TSTP Solution File: SWV409+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 21:12:34 EDT 2022
% Result : Theorem 0.72s 1.06s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 17:04:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/0.99 ============================== Prover9 ===============================
% 0.68/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.99 Process 594 was started by sandbox2 on n010.cluster.edu,
% 0.68/0.99 Tue Jun 14 17:04:25 2022
% 0.68/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_420_n010.cluster.edu".
% 0.68/0.99 ============================== end of head ===========================
% 0.68/0.99
% 0.68/0.99 ============================== INPUT =================================
% 0.68/0.99
% 0.68/0.99 % Reading from file /tmp/Prover9_420_n010.cluster.edu
% 0.68/0.99
% 0.68/0.99 set(prolog_style_variables).
% 0.68/0.99 set(auto2).
% 0.68/0.99 % set(auto2) -> set(auto).
% 0.68/0.99 % set(auto) -> set(auto_inference).
% 0.68/0.99 % set(auto) -> set(auto_setup).
% 0.68/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.99 % set(auto) -> set(auto_limits).
% 0.68/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.99 % set(auto) -> set(auto_denials).
% 0.68/0.99 % set(auto) -> set(auto_process).
% 0.68/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.99 % set(auto2) -> assign(stats, some).
% 0.68/0.99 % set(auto2) -> clear(echo_input).
% 0.68/0.99 % set(auto2) -> set(quiet).
% 0.68/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.99 % set(auto2) -> clear(print_given).
% 0.68/0.99 assign(lrs_ticks,-1).
% 0.68/0.99 assign(sos_limit,10000).
% 0.68/0.99 assign(order,kbo).
% 0.68/0.99 set(lex_order_vars).
% 0.68/0.99 clear(print_given).
% 0.68/0.99
% 0.68/0.99 % formulas(sos). % not echoed (22 formulas)
% 0.68/0.99
% 0.68/0.99 ============================== end of input ==========================
% 0.68/0.99
% 0.68/0.99 % From the command line: assign(max_seconds, 300).
% 0.68/0.99
% 0.68/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.99
% 0.68/0.99 % Formulas that are not ordinary clauses:
% 0.68/0.99 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].
% 0.68/0.99 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 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].
% 0.68/0.99 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 6 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 7 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 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].
% 0.68/0.99 9 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.99 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].
% 0.68/0.99 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].
% 0.68/0.99 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].
% 0.68/0.99 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].
% 0.68/0.99 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].
% 0.72/1.06 15 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 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].
% 0.72/1.06 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].
% 0.72/1.06 18 (all U all V (contains_slb(U,V) -> (exists W pair_in_list(U,V,W)))) # label(l45_li4647) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 19 (all U all V all W all X (pair_in_list(U,V,W) & strictly_less_than(V,X) & strictly_less_than(W,X) -> pair_in_list(update_slb(U,X),V,X))) # label(l45_l48) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 20 (all U all V all W all X (pair_in_list(U,V,W) & strictly_less_than(V,X) & less_than(X,W) -> (exists Y (pair_in_list(update_slb(U,X),V,Y) & less_than(X,Y))))) # label(l45_l49) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 21 -(all U all V all W (contains_slb(U,V) & strictly_less_than(V,W) -> pair_in_list(update_slb(U,W),V,W) | (exists X (pair_in_list(update_slb(U,W),V,X) & less_than(W,X))))) # label(l45_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.06
% 0.72/1.06 ============================== end of process non-clausal formulas ===
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.06
% 0.72/1.06 ============================== PREDICATE ELIMINATION =================
% 0.72/1.06
% 0.72/1.06 ============================== end predicate elimination =============
% 0.72/1.06
% 0.72/1.06 Auto_denials: (non-Horn, no changes).
% 0.72/1.06
% 0.72/1.06 Term ordering decisions:
% 0.72/1.06 Function symbol KB weights: create_slb=1. bottom=1. c1=1. c2=1. c3=1. insert_slb=1. pair=1. update_slb=1. lookup_slb=1. remove_slb=1. f1=1. f2=1.
% 0.72/1.06
% 0.72/1.06 ============================== end of process initial clauses ========
% 0.72/1.06
% 0.72/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.06
% 0.72/1.06 ============================== end of clauses for search =============
% 0.72/1.06
% 0.72/1.06 ============================== SEARCH ================================
% 0.72/1.06
% 0.72/1.06 % Starting search at 0.01 seconds.
% 0.72/1.06
% 0.72/1.06 ============================== PROOF =================================
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06 % SZS output start Refutation
% 0.72/1.06
% 0.72/1.06 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.72/1.06 % Length of proof is 25.
% 0.72/1.06 % Level of proof is 7.
% 0.72/1.06 % Maximum clause weight is 20.000.
% 0.72/1.06 % Given clauses 116.
% 0.72/1.06
% 0.72/1.06 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 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].
% 0.72/1.06 18 (all U all V (contains_slb(U,V) -> (exists W pair_in_list(U,V,W)))) # label(l45_li4647) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 19 (all U all V all W all X (pair_in_list(U,V,W) & strictly_less_than(V,X) & strictly_less_than(W,X) -> pair_in_list(update_slb(U,X),V,X))) # label(l45_l48) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 20 (all U all V all W all X (pair_in_list(U,V,W) & strictly_less_than(V,X) & less_than(X,W) -> (exists Y (pair_in_list(update_slb(U,X),V,Y) & less_than(X,Y))))) # label(l45_l49) # label(lemma) # label(non_clause). [assumption].
% 0.72/1.06 21 -(all U all V all W (contains_slb(U,V) & strictly_less_than(V,W) -> pair_in_list(update_slb(U,W),V,W) | (exists X (pair_in_list(update_slb(U,W),V,X) & less_than(W,X))))) # label(l45_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.06 24 contains_slb(c1,c2) # label(l45_co) # label(negated_conjecture). [clausify(21)].
% 0.72/1.06 25 strictly_less_than(c2,c3) # label(l45_co) # label(negated_conjecture). [clausify(21)].
% 0.72/1.06 27 less_than(A,B) | less_than(B,A) # label(totality) # label(axiom). [clausify(2)].
% 0.72/1.06 35 -pair_in_list(update_slb(c1,c3),c2,c3) # label(l45_co) # label(negated_conjecture). [clausify(21)].
% 0.72/1.06 36 -pair_in_list(update_slb(c1,c3),c2,A) | -less_than(c3,A) # label(l45_co) # label(negated_conjecture). [clausify(21)].
% 0.72/1.06 39 strictly_less_than(A,B) | -less_than(A,B) | less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 0.72/1.06 40 -contains_slb(A,B) | pair_in_list(A,B,f1(A,B)) # label(l45_li4647) # label(lemma). [clausify(18)].
% 0.72/1.06 48 -pair_in_list(A,B,C) | -strictly_less_than(B,D) | -strictly_less_than(C,D) | pair_in_list(update_slb(A,D),B,D) # label(l45_l48) # label(lemma). [clausify(19)].
% 0.72/1.06 50 -pair_in_list(A,B,C) | -strictly_less_than(B,D) | -less_than(D,C) | less_than(D,f2(A,B,C,D)) # label(l45_l49) # label(lemma). [clausify(20)].
% 0.72/1.06 53 -pair_in_list(A,B,C) | -strictly_less_than(B,D) | -less_than(D,C) | pair_in_list(update_slb(A,D),B,f2(A,B,C,D)) # label(l45_l49) # label(lemma). [clausify(20)].
% 0.72/1.06 63 strictly_less_than(A,B) | less_than(B,A). [resolve(39,b,27,b),merge(c)].
% 0.72/1.06 64 pair_in_list(c1,c2,f1(c1,c2)). [resolve(40,a,24,a)].
% 0.72/1.06 83 -strictly_less_than(c2,A) | -less_than(A,f1(c1,c2)) | pair_in_list(update_slb(c1,A),c2,f2(c1,c2,f1(c1,c2),A)). [resolve(64,a,53,a)].
% 0.72/1.06 84 -strictly_less_than(c2,A) | -less_than(A,f1(c1,c2)) | less_than(A,f2(c1,c2,f1(c1,c2),A)). [resolve(64,a,50,a)].
% 0.72/1.06 87 -strictly_less_than(f1(c1,c2),c3). [ur(48,a,64,a,b,25,a,d,35,a)].
% 0.72/1.06 90 less_than(c3,f1(c1,c2)). [resolve(87,a,63,a)].
% 0.72/1.06 302 pair_in_list(update_slb(c1,c3),c2,f2(c1,c2,f1(c1,c2),c3)). [resolve(83,a,25,a),unit_del(a,90)].
% 0.72/1.06 307 -less_than(c3,f2(c1,c2,f1(c1,c2),c3)). [resolve(302,a,36,a)].
% 0.72/1.06 312 $F. [resolve(84,a,25,a),unit_del(a,90),unit_del(b,307)].
% 0.72/1.06
% 0.72/1.06 % SZS output end Refutation
% 0.72/1.06 ============================== end of proof ==========================
% 0.72/1.06
% 0.72/1.06 ============================== STATISTICS ============================
% 0.72/1.06
% 0.72/1.06 Given=116. Generated=1818. Kept=290. proofs=1.
% 0.72/1.06 Usable=114. Sos=168. Demods=12. Limbo=1, Disabled=40. Hints=0.
% 0.72/1.06 Megabytes=0.41.
% 0.72/1.06 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.72/1.06
% 0.72/1.06 ============================== end of statistics =====================
% 0.72/1.06
% 0.72/1.06 ============================== end of search =========================
% 0.72/1.06
% 0.72/1.06 THEOREM PROVED
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06
% 0.72/1.06 Exiting with 1 proof.
% 0.72/1.06
% 0.72/1.06 Process 594 exit (max_proofs) Tue Jun 14 17:04:25 2022
% 0.72/1.06 Prover9 interrupted
%------------------------------------------------------------------------------