TSTP Solution File: SWV366+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : Wed Jul 20 21:12:25 EDT 2022
% Result : Theorem 0.44s 1.07s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 05:40:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.05 ============================== Prover9 ===============================
% 0.44/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.05 Process 30401 was started by sandbox on n026.cluster.edu,
% 0.44/1.05 Wed Jun 15 05:40:53 2022
% 0.44/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30248_n026.cluster.edu".
% 0.44/1.05 ============================== end of head ===========================
% 0.44/1.05
% 0.44/1.05 ============================== INPUT =================================
% 0.44/1.05
% 0.44/1.05 % Reading from file /tmp/Prover9_30248_n026.cluster.edu
% 0.44/1.05
% 0.44/1.05 set(prolog_style_variables).
% 0.44/1.05 set(auto2).
% 0.44/1.05 % set(auto2) -> set(auto).
% 0.44/1.05 % set(auto) -> set(auto_inference).
% 0.44/1.05 % set(auto) -> set(auto_setup).
% 0.44/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.05 % set(auto) -> set(auto_limits).
% 0.44/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.05 % set(auto) -> set(auto_denials).
% 0.44/1.05 % set(auto) -> set(auto_process).
% 0.44/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.05 % set(auto2) -> assign(stats, some).
% 0.44/1.05 % set(auto2) -> clear(echo_input).
% 0.44/1.05 % set(auto2) -> set(quiet).
% 0.44/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.05 % set(auto2) -> clear(print_given).
% 0.44/1.05 assign(lrs_ticks,-1).
% 0.44/1.05 assign(sos_limit,10000).
% 0.44/1.05 assign(order,kbo).
% 0.44/1.05 set(lex_order_vars).
% 0.44/1.05 clear(print_given).
% 0.44/1.05
% 0.44/1.05 % formulas(sos). % not echoed (63 formulas)
% 0.44/1.05
% 0.44/1.05 ============================== end of input ==========================
% 0.44/1.05
% 0.44/1.05 % From the command line: assign(max_seconds, 300).
% 0.44/1.05
% 0.44/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.05
% 0.44/1.05 % Formulas that are not ordinary clauses:
% 0.44/1.05 1 (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].
% 0.44/1.05 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 4 (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].
% 0.44/1.05 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 6 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 7 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 8 (all U all V all W (contains_pq(insert_pq(U,V),W) <-> contains_pq(U,W) | V = W)) # label(ax9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 9 (all U all V (issmallestelement_pq(U,V) <-> (all W (contains_pq(U,W) -> less_than(V,W))))) # label(ax10) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 10 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 11 (all U all V all W (contains_pq(U,W) & V != W -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 12 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_eff(U,V) = U)) # label(ax13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 13 (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].
% 0.44/1.05 14 (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].
% 0.44/1.05 15 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> removemin_pq_res(U,V) = V)) # label(ax16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 16 (all U all V all W insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V)) # label(ax17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 17 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 18 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 19 (all U all V all W all X (contains_slb(insert_slb(U,pair(V,X)),W) <-> contains_slb(U,W) | V = W)) # label(ax21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 20 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 21 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> pair_in_list(U,W,Y) | V = W & X = Y)) # label(ax23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 22 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 23 (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].
% 0.44/1.05 24 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 25 (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].
% 0.44/1.05 26 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 27 (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].
% 0.44/1.05 28 (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].
% 0.44/1.05 29 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 30 (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].
% 0.44/1.05 31 (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].
% 0.44/1.05 32 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 33 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 34 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 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].
% 0.44/1.05 36 (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].
% 0.44/1.05 37 (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].
% 0.44/1.05 38 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 39 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 40 (all U all V all W all X insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W)) # label(ax42) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 41 (all U all V all W all X (-contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(U,V,bad))) # label(ax43) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.05 42 (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].
% 0.44/1.06 43 (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].
% 0.44/1.06 44 (all U all V findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad)) # label(ax46) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 45 (all U all V all W all X (V != create_slb & -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(ax47) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 46 (all U all V all W all X (V != create_slb & 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].
% 0.44/1.06 47 (all U all V all W all X (V != create_slb & contains_slb(V,findmin_pqp_res(U)) & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) -> 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].
% 0.44/1.06 48 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06 50 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 51 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 52 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 53 (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].
% 0.44/1.06 54 (all U all V (pi_sharp_remove(U,V) <-> contains_pq(U,V))) # label(ax56) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 55 (all U all V (pi_remove(U,V) <-> pi_sharp_remove(i(U),V))) # label(ax57) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 56 (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].
% 0.44/1.06 57 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 58 (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].
% 0.44/1.06 59 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 60 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 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].
% 0.44/1.06
% 0.44/1.06 ============================== end of process non-clausal formulas ===
% 0.44/1.06
% 0.44/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.06
% 0.44/1.06 ============================== PREDICATE ELIMINATION =================
% 0.44/1.06 62 -issmallestelement_pq(A,B) | -contains_pq(A,C) | less_than(B,C) # label(ax10) # label(axiom). [clausify(9)].
% 0.44/1.06 63 issmallestelement_pq(A,B) | contains_pq(A,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 0.44/1.06 64 -pi_sharp_find_min(A,B) | issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(56)].
% 0.44/1.06 65 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.44/1.06 66 issmallestelement_pq(A,B) | -less_than(B,f1(A,B)) # label(ax10) # label(axiom). [clausify(9)].
% 0.44/1.06 Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)). [resolve(62,a,63,a)].
% 0.44/1.06 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C). [resolve(62,a,64,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(62,a,65,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)). [resolve(62,a,66,a)].
% 0.44/1.06 67 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax58) # label(axiom). [clausify(56)].
% 0.44/1.06 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(67,c,63,a)].
% 0.44/1.06 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(67,c,65,b)].
% 0.44/1.06 Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(67,c,66,a)].
% 0.44/1.06 68 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.44/1.06 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(68,c,63,a)].
% 0.44/1.06 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(68,c,64,b)].
% 0.44/1.06 Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(68,c,66,a)].
% 0.44/1.06 69 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom). [clausify(12)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)). [resolve(69,b,63,a)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B). [resolve(69,b,64,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(69,b,65,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)). [resolve(69,b,66,a)].
% 0.44/1.06 70 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom). [clausify(13)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(70,b,63,a)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(70,b,64,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(70,b,65,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(70,b,66,a)].
% 0.44/1.06 71 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom). [clausify(15)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)). [resolve(71,b,63,a)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B). [resolve(71,b,64,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(71,b,65,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)). [resolve(71,b,66,a)].
% 0.44/1.06 72 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom). [clausify(14)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(72,b,63,a)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(72,b,64,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(72,b,65,b)].
% 0.44/1.06 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)). [resolve(72,b,66,a)].
% 0.44/1.06 73 phi(A) | -succ_cpq(A,B) | -ok(B) | -check_cpq(B) # label(ax62) # label(axiom). [clausify(60)].
% 0.44/1.06 74 -phi(A) | ok(f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.44/1.06 75 -phi(A) | check_cpq(f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.44/1.06 76 -phi(A) | succ_cpq(A,f4(A)) # label(ax62) # label(axiom). [clausify(60)].
% 0.44/1.06 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | ok(f4(A)). [resolve(73,a,74,a)].
% 0.44/1.06 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | check_cpq(f4(A)). [resolve(73,a,75,a)].
% 0.44/1.06 Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | succ_cpq(A,f4(A)). [resolve(73,a,76,a)].
% 0.44/1.06 77 -pi_find_min(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax59) # label(axiom). [clausify(57)].
% 0.44/1.07 78 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom). [clausify(57)].
% 0.44/1.07 Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B). [resolve(77,a,78,a)].
% 0.44/1.07 79 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(68,c,63,a)].
% 0.44/1.07 80 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom). [clausify(58)].
% 0.44/1.07 81 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C). [resolve(62,a,65,b)].
% 0.44/1.07 82 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(67,c,65,b)].
% 0.44/1.07 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(79,a,81,c)].
% 0.44/1.07 Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(79,a,82,c)].
% 0.44/1.07 83 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(68,c,64,b)].
% 0.44/1.07 Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C). [resolve(83,a,81,c)].
% 0.44/1.07 84 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)). [resolve(68,c,66,a)].
% 0.44/1.07 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C). [resolve(84,a,81,c)].
% 0.44/1.07 Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | pi_sharp_find_min(A,B) | -contains_pq(A,B). [resolve(84,a,82,c)].
% 0.44/1.07 85 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B). [resolve(69,b,65,b)].
% 0.44/1.07 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(85,c,79,a)].
% 0.44/1.07 Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(85,c,83,a)].
% 0.44/1.07 86 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(70,b,65,b)].
% 0.44/1.07 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(86,c,79,a)].
% 0.44/1.07 Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(86,c,83,a)].
% 0.44/1.07 87 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B). [resolve(71,b,65,b)].
% 0.44/1.07 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)). [resolve(87,c,79,a)].
% 0.44/1.07 Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(87,c,83,a)].
% 0.44/1.07 88 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B). [resolve(72,b,65,b)].
% 0.44/1.07 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(88,c,79,a)].
% 0.44/1.07 Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B). [resolve(88,c,83,a)].
% 0.44/1.07 89 -pi_removemin(A) | pi_sharp_find_min(i(A),f3(A)) # label(ax61) # label(axiom). [clausify(59)].
% 0.44/1.07 90 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom). [clausify(59)].
% 0.44/1.07 Derived: pi_sharp_find_min(i(A),f3(A)) | -pi_sharp_find_min(i(A),B). [resolve(89,a,90,a)].
% 0.44/1.07 91 pi_remove(A,B) | -pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 0.44/1.07 92 -pi_remove(A,B) | pi_sharp_remove(i(A),B) # label(ax57) # label(axiom). [clausify(55)].
% 0.44/1.07 93 pi_sharp_remove(A,B) | -contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 0.44/1.07 94 -pi_sharp_remove(A,B) | contains_pq(A,B) # label(ax56) # label(axiom). [clausify(54)].
% 0.44/1.07
% 0.44/1.07 ============================== end predicate elimination =============
% 0.44/1.07
% 0.44/1.07 Auto_denials: (non-Horn, no changes).
% 0.44/1.07
% 0.44/1.07 Term ordering decisions:
% 0.44/1.07 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. remove_pq=1. update_slb=1. lookup_slb=1. findmin_pq_eff=1. findmin_pq_res=1. remove_cpq=1. remove_slb=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.
% 0.44/1.07
% 0.44/1.07 ============================== end of process initial clauses ========
% 0.44/1.07
% 0.44/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.07
% 0.44/1.07 ============================== end of clauses for search =============
% 0.44/1.07
% 0.44/1.07 ============================== SEARCH ================================
% 0.44/1.07
% 0.44/1.07 % Starting search at 0.03 seconds.
% 0.44/1.07
% 0.44/1.07 ============================== PROOF =================================
% 0.44/1.07 % SZS status Theorem
% 0.44/1.07 % SZS output start Refutation
% 0.44/1.07
% 0.44/1.07 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.44/1.07 % Length of proof is 8.
% 0.44/1.07 % Level of proof is 3.
% 0.44/1.07 % Maximum clause weight is 17.000.
% 0.44/1.07 % Given clauses 23.
% 0.44/1.07
% 0.44/1.07 53 (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].
% 0.44/1.07 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].
% 0.44/1.07 115 i(triple(A,c1,B)) = i(triple(C,c1,D)) # label(l2_co) # label(negated_conjecture). [clausify(61)].
% 0.44/1.07 119 i(triple(A,insert_slb(B,pair(C,D)),E)) = insert_pq(i(triple(A,B,E)),C) # label(ax55) # label(axiom). [clausify(53)].
% 0.44/1.07 129 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)].
% 0.44/1.07 130 insert_pq(i(triple(c3,c1,c5)),c6) != insert_pq(i(triple(c2,c1,c4)),c6). [copy(129),rewrite([119(9),119(16)])].
% 0.44/1.07 201 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)])].
% 0.44/1.07 202 $F. [resolve(201,a,130,a)].
% 0.44/1.07
% 0.44/1.07 % SZS output end Refutation
% 0.44/1.07 ============================== end of proof ==========================
% 0.44/1.07
% 0.44/1.07 ============================== STATISTICS ============================
% 0.44/1.07
% 0.44/1.07 Given=23. Generated=137. Kept=93. proofs=1.
% 0.44/1.07 Usable=23. Sos=69. Demods=13. Limbo=0, Disabled=132. Hints=0.
% 0.44/1.07 Megabytes=0.33.
% 0.44/1.07 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.44/1.07
% 0.44/1.07 ============================== end of statistics =====================
% 0.44/1.07
% 0.44/1.07 ============================== end of search =========================
% 0.44/1.07
% 0.44/1.07 THEOREM PROVED
% 0.44/1.07 % SZS status Theorem
% 0.44/1.07
% 0.44/1.07 Exiting with 1 proof.
% 0.44/1.07
% 0.44/1.07 Process 30401 exit (max_proofs) Wed Jun 15 05:40:53 2022
% 0.44/1.07 Prover9 interrupted
%------------------------------------------------------------------------------