38,b,37,a),flip(b)]. 0.81/1.15 48 unordered_pair(c5,c5) = unordered_pair(c3,c3) | c6 = c3. [resolve(38,b,36,a)]. 0.81/1.15 58 c6 = c5 | c5 = c3. [resolve(47,a,36,a)]. 0.81/1.15 92 c6 = c3 | c5 = c3. [resolve(48,a,36,a)]. 0.81/1.15 109 c5 = c3. [para(92(a,1),58(a,1)),flip(b),merge(b),merge(c)]. 0.81/1.15 117 unordered_pair(c3,c3) = A | unordered_pair(c3,c6) = A | unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)) != unordered_pair(A,B). [back_rewrite(43),rewrite([109(1),109(2),109(5)])]. 0.81/1.15 119 unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c6)) = unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)). [back_rewrite(32),rewrite([109(1),109(2),109(4)])]. 0.81/1.15 120 c6 != c4. [back_rewrite(24),rewrite([109(1)]),xx(a)]. 0.81/1.15 121 unordered_pair(c4,c6) != unordered_pair(A,A). [ur(37,b,120,a),rewrite([17(3)])]. 0.81/1.15 122 unordered_pair(c4,c4) != unordered_pair(A,c6). [ur(36,b,120,a),flip(a)]. 0.81/1.15 126 unordered_pair(unordered_pair(c4,c6),unordered_pair(A,A)) != unordered_pair(B,B). [ur(37,b,121,a)]. 0.81/1.15 140 unordered_pair(unordered_pair(A,c6),unordered_pair(B,c6)) != unordered_pair(C,unordered_pair(c4,c4)). [ur(31,a,122,a(flip),b,122,a(flip)),rewrite([17(9)])]. 0.81/1.15 192 unordered_pair(c3,c4) = unordered_pair(c3,c3) | unordered_pair(c3,c6) = unordered_pair(c3,c4). [resolve(117,c,17,a),flip(a)]. 0.81/1.15 318 unordered_pair(c3,c4) = unordered_pair(c3,c3) | c3 = A | c6 = A | unordered_pair(c3,c4) != unordered_pair(A,B). [para(192(b,1),31(c,1))]. 0.81/1.15 429 unordered_pair(unordered_pair(unordered_pair(A,c6),unordered_pair(B,c6)),unordered_pair(C,C)) != unordered_pair(D,unordered_pair(unordered_pair(c4,c4),unordered_pair(c4,c6))). [ur(31,a,140,a,b,126,a(flip)),rewrite([17(14),17(15)])]. 0.81/1.15 493 unordered_pair(c3,c4) = unordered_pair(c3,c3) | c4 = c3. [resolve(318,d,17,a),flip(b),unit_del(c,120)]. 0.81/1.15 494 c4 = c3. [resolve(493,a,37,a),flip(b),merge(b)]. 0.81/1.15 544 $F. [back_rewrite(429),rewrite([494(8),494(9),494(11),119(14),494(12)]),xx(a)]. 0.81/1.15 0.81/1.15 % SZS output end Refutation 0.81/1.15 ============================== end of proof ========================== 0.81/1.15 0.81/1.15 ============================== STATISTICS ============================ 0.81/1.15 0.81/1.15 Given=63. Generated=1267. Kept=525. proofs=1. 0.81/1.15 Usable=52. Sos=212. Demods=6. Limbo=50, Disabled=224. Hints=0. 0.81/1.15 Megabytes=0.50. 0.81/1.15 User_CPU=0.08, System_CPU=0.00, Wall_clock=0. 0.81/1.15 0.81/1.15 ============================== end of statistics ===================== 0.81/1.15 0.81/1.15 ============================== end of search ========================= 0.81/1.15 0.81/1.15 THEOREM PROVED 0.81/1.15 % SZS status Theorem 0.81/1.15 0.81/1.15 Exiting with 1 proof. 0.81/1.15 0.81/1.15 Process 6022 exit (max_proofs) Tue Jul 13 16:56:20 2021 0.81/1.16 Prover9 interrupted 0.81/1.16 EOF