0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n025.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % DateTime : Thu Jul 2 07:31:18 EDT 2020 0.11/0.32 % CPUTime : 0.81/1.14 ============================== Prover9 =============================== 0.81/1.14 Prover9 (32) version 2009-11A, November 2009. 0.81/1.14 Process 29882 was started by sandbox2 on n025.cluster.edu, 0.81/1.14 Thu Jul 2 07:31:19 2020 0.81/1.14 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_29723_n025.cluster.edu". 0.81/1.14 ============================== end of head =========================== 0.81/1.14 0.81/1.14 ============================== INPUT ================================= 0.81/1.14 0.81/1.14 % Reading from file /tmp/Prover9_29723_n025.cluster.edu 0.81/1.14 0.81/1.14 set(prolog_style_variables). 0.81/1.14 set(auto2). 0.81/1.14 % set(auto2) -> set(auto). 0.81/1.14 % set(auto) -> set(auto_inference). 0.81/1.14 % set(auto) -> set(auto_setup). 0.81/1.14 % set(auto_setup) -> set(predicate_elim). 0.81/1.14 % set(auto_setup) -> assign(eq_defs, unfold). 0.81/1.14 % set(auto) -> set(auto_limits). 0.81/1.14 % set(auto_limits) -> assign(max_weight, "100.000"). 0.81/1.14 % set(auto_limits) -> assign(sos_limit, 20000). 0.81/1.14 % set(auto) -> set(auto_denials). 0.81/1.14 % set(auto) -> set(auto_process). 0.81/1.14 % set(auto2) -> assign(new_constants, 1). 0.81/1.14 % set(auto2) -> assign(fold_denial_max, 3). 0.81/1.14 % set(auto2) -> assign(max_weight, "200.000"). 0.81/1.14 % set(auto2) -> assign(max_hours, 1). 0.81/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.81/1.14 % set(auto2) -> assign(max_seconds, 0). 0.81/1.14 % set(auto2) -> assign(max_minutes, 5). 0.81/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.81/1.14 % set(auto2) -> set(sort_initial_sos). 0.81/1.14 % set(auto2) -> assign(sos_limit, -1). 0.81/1.14 % set(auto2) -> assign(lrs_ticks, 3000). 0.81/1.14 % set(auto2) -> assign(max_megs, 400). 0.81/1.14 % set(auto2) -> assign(stats, some). 0.81/1.14 % set(auto2) -> clear(echo_input). 0.81/1.14 % set(auto2) -> set(quiet). 0.81/1.14 % set(auto2) -> clear(print_initial_clauses). 0.81/1.14 % set(auto2) -> clear(print_given). 0.81/1.14 assign(lrs_ticks,-1). 0.81/1.14 assign(sos_limit,10000). 0.81/1.14 assign(order,kbo). 0.81/1.14 set(lex_order_vars). 0.81/1.14 clear(print_given). 0.81/1.14 0.81/1.14 % formulas(sos). % not echoed (63 formulas) 0.81/1.14 0.81/1.14 ============================== end of input ========================== 0.81/1.14 0.81/1.14 % From the command line: assign(max_seconds, 960). 0.81/1.14 0.81/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.81/1.14 0.81/1.14 % Formulas that are not ordinary clauses: 0.81/1.14 1 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 2 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 3 (all U all V (-less_than(V,U) & less_than(U,V) <-> strictly_less_than(U,V))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 4 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 5 (all U all V all W (less_than(U,V) & less_than(V,W) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 6 (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]. 0.81/1.14 7 (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]. 0.81/1.14 8 (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]. 0.81/1.14 9 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 10 (all U all V all W (V = W | contains_pq(U,W) <-> contains_pq(insert_pq(U,V),W))) # label(ax9) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 11 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_res(U,V) = V)) # label(ax14) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 12 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> removemin_pq_eff(U,V) = remove_pq(U,V))) # label(ax15) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 13 (all U all V all W (contains_pq(U,W) & V != W -> insert_pq(remove_pq(U,W),V) = remove_pq(insert_pq(U,V),W))) # label(ax12) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 14 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 15 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> V = removemin_pq_res(U,V))) # label(ax16) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 16 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 17 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 18 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 19 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> Y = X & W = V | pair_in_list(U,W,Y))) # label(ax23) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 20 (all U all V all W all X (V = W | contains_slb(U,W) <-> contains_slb(insert_slb(U,pair(V,X)),W))) # label(ax21) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 21 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 22 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 23 (all U all V all W all X (strictly_less_than(X,W) -> insert_slb(update_slb(U,W),pair(V,W)) = update_slb(insert_slb(U,pair(V,X)),W))) # label(ax29) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 24 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 25 (all U all V all W all X (V != W & contains_slb(U,W) -> remove_slb(insert_slb(U,pair(V,X)),W) = insert_slb(remove_slb(U,W),pair(V,X)))) # label(ax25) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 26 (all U all V all W all X (less_than(W,X) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)))) # label(ax30) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 27 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 28 (all U all V all W all X (V != W & contains_slb(U,W) -> lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W))) # label(ax27) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 29 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 30 (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]. 0.81/1.14 31 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 32 (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]. 0.81/1.14 33 (all U findmin_cpq_res(U) = removemin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 34 (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 -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W))) # label(ax49) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 35 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 36 (all U all V all W all X (contains_slb(V,X) & less_than(lookup_slb(V,X),X) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W))) # label(ax44) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 37 (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]. 0.81/1.14 38 (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]. 0.81/1.14 39 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 40 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 41 (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]. 0.81/1.14 42 (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]. 0.81/1.14 43 (all U all V all W all X (create_slb != V & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) & contains_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]. 0.81/1.14 44 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 45 (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]. 0.81/1.14 46 (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]. 0.81/1.14 47 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 48 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 49 (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]. 0.81/1.14 50 (all U all V all W all X (-contains_slb(V,findmin_pqp_res(U)) & V != create_slb -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax47) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 51 (all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,lookup_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]. 0.81/1.14 52 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_removemin(U,V))) # label(ax60) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 53 (all U all V (pi_sharp_remove(i(U),V) <-> pi_remove(U,V))) # label(ax57) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 54 (all U ((exists V pi_sharp_find_min(i(U),V)) <-> pi_find_min(U))) # label(ax59) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 55 (all U all V (pi_sharp_find_min(U,V) <-> contains_pq(U,V) & issmallestelement_pq(U,V))) # label(ax58) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 56 (all U all V all W all X all Y insert_pq(i(triple(U,V,W)),X) = i(triple(U,insert_slb(V,pair(X,Y)),W))) # label(ax55) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 57 (all U ((exists V pi_sharp_find_min(i(U),V)) <-> pi_removemin(U))) # label(ax61) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 58 (all U all V (contains_pq(U,V) <-> pi_sharp_remove(U,V))) # label(ax56) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 59 (all U (phi(U) <-> (exists V (ok(V) & check_cpq(V) & succ_cpq(U,V))))) # label(ax62) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 60 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 61 -(all U ((all V all W all X all Y i(triple(V,U,X)) = i(triple(W,U,Y))) -> (all Z all X1 all X2 all X3 all X4 all X5 i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3))))) # label(l2_co) # label(negated_conjecture) # label(non_clause). [assumption]. 0.81/1.14 0.81/1.14 ============================== end of process non-clausal formulas === 0.81/1.14 0.81/1.14 ============================== PROCESS INITIAL CLAUSES =============== 0.81/1.14 0.81/1.14 ============================== PREDICATE ELIMINATION ================= 0.81/1.14 62 -contains_pq(A,B) | less_than(C,B) | -issmallestelement_pq(A,C) # label(ax10) # label(axiom). [clausify(8)]. 0.81/1.14 63 contains_pq(A,f1(A,B)) | issmallestelement_pq(A,B) # label(ax10) # label(axiom). [clausify(8)]. 0.81/1.14 64 issmallestelement_pq(A,B) | -pi_sharp_removemin(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.81/1.14 65 -pi_sharp_find_min(A,B) | issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(55)]. 0.81/1.14 66 -less_than(A,f1(B,A)) | issmallestelement_pq(B,A) # label(ax10) # label(axiom). [clausify(8)]. 0.81/1.14 Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)). [resolve(62,c,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(62,c,64,a)]. 0.81/1.14 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C). [resolve(62,c,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)). [resolve(62,c,66,b)]. 0.81/1.14 67 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_removemin(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.81/1.14 Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | contains_pq(A,f1(A,B)). [resolve(67,b,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | -pi_sharp_find_min(A,B). [resolve(67,b,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | -less_than(B,f1(A,B)). [resolve(67,b,66,b)]. 0.81/1.14 68 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(55)]. 0.81/1.14 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(68,c,63,b)]. 0.81/1.14 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(68,c,64,a)]. 0.81/1.14 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(68,c,66,b)]. 0.81/1.14 69 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom). [clausify(6)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)). [resolve(69,b,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(69,b,64,a)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B). [resolve(69,b,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)). [resolve(69,b,66,b)]. 0.81/1.14 70 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom). [clausify(11)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(70,b,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(70,b,64,a)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(70,b,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(70,b,66,b)]. 0.81/1.14 71 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom). [clausify(15)]. 0.81/1.14 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(71,a,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(71,a,64,a)]. 0.81/1.14 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(71,a,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(71,a,66,b)]. 0.81/1.14 72 -issmallestelement_pq(A,B) | -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) # label(ax15) # label(axiom). [clausify(12)]. 0.81/1.14 Derived: -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | contains_pq(A,f1(A,B)). [resolve(72,a,63,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | -pi_sharp_removemin(A,B). [resolve(72,a,64,a)]. 0.81/1.14 Derived: -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | -pi_sharp_find_min(A,B). [resolve(72,a,65,b)]. 0.81/1.14 Derived: -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | -less_than(B,f1(A,B)). [resolve(72,a,66,b)]. 0.81/1.14 73 phi(A) | -ok(B) | -check_cpq(B) | -succ_cpq(A,B) # label(ax62) # label(axiom). [clausify(59)]. 0.81/1.14 74 -phi(A) | ok(f4(A)) # label(ax62) # label(axiom). [clausify(59)]. 0.81/1.14 75 -phi(A) | check_cpq(f4(A)) # label(ax62) # label(axiom). [clausify(59)]. 0.81/1.14 76 -phi(A) | succ_cpq(A,f4(A)) # label(ax62) # label(axiom). [clausify(59)]. 0.81/1.14 Derived: -ok(A) | -check_cpq(A) | -succ_cpq(B,A) | ok(f4(B)). [resolve(73,a,74,a)]. 0.81/1.14 Derived: -ok(A) | -check_cpq(A) | -succ_cpq(B,A) | check_cpq(f4(B)). [resolve(73,a,75,a)]. 0.81/1.14 Derived: -ok(A) | -check_cpq(A) | -succ_cpq(B,A) | succ_cpq(B,f4(B)). [resolve(73,a,76,a)]. 0.81/1.14 77 -contains_pq(A,B) | pi_sharp_removemin(A,B) | contains_pq(A,f1(A,B)). [resolve(67,b,63,b)]. 0.81/1.15 78 contains_pq(A,B) | -pi_sharp_removemin(A,B) # label(ax60) # label(axiom). [clausify(52)]. 0.81/1.15 79 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(62,c,64,a)]. 0.81/1.15 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(77,b,79,c)]. 0.81/1.15 80 -contains_pq(A,B) | pi_sharp_removemin(A,B) | -pi_sharp_find_min(A,B). [resolve(67,b,65,b)]. 0.81/1.15 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(80,b,79,c)]. 0.81/1.15 81 -contains_pq(A,B) | pi_sharp_removemin(A,B) | -less_than(B,f1(A,B)). [resolve(67,b,66,b)]. 0.81/1.15 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(81,b,79,c)]. 0.81/1.15 82 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(68,c,64,a)]. 0.81/1.15 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(82,c,77,b)]. 0.81/1.15 83 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(69,b,64,a)]. 0.81/1.15 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(83,c,77,b)]. 0.81/1.15 84 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(70,b,64,a)]. 0.81/1.15 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(84,c,77,b)]. 0.81/1.15 85 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(71,a,64,a)]. 0.81/1.15 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,b)]. 0.81/1.15 86 -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | -pi_sharp_removemin(A,B). [resolve(72,a,64,a)]. 0.81/1.15 Derived: -contains_pq(A,B) | remove_pq(A,B) = removemin_pq_eff(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(86,c,77,b)]. 0.81/1.15 87 pi_sharp_find_min(i(A),f2(A)) | -pi_find_min(A) # label(ax59) # label(axiom). [clausify(54)]. 0.81/1.15 88 -pi_sharp_find_min(i(A),B) | pi_find_min(A) # label(ax59) # label(axiom). [clausify(54)]. 0.81/1.15 Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B). [resolve(87,b,88,b)]. 0.81/1.15 89 pi_sharp_find_min(i(A),f3(A)) | -pi_removemin(A) # label(ax61) # label(axiom). [clausify(57)]. 0.81/1.15 90 -pi_sharp_find_min(i(A),B) | pi_removemin(A) # label(ax61) # label(axiom). [clausify(57)]. 0.81/1.15 Derived: pi_sharp_find_min(i(A),f3(A)) | -pi_sharp_find_min(i(A),B). [resolve(89,b,90,b)]. 0.81/1.15 91 pi_sharp_remove(i(A),B) | -pi_remove(A,B) # label(ax57) # label(axiom). [clausify(53)]. 0.81/1.15 92 -pi_sharp_remove(i(A),B) | pi_remove(A,B) # label(ax57) # label(axiom). [clausify(53)]. 0.81/1.15 93 contains_pq(A,B) | -pi_sharp_remove(A,B) # label(ax56) # label(axiom). [clausify(58)]. 0.81/1.15 94 -contains_pq(A,B) | pi_sharp_remove(A,B) # label(ax56) # label(axiom). [clausify(58)]. 0.81/1.15 0.81/1.15 ============================== end predicate elimination ============= 0.81/1.15 0.81/1.15 Auto_denials: (non-Horn, no changes). 0.81/1.15 0.81/1.15 Term ordering decisions: 0.81/1.15 Function symbol KB weights: create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=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. 0.81/1.15 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 0.02 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 0.03 (+ 0.00) seconds. 0.81/1.15 % Length of proof is 8. 0.81/1.15 % Level of proof is 3. 0.81/1.15 % Maximum clause weight is 17.000. 0.81/1.15 % Given clauses 23. 0.81/1.15 0.81/1.15 56 (all U all V all W all X all Y insert_pq(i(triple(U,V,W)),X) = i(triple(U,insert_slb(V,pair(X,Y)),W))) # label(ax55) # label(axiom) # label(non_clause). [assumption]. 0.81/1.15 61 -(all U ((all V all W all X all Y i(triple(V,U,X)) = i(triple(W,U,Y))) -> (all Z all X1 all X2 all X3 all X4 all X5 i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3))))) # label(l2_co) # label(negated_conjecture) # label(non_clause). [assumption]. 0.81/1.15 115 i(triple(A,c1,B)) = i(triple(C,c1,D)) # label(l2_co) # label(negated_conjecture). [clausify(61)]. 0.81/1.15 119 i(triple(A,insert_slb(B,pair(C,D)),E)) = insert_pq(i(triple(A,B,E)),C) # label(ax55) # label(axiom). [clausify(56)]. 0.81/1.15 129 i(triple(c3,insert_slb(c1,pair(c6,c7)),c5)) != i(triple(c2,insert_slb(c1,pair(c6,c7)),c4)) # label(l2_co) # label(negated_conjecture). [clausify(61)]. 0.81/1.15 130 insert_pq(i(triple(c3,c1,c5)),c6) != insert_pq(i(triple(c2,c1,c4)),c6). [copy(129),rewrite([119(9),119(16)])]. 0.81/1.15 201 insert_pq(i(triple(A,c1,B)),C) = insert_pq(i(triple(D,c1,E)),C). [para(115(a,1),119(a,2,1)),rewrite([119(5)])]. 0.81/1.15 202 $F. [resolve(201,a,130,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=23. Generated=132. Kept=93. proofs=1. 0.81/1.15 Usable=23. Sos=69. Demods=13. Limbo=0, Disabled=127. Hints=0. 0.81/1.15 Megabytes=0.33. 0.81/1.15 User_CPU=0.03, 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 29882 exit (max_proofs) Thu Jul 2 07:31:19 2020 0.81/1.16 Prover9 interrupted 0.81/1.16 EOF