0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n005.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 : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 03:10:49 EDT 2022 0.12/0.33 % CPUTime : 0.42/1.01 ============================== Prover9 =============================== 0.42/1.01 Prover9 (32) version 2009-11A, November 2009. 0.42/1.01 Process 25739 was started by sandbox on n005.cluster.edu, 0.42/1.01 Tue Aug 9 03:10:50 2022 0.42/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_25556_n005.cluster.edu". 0.42/1.01 ============================== end of head =========================== 0.42/1.01 0.42/1.01 ============================== INPUT ================================= 0.42/1.01 0.42/1.01 % Reading from file /tmp/Prover9_25556_n005.cluster.edu 0.42/1.01 0.42/1.01 set(prolog_style_variables). 0.42/1.01 set(auto2). 0.42/1.01 % set(auto2) -> set(auto). 0.42/1.01 % set(auto) -> set(auto_inference). 0.42/1.01 % set(auto) -> set(auto_setup). 0.42/1.01 % set(auto_setup) -> set(predicate_elim). 0.42/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.42/1.01 % set(auto) -> set(auto_limits). 0.42/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.42/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.42/1.01 % set(auto) -> set(auto_denials). 0.42/1.01 % set(auto) -> set(auto_process). 0.42/1.01 % set(auto2) -> assign(new_constants, 1). 0.42/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.42/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.42/1.01 % set(auto2) -> assign(max_hours, 1). 0.42/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.42/1.01 % set(auto2) -> assign(max_seconds, 0). 0.42/1.01 % set(auto2) -> assign(max_minutes, 5). 0.42/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.42/1.01 % set(auto2) -> set(sort_initial_sos). 0.42/1.01 % set(auto2) -> assign(sos_limit, -1). 0.42/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.42/1.01 % set(auto2) -> assign(max_megs, 400). 0.42/1.01 % set(auto2) -> assign(stats, some). 0.42/1.01 % set(auto2) -> clear(echo_input). 0.42/1.01 % set(auto2) -> set(quiet). 0.42/1.01 % set(auto2) -> clear(print_initial_clauses). 0.42/1.01 % set(auto2) -> clear(print_given). 0.42/1.01 assign(lrs_ticks,-1). 0.42/1.01 assign(sos_limit,10000). 0.42/1.01 assign(order,kbo). 0.42/1.01 set(lex_order_vars). 0.42/1.01 clear(print_given). 0.42/1.01 0.42/1.01 % formulas(sos). % not echoed (14 formulas) 0.42/1.01 0.42/1.01 ============================== end of input ========================== 0.42/1.01 0.42/1.01 % From the command line: assign(max_seconds, 960). 0.42/1.01 0.42/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.42/1.01 0.42/1.01 % Formulas that are not ordinary clauses: 0.42/1.01 1 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 2 (all B all C (C = B <-> subset(C,B) & subset(B,C))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 3 (all B all C all D intersection(union(B,C),union(B,D)) = union(B,intersection(C,D))) # label(union_distributes_over_intersection) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 4 (all B all C all D (member(D,union(B,C)) <-> member(D,C) | member(D,B))) # label(union_defn) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 5 (all B all C all D intersection(B,intersection(C,D)) = intersection(intersection(B,C),D)) # label(associativity_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 6 (all B all C intersection(C,B) = intersection(B,C)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 7 (all B all C all D union(union(B,C),D) = union(B,union(C,D))) # label(associativity_of_union) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 8 (all B all C ((all D (member(D,B) -> member(D,C))) <-> subset(B,C))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 9 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 10 (all B B = intersection(B,B)) # label(idempotency_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 11 (all B all C B = union(B,intersection(B,C))) # label(union_intersection) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 12 (all B all C (B = C <-> (all D (member(D,C) <-> member(D,B))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 13 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption]. 0.42/1.01 14 -(all B all C all D union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B))) # label(prove_th72) # label(negated_conjecture) # label(non_clause). [assumption]. 0.92/1.22 0.92/1.22 ============================== end of process non-clausal formulas === 0.92/1.22 0.92/1.22 ============================== PROCESS INITIAL CLAUSES =============== 0.92/1.22 0.92/1.22 ============================== PREDICATE ELIMINATION ================= 0.92/1.22 0.92/1.22 ============================== end predicate elimination ============= 0.92/1.22 0.92/1.22 Auto_denials: (non-Horn, no changes). 0.92/1.22 0.92/1.22 Term ordering decisions: 0.92/1.22 Function symbol KB weights: c1=1. c2=1. c3=1. intersection=1. union=1. f1=1. f2=1. 0.92/1.22 0.92/1.22 ============================== end of process initial clauses ======== 0.92/1.22 0.92/1.22 ============================== CLAUSES FOR SEARCH ==================== 0.92/1.22 0.92/1.22 ============================== end of clauses for search ============= 0.92/1.22 0.92/1.22 ============================== SEARCH ================================ 0.92/1.22 0.92/1.22 % Starting search at 0.01 seconds. 0.92/1.22 0.92/1.22 ============================== PROOF ================================= 0.92/1.22 % SZS status Theorem 0.92/1.22 % SZS output start Refutation 0.92/1.22 0.92/1.22 % Proof 1 at 0.21 (+ 0.01) seconds. 0.92/1.22 % Length of proof is 48. 0.92/1.22 % Level of proof is 13. 0.92/1.22 % Maximum clause weight is 23.000. 0.92/1.22 % Given clauses 117. 0.92/1.22 0.92/1.22 1 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 3 (all B all C all D intersection(union(B,C),union(B,D)) = union(B,intersection(C,D))) # label(union_distributes_over_intersection) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 5 (all B all C all D intersection(B,intersection(C,D)) = intersection(intersection(B,C),D)) # label(associativity_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 6 (all B all C intersection(C,B) = intersection(B,C)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 7 (all B all C all D union(union(B,C),D) = union(B,union(C,D))) # label(associativity_of_union) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 10 (all B B = intersection(B,B)) # label(idempotency_of_intersection) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 11 (all B all C B = union(B,intersection(B,C))) # label(union_intersection) # label(axiom) # label(non_clause). [assumption]. 0.92/1.22 14 -(all B all C all D union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B))) # label(prove_th72) # label(negated_conjecture) # label(non_clause). [assumption]. 0.92/1.22 16 intersection(A,A) = A # label(idempotency_of_intersection) # label(axiom). [clausify(10)]. 0.92/1.22 17 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(1)]. 0.92/1.22 18 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(6)]. 0.92/1.22 19 union(A,intersection(A,B)) = A # label(union_intersection) # label(axiom). [clausify(11)]. 0.92/1.22 21 intersection(intersection(A,B),C) = intersection(A,intersection(B,C)) # label(associativity_of_intersection) # label(axiom). [clausify(5)]. 0.92/1.22 22 intersection(A,intersection(B,C)) = intersection(C,intersection(A,B)). [copy(21),rewrite([18(2)]),flip(a)]. 0.92/1.22 23 union(union(A,B),C) = union(A,union(B,C)) # label(associativity_of_union) # label(axiom). [clausify(7)]. 0.92/1.22 24 union(A,union(B,C)) = union(C,union(A,B)). [copy(23),rewrite([17(2)]),flip(a)]. 0.92/1.22 25 intersection(union(A,B),union(A,C)) = union(A,intersection(B,C)) # label(union_distributes_over_intersection) # label(axiom). [clausify(3)]. 0.92/1.22 27 intersection(intersection(union(c1,c2),union(c2,c3)),union(c3,c1)) != union(union(intersection(c1,c2),intersection(c2,c3)),intersection(c3,c1)) # label(prove_th72) # label(negated_conjecture). [clausify(14)]. 0.92/1.22 28 union(intersection(c1,c2),union(intersection(c1,c3),intersection(c2,c3))) != intersection(union(c1,c2),intersection(union(c1,c3),union(c2,c3))). [copy(27),rewrite([17(10),18(11),22(11,R),18(10),18(21),17(22),24(22,R),17(21)]),flip(a)]. 0.92/1.22 44 union(A,A) = A. [para(16(a,1),19(a,1,2))]. 0.92/1.22 46 union(A,union(B,intersection(A,C))) = union(A,B). [para(19(a,1),24(a,2,2)),rewrite([17(2),17(4)])]. 0.92/1.22 47 intersection(union(A,B),union(B,C)) = union(B,intersection(A,C)). [para(17(a,1),25(a,1,1))]. 0.92/1.22 48 union(A,union(A,B)) = union(A,B). [para(25(a,1),19(a,1,2)),rewrite([24(4,R),24(3),17(2),46(3),17(1)])]. 0.92/1.22 49 intersection(A,union(A,B)) = A. [para(19(a,1),25(a,1,1)),rewrite([18(4),22(4,R),18(3),19(5)])]. 0.92/1.22 50 intersection(union(A,union(B,C)),union(B,D)) = union(B,intersection(D,union(A,C))). [para(24(a,1),25(a,1,1)),rewrite([17(5),18(6)])]. 0.92/1.22 51 intersection(union(A,union(B,C)),union(C,D)) = union(C,intersection(D,union(A,B))). [para(24(a,2),25(a,1,1)),rewrite([18(6)])]. 0.92/1.22 93 intersection(A,intersection(B,union(A,C))) = intersection(A,B). [para(49(a,1),22(a,2,2)),rewrite([18(2),18(4)])]. 0.92/1.22 94 union(A,intersection(B,union(A,C))) = union(A,intersection(C,B)). [para(48(a,1),25(a,1,1)),rewrite([25(3),18(4)]),flip(a)]. 0.92/1.22 126 union(intersection(A,B),intersection(A,C)) = intersection(A,union(C,intersection(A,B))). [para(19(a,1),47(a,1,1)),rewrite([17(2)]),flip(a)]. 0.92/1.22 130 union(A,intersection(B,A)) = intersection(A,union(B,A)). [para(44(a,1),47(a,1,2)),rewrite([18(2)]),flip(a)]. 0.92/1.22 137 union(A,intersection(intersection(A,B),union(C,D))) = intersection(A,union(C,union(A,D))). [para(19(a,1),50(a,1,2)),rewrite([18(3)]),flip(a)]. 0.92/1.22 150 union(A,intersection(intersection(A,B),union(C,D))) = A. [back_rewrite(137),rewrite([24(6,R),17(5),49(7)])]. 0.92/1.22 156 intersection(intersection(A,B),union(C,intersection(A,B))) = intersection(A,union(intersection(B,C),intersection(A,B))). [para(22(a,1),130(a,1,2)),rewrite([18(2),22(3,R),18(2),126(4)]),flip(a)]. 0.92/1.22 160 union(A,intersection(B,intersection(intersection(A,C),union(D,E)))) = A. [para(150(a,1),25(a,1,1)),rewrite([49(2),18(4)]),flip(a)]. 0.92/1.22 162 intersection(A,union(B,A)) = A. [para(150(a,1),47(a,1,2)),rewrite([18(2),160(7)])]. 0.92/1.22 166 intersection(A,union(intersection(B,C),intersection(A,B))) = intersection(A,B). [back_rewrite(156),rewrite([162(4)]),flip(a)]. 0.92/1.22 173 union(intersection(A,B),intersection(C,union(A,D))) = intersection(union(A,D),union(C,intersection(A,B))). [para(46(a,1),51(a,1,1)),rewrite([17(3)]),flip(a)]. 0.92/1.22 865 intersection(A,union(B,intersection(A,B))) = intersection(A,B). [para(16(a,1),166(a,1,2,1))]. 0.92/1.22 867 intersection(A,union(intersection(B,C),intersection(A,C))) = intersection(A,C). [para(18(a,1),166(a,1,2,1))]. 0.92/1.22 879 intersection(union(A,B),union(C,B)) = union(B,intersection(A,C)). [para(865(a,1),51(a,2,2)),rewrite([18(1),17(2),46(3),17(2),18(4)])]. 0.92/1.22 880 union(intersection(c1,c2),union(intersection(c1,c3),intersection(c2,c3))) != intersection(union(c1,c2),union(c3,intersection(c1,c2))). [back_rewrite(28),rewrite([879(21)])]. 0.92/1.22 972 union(intersection(A,B),intersection(B,C)) = intersection(B,union(C,intersection(A,B))). [para(867(a,1),25(a,1)),rewrite([17(2),18(3),17(6),18(7),93(8),18(5)]),flip(a)]. 0.92/1.22 975 intersection(A,union(B,intersection(A,C))) = intersection(A,union(B,C)). [para(49(a,1),867(a,1,2,1)),rewrite([94(3),18(1)])]. 0.92/1.22 976 union(intersection(A,B),intersection(C,B)) = intersection(B,union(C,intersection(A,B))). [para(867(a,1),47(a,1)),rewrite([18(3),18(7),93(8)]),flip(a)]. 0.92/1.22 992 union(intersection(A,B),intersection(A,C)) = intersection(A,union(B,C)). [back_rewrite(126),rewrite([975(6),17(4)])]. 0.92/1.22 993 union(intersection(c1,c2),intersection(c3,union(c2,intersection(c1,c3)))) != intersection(union(c1,c2),union(c3,intersection(c1,c2))). [back_rewrite(880),rewrite([976(10)])]. 0.92/1.22 1029 intersection(A,union(B,intersection(C,A))) = intersection(A,union(C,B)). [para(18(a,1),992(a,1,1)),rewrite([972(3)])]. 0.92/1.22 1051 $F. [back_rewrite(993),rewrite([1029(10),173(9)]),xx(a)]. 0.92/1.22 0.92/1.22 % SZS output end Refutation 0.92/1.22 ============================== end of proof ========================== 0.92/1.22 0.92/1.22 ============================== STATISTICS ============================ 0.92/1.22 0.92/1.22 Given=117. Generated=5117. Kept=1033. proofs=1. 0.92/1.22 Usable=104. Sos=837. Demods=140. Limbo=22, Disabled=95. Hints=0. 0.92/1.22 Megabytes=0.94. 0.92/1.22 User_CPU=0.21, System_CPU=0.01, Wall_clock=0. 0.92/1.22 0.92/1.22 ============================== end of statistics ===================== 0.92/1.22 0.92/1.22 ============================== end of search ========================= 0.92/1.22 0.92/1.22 THEOREM PROVED 0.92/1.22 % SZS status Theorem 0.92/1.22 0.92/1.22 Exiting with 1 proof. 0.92/1.22 0.92/1.22 Process 25739 exit (max_proofs) Tue Aug 9 03:10:50 2022 0.92/1.22 Prover9 interrupted 0.92/1.22 EOF