TSTP Solution File: SWV390+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV390+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 21:12:30 EDT 2022
% Result : Theorem 0.43s 1.03s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV390+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.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 : Tue Jun 14 21:54:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 4913 was started by sandbox on n019.cluster.edu,
% 0.43/1.00 Tue Jun 14 21:54:10 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4732_n019.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_4732_n019.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 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].
% 0.43/1.00 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 9 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 15 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 18 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 21 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 22 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 23 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 27 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 28 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 37 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.03 40 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 41 (all U all V all W (check_cpq(triple(U,V,W)) <-> (all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))))) # label(l26_li4142) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.03 42 -(all U all V all W (-check_cpq(triple(U,V,W)) -> (all X -check_cpq(insert_cpq(triple(U,V,W),X))))) # label(l26_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.03
% 0.43/1.03 ============================== end of process non-clausal formulas ===
% 0.43/1.03
% 0.43/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.03
% 0.43/1.03 ============================== PREDICATE ELIMINATION =================
% 0.43/1.03
% 0.43/1.03 ============================== end predicate elimination =============
% 0.43/1.03
% 0.43/1.03 Auto_denials: (non-Horn, no changes).
% 0.43/1.03
% 0.43/1.03 Term ordering decisions:
% 0.43/1.03 Function symbol KB weights: create_slb=1. bad=1. bottom=1. c1=1. c2=1. c3=1. c4=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. removemin_cpq_eff=1. removemin_cpq_res=1. triple=1. f1=1. f2=1.
% 0.43/1.03
% 0.43/1.03 ============================== end of process initial clauses ========
% 0.43/1.03
% 0.43/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.03
% 0.43/1.03 ============================== end of clauses for search =============
% 0.43/1.03
% 0.43/1.03 ============================== SEARCH ================================
% 0.43/1.03
% 0.43/1.03 % Starting search at 0.01 seconds.
% 0.43/1.03
% 0.43/1.03 ============================== PROOF =================================
% 0.43/1.03 % SZS status Theorem
% 0.43/1.03 % SZS output start Refutation
% 0.43/1.03
% 0.43/1.03 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.43/1.03 % Length of proof is 19.
% 0.43/1.03 % Level of proof is 6.
% 0.43/1.03 % Maximum clause weight is 19.000.
% 0.43/1.03 % Given clauses 178.
% 0.43/1.03
% 0.43/1.03 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 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].
% 0.43/1.04 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].
% 0.43/1.04 41 (all U all V all W (check_cpq(triple(U,V,W)) <-> (all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))))) # label(l26_li4142) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.04 42 -(all U all V all W (-check_cpq(triple(U,V,W)) -> (all X -check_cpq(insert_cpq(triple(U,V,W),X))))) # label(l26_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.04 44 less_than(bottom,A) # label(bottom_smallest) # label(axiom). [clausify(5)].
% 0.43/1.04 52 check_cpq(insert_cpq(triple(c1,c2,c3),c4)) # label(l26_co) # label(negated_conjecture). [clausify(42)].
% 0.43/1.04 62 check_cpq(triple(A,B,C)) | pair_in_list(B,f1(A,B,C),f2(A,B,C)) # label(l26_li4142) # label(lemma). [clausify(41)].
% 0.43/1.04 63 triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B) # label(ax42) # label(axiom). [clausify(29)].
% 0.43/1.04 69 -check_cpq(triple(c1,c2,c3)) # label(l26_co) # label(negated_conjecture). [clausify(42)].
% 0.43/1.04 85 -check_cpq(triple(A,B,C)) | -pair_in_list(B,D,E) | less_than(E,D) # label(l26_li4142) # label(lemma). [clausify(41)].
% 0.43/1.04 88 check_cpq(triple(A,B,C)) | -less_than(f2(A,B,C),f1(A,B,C)) # label(l26_li4142) # label(lemma). [clausify(41)].
% 0.43/1.04 92 -less_than(A,B) | -check_cpq(triple(C,insert_slb(D,pair(B,A)),E)) | check_cpq(triple(C,D,E)) # label(ax37) # label(axiom). [clausify(24)].
% 0.43/1.04 128 -check_cpq(triple(A,B,C)) | less_than(f2(D,B,E),f1(D,B,E)) | check_cpq(triple(D,B,E)). [resolve(85,b,62,b)].
% 0.43/1.04 150 -check_cpq(triple(c1,insert_slb(c2,pair(A,bottom)),c3)). [ur(92,a,44,a,c,69,a)].
% 0.43/1.04 205 -less_than(f2(c1,insert_slb(c2,pair(A,bottom)),c3),f1(c1,insert_slb(c2,pair(A,bottom)),c3)). [ur(88,a,150,a)].
% 0.43/1.04 577 -check_cpq(triple(A,insert_slb(c2,pair(B,bottom)),C)). [ur(128,b,205,a,c,150,a)].
% 0.43/1.04 591 -check_cpq(insert_cpq(triple(A,c2,B),C)). [para(63(a,1),577(a,1))].
% 0.43/1.04 592 $F. [resolve(591,a,52,a)].
% 0.43/1.04
% 0.43/1.04 % SZS output end Refutation
% 0.43/1.04 ============================== end of proof ==========================
% 0.43/1.04
% 0.43/1.04 ============================== STATISTICS ============================
% 0.43/1.04
% 0.43/1.04 Given=178. Generated=858. Kept=546. proofs=1.
% 0.43/1.04 Usable=168. Sos=334. Demods=12. Limbo=4, Disabled=94. Hints=0.
% 0.43/1.04 Megabytes=0.88.
% 0.43/1.04 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.43/1.04
% 0.43/1.04 ============================== end of statistics =====================
% 0.43/1.04
% 0.43/1.04 ============================== end of search =========================
% 0.43/1.04
% 0.43/1.04 THEOREM PROVED
% 0.43/1.04 % SZS status Theorem
% 0.43/1.04
% 0.43/1.04 Exiting with 1 proof.
% 0.43/1.04
% 0.43/1.04 Process 4913 exit (max_proofs) Tue Jun 14 21:54:10 2022
% 0.43/1.04 Prover9 interrupted
%------------------------------------------------------------------------------