0.07/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n010.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 02:12:05 EDT 2022 0.12/0.33 % CPUTime : 0.42/0.99 ============================== Prover9 =============================== 0.42/0.99 Prover9 (32) version 2009-11A, November 2009. 0.42/0.99 Process 18670 was started by sandbox2 on n010.cluster.edu, 0.42/0.99 Tue Aug 9 02:12:06 2022 0.42/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_18516_n010.cluster.edu". 0.42/0.99 ============================== end of head =========================== 0.42/0.99 0.42/0.99 ============================== INPUT ================================= 0.42/0.99 0.42/0.99 % Reading from file /tmp/Prover9_18516_n010.cluster.edu 0.42/0.99 0.42/0.99 set(prolog_style_variables). 0.42/0.99 set(auto2). 0.42/0.99 % set(auto2) -> set(auto). 0.42/0.99 % set(auto) -> set(auto_inference). 0.42/0.99 % set(auto) -> set(auto_setup). 0.42/0.99 % set(auto_setup) -> set(predicate_elim). 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold). 0.42/0.99 % set(auto) -> set(auto_limits). 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000"). 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000). 0.42/0.99 % set(auto) -> set(auto_denials). 0.42/0.99 % set(auto) -> set(auto_process). 0.42/0.99 % set(auto2) -> assign(new_constants, 1). 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3). 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000"). 0.42/0.99 % set(auto2) -> assign(max_hours, 1). 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.42/0.99 % set(auto2) -> assign(max_seconds, 0). 0.42/0.99 % set(auto2) -> assign(max_minutes, 5). 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.42/0.99 % set(auto2) -> set(sort_initial_sos). 0.42/0.99 % set(auto2) -> assign(sos_limit, -1). 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000). 0.42/0.99 % set(auto2) -> assign(max_megs, 400). 0.42/0.99 % set(auto2) -> assign(stats, some). 0.42/0.99 % set(auto2) -> clear(echo_input). 0.42/0.99 % set(auto2) -> set(quiet). 0.42/0.99 % set(auto2) -> clear(print_initial_clauses). 0.42/0.99 % set(auto2) -> clear(print_given). 0.42/0.99 assign(lrs_ticks,-1). 0.42/0.99 assign(sos_limit,10000). 0.42/0.99 assign(order,kbo). 0.42/0.99 set(lex_order_vars). 0.42/0.99 clear(print_given). 0.42/0.99 0.42/0.99 % formulas(sos). % not echoed (64 formulas) 0.42/0.99 0.42/0.99 ============================== end of input ========================== 0.42/0.99 0.42/0.99 % From the command line: assign(max_seconds, 960). 0.42/0.99 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.42/0.99 0.42/0.99 % Formulas that are not ordinary clauses: 0.42/0.99 1 (all U all V (less_than(V,U) | less_than(U,V))) # label(totality) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 2 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 3 (all U all V all W (less_than(V,W) & less_than(U,V) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 4 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 5 (all U all V (strictly_less_than(U,V) <-> less_than(U,V) & -less_than(V,U))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 6 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 7 (all U all V ((all W (contains_pq(U,W) -> less_than(V,W))) <-> issmallestelement_pq(U,V))) # label(ax10) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 8 (all U all V all W (V != W & contains_pq(U,W) -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 9 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 10 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> U = findmin_pq_eff(U,V))) # label(ax13) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 11 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> removemin_pq_eff(U,V) = remove_pq(U,V))) # label(ax15) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 12 (all U all V all W (contains_pq(U,W) | W = V <-> contains_pq(insert_pq(U,V),W))) # label(ax9) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 13 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 14 (all U all V all W insert_pq(insert_pq(U,W),V) = insert_pq(insert_pq(U,V),W)) # label(ax17) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 15 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> V = removemin_pq_res(U,V))) # label(ax16) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 16 (all U all V U = remove_pq(insert_pq(U,V),V)) # label(ax11) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 17 (all U all V all W all X (strictly_less_than(X,W) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)))) # label(ax29) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 18 (all U all V all W all X (contains_slb(U,W) & V != W -> insert_slb(remove_slb(U,W),pair(V,X)) = remove_slb(insert_slb(U,pair(V,X)),W))) # label(ax25) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 19 (all U create_slb = update_slb(create_slb,U)) # label(ax28) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 20 (all U all V all W all X (contains_slb(insert_slb(U,pair(V,X)),W) <-> contains_slb(U,W) | W = V)) # label(ax21) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 21 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 22 (all U all V all W all X (W != V & contains_slb(U,W) -> lookup_slb(U,W) = lookup_slb(insert_slb(U,pair(V,X)),W))) # label(ax27) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 23 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 24 (all U all V all W all X all Y (W = V & Y = X | pair_in_list(U,W,Y) <-> pair_in_list(insert_slb(U,pair(V,X)),W,Y))) # label(ax23) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 25 (all U all V all W U = remove_slb(insert_slb(U,pair(V,W)),V)) # label(ax24) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 26 (all U all V all W all X (less_than(W,X) -> insert_slb(update_slb(U,W),pair(V,X)) = update_slb(insert_slb(U,pair(V,X)),W))) # label(ax30) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 27 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 28 (all U all V all W W = lookup_slb(insert_slb(U,pair(V,W)),V)) # label(ax26) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 29 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 30 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 31 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 32 (all U all V all W all X (strictly_less_than(X,lookup_slb(V,X)) & contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad))) # label(ax45) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 33 (all U all V all W all X (V != create_slb -> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U))) # label(ax51) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 34 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,remove_cpq(V,W)))) # label(ax33) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 35 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> check_cpq(triple(U,V,W))))) # label(ax37) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 36 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 37 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,insert_cpq(V,W)))) # label(ax32) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 38 (all U all V all W all X all Y (strictly_less_than(X,Y) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 39 (all U all V all W all X triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W) = insert_cpq(triple(U,V,W),X)) # label(ax42) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 40 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_slb(V,X))) # label(ax39) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 41 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption]. 0.42/0.99 42 (all U all V triple(U,create_slb,bad) = findmin_cpq_eff(triple(U,create_slb,V))) # label(ax46) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 43 (all U remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)) = removemin_cpq_eff(U)) # label(ax52) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 44 (all U findmin_cpq_res(U) = removemin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 45 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 46 (all U all V all W all X (-contains_slb(V,findmin_pqp_res(U)) & create_slb != V -> triple(U,update_slb(V,findmin_pqp_res(U)),bad) = findmin_cpq_eff(triple(U,V,W)))) # label(ax47) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 47 (all U all V all W all X (create_slb != V & contains_slb(V,findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax48) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 48 (all U all V all W all X (less_than(lookup_slb(V,X),X) & contains_slb(V,X) -> triple(remove_pqp(U,X),remove_slb(V,X),W) = remove_cpq(triple(U,V,W),X))) # label(ax44) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 49 (all U all V all W all X (-contains_slb(V,X) -> triple(U,V,bad) = remove_cpq(triple(U,V,W),X))) # label(ax43) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 50 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 51 (all U all V all W all X (contains_slb(V,findmin_pqp_res(U)) & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) & create_slb != V -> triple(U,update_slb(V,findmin_pqp_res(U)),W) = findmin_cpq_eff(triple(U,V,W)))) # label(ax49) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 52 (all U all V (pi_sharp_removemin(U,V) <-> contains_pq(U,V) & issmallestelement_pq(U,V))) # label(ax60) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 53 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 54 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 55 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 56 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_find_min(U,V))) # label(ax58) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 57 (all U all V (contains_pq(U,V) <-> pi_sharp_remove(U,V))) # label(ax56) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 58 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 59 (all U all V all W all X all Y i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X)) # label(ax55) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 60 (all U all V (pi_sharp_remove(i(U),V) <-> pi_remove(U,V))) # label(ax57) # label(axiom) # label(non_clause). [assumption]. 0.42/1.00 61 (all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(main4_l7) # label(lemma) # label(non_clause). [assumption]. 0.42/1.00 62 -(all U all V all W (pi_find_min(triple(U,V,W)) -> (phi(findmin_cpq_eff(triple(U,V,W))) -> (exists X (pi_sharp_find_min(i(triple(U,V,W)),X) & findmin_pq_res(i(triple(U,V,W)),X) = findmin_cpq_res(triple(U,V,W))))))) # label(co4) # label(negated_conjecture) # label(non_clause). [assumption]. 0.42/1.00 0.42/1.00 ============================== end of process non-clausal formulas === 0.42/1.00 0.42/1.00 ============================== PROCESS INITIAL CLAUSES =============== 0.42/1.00 0.42/1.00 ============================== PREDICATE ELIMINATION ================= 0.42/1.00 63 -pi_find_min(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax59) # label(axiom). [clausify(53)]. 0.42/1.00 64 pi_find_min(triple(c1,c2,c3)) # label(co4) # label(negated_conjecture). [clausify(62)]. 0.42/1.00 65 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom). [clausify(53)]. 0.42/1.00 Derived: pi_sharp_find_min(i(triple(c1,c2,c3)),f2(triple(c1,c2,c3))). [resolve(63,a,64,a)]. 0.42/1.00 Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B). [resolve(63,a,65,a)]. 0.42/1.00 66 -contains_pq(A,B) | less_than(C,B) | -issmallestelement_pq(A,C) # label(ax10) # label(axiom). [clausify(7)]. 0.42/1.00 67 contains_pq(A,f1(A,B)) | issmallestelement_pq(A,B) # label(ax10) # label(axiom). [clausify(7)]. 0.42/1.00 68 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.42/1.00 69 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom). [clausify(56)]. 0.42/1.00 70 -less_than(A,f1(B,A)) | issmallestelement_pq(B,A) # label(ax10) # label(axiom). [clausify(7)]. 0.42/1.00 Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)). [resolve(66,c,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(66,c,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C). [resolve(66,c,69,a)]. 0.42/1.00 Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)). [resolve(66,c,70,b)]. 0.42/1.00 71 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.42/1.00 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(71,c,67,b)]. 0.42/1.00 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(71,c,69,a)]. 0.42/1.00 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(71,c,70,b)]. 0.42/1.00 72 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_find_min(A,B) # label(ax58) # label(axiom). [clausify(56)]. 0.42/1.00 Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | contains_pq(A,f1(A,B)). [resolve(72,b,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B). [resolve(72,b,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -less_than(B,f1(A,B)). [resolve(72,b,70,b)]. 0.42/1.00 73 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom). [clausify(6)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(73,b,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(73,b,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(73,b,69,a)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(73,b,70,b)]. 0.42/1.00 74 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom). [clausify(10)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)). [resolve(74,b,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(74,b,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B). [resolve(74,b,69,a)]. 0.42/1.00 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)). [resolve(74,b,70,b)]. 0.42/1.00 75 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom). [clausify(15)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(75,b,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(75,b,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(75,b,69,a)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(75,b,70,b)]. 0.42/1.00 76 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom). [clausify(11)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(76,b,67,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(76,b,68,b)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(76,b,69,a)]. 0.42/1.00 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)). [resolve(76,b,70,b)]. 0.74/1.16 77 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(71,c,67,b)]. 0.74/1.16 78 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.74/1.16 79 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(66,c,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(77,a,79,c)]. 0.74/1.16 80 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(71,c,69,a)]. 0.74/1.16 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(80,a,79,c)]. 0.74/1.16 81 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(71,c,70,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(81,a,79,c)]. 0.74/1.16 82 -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B). [resolve(72,b,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(82,c,77,a)]. 0.74/1.16 83 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(73,b,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(83,c,77,a)]. 0.74/1.16 84 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(74,b,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(84,c,77,a)]. 0.74/1.16 85 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(75,b,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(85,c,77,a)]. 0.74/1.16 86 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(76,b,68,b)]. 0.74/1.16 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(86,c,77,a)]. 0.74/1.16 87 -pi_removemin(A) | pi_sharp_find_min(i(A),f4(A)) # label(ax61) # label(axiom). [clausify(58)]. 0.74/1.16 88 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom). [clausify(58)]. 0.74/1.16 Derived: pi_sharp_find_min(i(A),f4(A)) | -pi_sharp_find_min(i(A),B). [resolve(87,a,88,a)]. 0.74/1.16 89 pi_sharp_remove(i(A),B) | -pi_remove(A,B) # label(ax57) # label(axiom). [clausify(60)]. 0.74/1.16 90 -pi_sharp_remove(i(A),B) | pi_remove(A,B) # label(ax57) # label(axiom). [clausify(60)]. 0.74/1.16 91 contains_pq(A,B) | -pi_sharp_remove(A,B) # label(ax56) # label(axiom). [clausify(57)]. 0.74/1.16 92 -contains_pq(A,B) | pi_sharp_remove(A,B) # label(ax56) # label(axiom). [clausify(57)]. 0.74/1.16 0.74/1.16 ============================== end predicate elimination ============= 0.74/1.16 0.74/1.16 Auto_denials: (non-Horn, no changes). 0.74/1.16 0.74/1.16 Term ordering decisions: 0.74/1.16 Function symbol KB weights: create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. insert_slb=1. pair=1. insert_pq=1. update_slb=1. lookup_slb=1. remove_pq=1. remove_cpq=1. remove_slb=1. findmin_pq_eff=1. findmin_pq_res=1. removemin_pq_eff=1. removemin_pq_res=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. f1=1. findmin_pqp_res=1. i=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. f2=1. f3=1. f4=1. triple=1. 0.74/1.16 0.74/1.16 ============================== end of process initial clauses ======== 0.74/1.16 0.74/1.16 ============================== CLAUSES FOR SEARCH ==================== 0.74/1.16 0.74/1.16 ============================== end of clauses for search ============= 0.74/1.16 0.74/1.16 ============================== SEARCH ================================ 0.74/1.16 0.74/1.16 % Starting search at 0.02 seconds. 0.74/1.16 0.74/1.16 ============================== PROOF ================================= 0.74/1.16 % SZS status Theorem 0.74/1.16 % SZS output start Refutation 0.74/1.16 0.74/1.16 % Proof 1 at 0.17 (+ 0.01) seconds. 0.74/1.16 % Length of proof is 17. 0.74/1.16 % Level of proof is 4. 0.74/1.16 % Maximum clause weight is 28.000. 0.74/1.16 % Given clauses 442. 0.74/1.16 0.74/1.16 6 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause). [assumption]. 0.74/1.16 56 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_find_min(U,V))) # label(ax58) # label(axiom) # label(non_clause). [assumption]. 0.74/1.16 61 (all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(main4_l7) # label(lemma) # label(non_clause). [assumption]. 0.74/1.16 62 -(all U all V all W (pi_find_min(triple(U,V,W)) -> (phi(findmin_cpq_eff(triple(U,V,W))) -> (exists X (pi_sharp_find_min(i(triple(U,V,W)),X) & findmin_pq_res(i(triple(U,V,W)),X) = findmin_cpq_res(triple(U,V,W))))))) # label(co4) # label(negated_conjecture) # label(non_clause). [assumption]. 0.74/1.16 69 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom). [clausify(56)]. 0.74/1.16 73 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom). [clausify(6)]. 0.74/1.16 102 phi(findmin_cpq_eff(triple(c1,c2,c3))) # label(co4) # label(negated_conjecture). [clausify(62)]. 0.74/1.16 128 -pi_sharp_find_min(i(triple(c1,c2,c3)),A) | findmin_cpq_res(triple(c1,c2,c3)) != findmin_pq_res(i(triple(c1,c2,c3)),A) # label(co4) # label(negated_conjecture). [clausify(62)]. 0.74/1.16 129 -pi_sharp_find_min(i(triple(c1,c2,c3)),A) | findmin_pq_res(i(triple(c1,c2,c3)),A) != findmin_cpq_res(triple(c1,c2,c3)). [copy(128),flip(b)]. 0.74/1.16 134 contains_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom). [clausify(56)]. 0.74/1.16 159 -phi(findmin_cpq_eff(triple(A,B,C))) | pi_sharp_find_min(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C))) # label(main4_l7) # label(lemma). [clausify(61)]. 0.74/1.16 177 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(73,b,69,a)]. 0.74/1.16 262 pi_sharp_find_min(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))). [resolve(159,a,102,a)]. 0.74/1.16 2069 -contains_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) | findmin_pq_res(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) = findmin_cpq_res(triple(c1,c2,c3)). [resolve(262,a,177,c)]. 0.74/1.16 2071 contains_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))). [resolve(262,a,134,b)]. 0.74/1.16 2072 findmin_pq_res(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) != findmin_cpq_res(triple(c1,c2,c3)). [resolve(262,a,129,a)]. 0.74/1.16 2074 $F. [back_unit_del(2069),unit_del(a,2071),unit_del(b,2072)]. 0.74/1.16 0.74/1.16 % SZS output end Refutation 0.74/1.16 ============================== end of proof ========================== 0.74/1.16 0.74/1.16 ============================== STATISTICS ============================ 0.74/1.16 0.74/1.16 Given=442. Generated=4448. Kept=1969. proofs=1. 0.74/1.16 Usable=440. Sos=1449. Demods=58. Limbo=3, Disabled=204. Hints=0. 0.74/1.16 Megabytes=3.95. 0.74/1.16 User_CPU=0.17, System_CPU=0.01, Wall_clock=0. 0.74/1.16 0.74/1.16 ============================== end of statistics ===================== 0.74/1.16 0.74/1.16 ============================== end of search ========================= 0.74/1.16 0.74/1.16 THEOREM PROVED 0.74/1.16 % SZS status Theorem 0.74/1.16 0.74/1.16 Exiting with 1 proof. 0.74/1.16 0.74/1.16 Process 18670 exit (max_proofs) Tue Aug 9 02:12:06 2022 0.74/1.16 Prover9 interrupted 0.74/1.17 EOF