TSTP Solution File: SWV376+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 21:12:27 EDT 2022
% Result : Theorem 0.43s 1.05s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 20:05:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 6337 was started by sandbox2 on n017.cluster.edu,
% 0.43/1.02 Wed Jun 15 20:05:55 2022
% 0.43/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6183_n017.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_6183_n017.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (44 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02 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].
% 0.43/1.02 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 6 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 7 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 8 (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].
% 0.43/1.02 9 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 10 (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].
% 0.43/1.02 11 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 12 (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].
% 0.43/1.02 13 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 14 (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].
% 0.43/1.02 15 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 16 (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].
% 0.43/1.02 17 (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].
% 0.43/1.02 18 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 19 (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].
% 0.43/1.02 20 (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].
% 0.43/1.02 21 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 22 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 23 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 24 (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].
% 0.43/1.02 25 (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].
% 0.43/1.02 26 (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].
% 0.43/1.02 27 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 28 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 29 (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].
% 0.43/1.02 30 (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].
% 0.43/1.02 31 (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].
% 0.43/1.02 32 (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].
% 0.43/1.02 33 (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].
% 0.43/1.02 34 (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].
% 0.43/1.02 35 (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].
% 0.43/1.02 36 (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].
% 0.43/1.02 37 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 38 (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].
% 0.43/1.02 39 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 40 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 41 (all U all V all W all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> (-ok(triple(X,Y,Z)) -> -ok(im_succ_cpq(triple(X,Y,Z)))))) -> (all X1 all X2 all X3 (-ok(triple(X1,X2,X3)) -> (all X4 all X5 all X6 (succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) -> -ok(triple(X4,X5,X6)))))) # label(l12_induction) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 42 (all U all V all W (-ok(triple(U,V,W)) -> -ok(im_succ_cpq(triple(U,V,W))))) # label(l12_l13) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.05 43 -(all U all V all W (-ok(triple(U,V,W)) -> (all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> -ok(triple(X,Y,Z)))))) # label(l12_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.05
% 0.43/1.05 ============================== end of process non-clausal formulas ===
% 0.43/1.05
% 0.43/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.05
% 0.43/1.05 ============================== PREDICATE ELIMINATION =================
% 0.43/1.05
% 0.43/1.05 ============================== end predicate elimination =============
% 0.43/1.05
% 0.43/1.05 Auto_denials: (non-Horn, no changes).
% 0.43/1.05
% 0.43/1.05 Term ordering decisions:
% 0.43/1.05 Function symbol KB weights: create_slb=1. bad=1. bottom=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. insert_slb=1. pair=1. update_slb=1. lookup_slb=1. remove_cpq=1. remove_slb=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. findmin_pqp_res=1. findmin_cpq_eff=1. findmin_cpq_res=1. im_succ_cpq=1. removemin_cpq_eff=1. removemin_cpq_res=1. triple=1.
% 0.43/1.05
% 0.43/1.05 ============================== end of process initial clauses ========
% 0.43/1.05
% 0.43/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.05
% 0.43/1.05 ============================== end of clauses for search =============
% 0.43/1.05
% 0.43/1.05 ============================== SEARCH ================================
% 0.43/1.05
% 0.43/1.05 % Starting search at 0.02 seconds.
% 0.43/1.05
% 0.43/1.05 ============================== PROOF =================================
% 0.43/1.05 % SZS status Theorem
% 0.43/1.05 % SZS output start Refutation
% 0.43/1.05
% 0.43/1.05 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.43/1.05 % Length of proof is 20.
% 0.43/1.05 % Level of proof is 6.
% 0.43/1.05 % Maximum clause weight is 25.000.
% 0.43/1.05 % Given clauses 97.
% 0.43/1.05
% 0.43/1.05 27 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 28 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 41 (all U all V all W all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> (-ok(triple(X,Y,Z)) -> -ok(im_succ_cpq(triple(X,Y,Z)))))) -> (all X1 all X2 all X3 (-ok(triple(X1,X2,X3)) -> (all X4 all X5 all X6 (succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) -> -ok(triple(X4,X5,X6)))))) # label(l12_induction) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.05 42 (all U all V all W (-ok(triple(U,V,W)) -> -ok(im_succ_cpq(triple(U,V,W))))) # label(l12_l13) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.05 43 -(all U all V all W (-ok(triple(U,V,W)) -> (all X all Y all Z (succ_cpq(triple(U,V,W),triple(X,Y,Z)) -> -ok(triple(X,Y,Z)))))) # label(l12_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.05 50 ok(triple(c10,c11,c12)) # label(l12_co) # label(negated_conjecture). [clausify(43)].
% 0.43/1.05 54 ok(triple(A,B,C)) | bad = C # label(ax41) # label(axiom). [clausify(28)].
% 0.43/1.05 58 succ_cpq(triple(c7,c8,c9),triple(c10,c11,c12)) # label(l12_co) # label(negated_conjecture). [clausify(43)].
% 0.43/1.05 69 -ok(triple(A,B,bad)) # label(ax40) # label(axiom). [clausify(27)].
% 0.43/1.05 70 -ok(triple(c7,c8,c9)) # label(l12_co) # label(negated_conjecture). [clausify(43)].
% 0.43/1.05 85 ok(triple(A,B,C)) | -ok(im_succ_cpq(triple(A,B,C))) # label(l12_l13) # label(lemma). [clausify(42)].
% 0.43/1.05 99 -ok(triple(c4,c5,c6)) | ok(triple(A,B,C)) | -succ_cpq(triple(A,B,C),triple(D,E,F)) | -ok(triple(D,E,F)) # label(l12_induction) # label(axiom). [clausify(41)].
% 0.43/1.05 100 ok(im_succ_cpq(triple(c4,c5,c6))) | ok(triple(A,B,C)) | -succ_cpq(triple(A,B,C),triple(D,E,F)) | -ok(triple(D,E,F)) # label(l12_induction) # label(axiom). [clausify(41)].
% 0.43/1.05 111 c9 = bad. [resolve(70,a,54,a),flip(a)].
% 0.43/1.05 112 succ_cpq(triple(c7,c8,bad),triple(c10,c11,c12)). [back_rewrite(58),rewrite([111(3)])].
% 0.43/1.05 133 -ok(im_succ_cpq(triple(A,B,bad))). [ur(85,a,69,a)].
% 0.43/1.05 269 ok(im_succ_cpq(triple(c4,c5,c6))). [resolve(112,a,100,c),unit_del(b,69),unit_del(c,50)].
% 0.43/1.05 270 -ok(triple(c4,c5,c6)). [resolve(112,a,99,c),unit_del(b,69),unit_del(c,50)].
% 0.43/1.05 275 c6 = bad. [resolve(270,a,54,a),flip(a)].
% 0.43/1.05 276 $F. [back_rewrite(269),rewrite([275(3)]),unit_del(a,133)].
% 0.43/1.05
% 0.43/1.05 % SZS output end Refutation
% 0.43/1.05 ============================== end of proof ==========================
% 0.43/1.05
% 0.43/1.05 ============================== STATISTICS ============================
% 0.43/1.05
% 0.43/1.05 Given=97. Generated=380. Kept=229. proofs=1.
% 0.43/1.05 Usable=89. Sos=110. Demods=13. Limbo=1, Disabled=86. Hints=0.
% 0.43/1.05 Megabytes=0.51.
% 0.43/1.05 User_CPU=0.04, System_CPU=0.01, Wall_clock=0.
% 0.43/1.05
% 0.43/1.05 ============================== end of statistics =====================
% 0.43/1.05
% 0.43/1.05 ============================== end of search =========================
% 0.43/1.05
% 0.43/1.05 THEOREM PROVED
% 0.43/1.05 % SZS status Theorem
% 0.43/1.05
% 0.43/1.05 Exiting with 1 proof.
% 0.43/1.05
% 0.43/1.05 Process 6337 exit (max_proofs) Wed Jun 15 20:05:55 2022
% 0.43/1.05 Prover9 interrupted
%------------------------------------------------------------------------------