TSTP Solution File: SWV403+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 21:12:32 EDT 2022
% Result : Theorem 3.62s 3.93s
% Output : Refutation 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jun 14 20:42:13 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.49/0.81 ============================== Prover9 ===============================
% 0.49/0.81 Prover9 (32) version 2009-11A, November 2009.
% 0.49/0.81 Process 21800 was started by sandbox on n032.cluster.edu,
% 0.49/0.81 Tue Jun 14 20:42:13 2022
% 0.49/0.81 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21647_n032.cluster.edu".
% 0.49/0.81 ============================== end of head ===========================
% 0.49/0.81
% 0.49/0.81 ============================== INPUT =================================
% 0.49/0.81
% 0.49/0.81 % Reading from file /tmp/Prover9_21647_n032.cluster.edu
% 0.49/0.81
% 0.49/0.81 set(prolog_style_variables).
% 0.49/0.81 set(auto2).
% 0.49/0.81 % set(auto2) -> set(auto).
% 0.49/0.81 % set(auto) -> set(auto_inference).
% 0.49/0.81 % set(auto) -> set(auto_setup).
% 0.49/0.81 % set(auto_setup) -> set(predicate_elim).
% 0.49/0.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/0.81 % set(auto) -> set(auto_limits).
% 0.49/0.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/0.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/0.81 % set(auto) -> set(auto_denials).
% 0.49/0.81 % set(auto) -> set(auto_process).
% 0.49/0.81 % set(auto2) -> assign(new_constants, 1).
% 0.49/0.81 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/0.81 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/0.81 % set(auto2) -> assign(max_hours, 1).
% 0.49/0.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/0.81 % set(auto2) -> assign(max_seconds, 0).
% 0.49/0.81 % set(auto2) -> assign(max_minutes, 5).
% 0.49/0.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/0.81 % set(auto2) -> set(sort_initial_sos).
% 0.49/0.81 % set(auto2) -> assign(sos_limit, -1).
% 0.49/0.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/0.81 % set(auto2) -> assign(max_megs, 400).
% 0.49/0.81 % set(auto2) -> assign(stats, some).
% 0.49/0.81 % set(auto2) -> clear(echo_input).
% 0.49/0.81 % set(auto2) -> set(quiet).
% 0.49/0.81 % set(auto2) -> clear(print_initial_clauses).
% 0.49/0.81 % set(auto2) -> clear(print_given).
% 0.49/0.81 assign(lrs_ticks,-1).
% 0.49/0.81 assign(sos_limit,10000).
% 0.49/0.81 assign(order,kbo).
% 0.49/0.81 set(lex_order_vars).
% 0.49/0.81 clear(print_given).
% 0.49/0.81
% 0.49/0.81 % formulas(sos). % not echoed (19 formulas)
% 0.49/0.81
% 0.49/0.81 ============================== end of input ==========================
% 0.49/0.81
% 0.49/0.81 % From the command line: assign(max_seconds, 300).
% 0.49/0.81
% 0.49/0.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/0.81
% 0.49/0.81 % Formulas that are not ordinary clauses:
% 0.49/0.81 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].
% 0.49/0.81 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 3 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 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].
% 0.49/0.81 5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 6 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 7 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 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].
% 0.49/0.81 9 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.81 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].
% 0.49/0.81 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].
% 0.49/0.81 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].
% 0.49/0.81 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].
% 0.49/0.81 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].
% 3.62/3.93 15 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.93 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].
% 3.62/3.93 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].
% 3.62/3.93 18 -(all U ((all V all W all X (pair_in_list(U,V,W) & strictly_less_than(W,X) -> pair_in_list(update_slb(U,X),V,X))) -> (all Y all Z all X1 all X2 all X3 (pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) & strictly_less_than(Z,X1) -> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1))))) # label(l39_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.62/3.93
% 3.62/3.93 ============================== end of process non-clausal formulas ===
% 3.62/3.93
% 3.62/3.93 ============================== PROCESS INITIAL CLAUSES ===============
% 3.62/3.93
% 3.62/3.93 ============================== PREDICATE ELIMINATION =================
% 3.62/3.93 19 -strictly_less_than(A,B) | -less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 3.62/3.93 20 strictly_less_than(c3,c4) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 Derived: -less_than(c4,c3). [resolve(19,a,20,a)].
% 3.62/3.93 21 -strictly_less_than(A,B) | less_than(A,B) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 3.62/3.93 Derived: less_than(c3,c4). [resolve(21,a,20,a)].
% 3.62/3.93 22 strictly_less_than(A,B) | -less_than(A,B) | less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 3.62/3.93 23 -pair_in_list(c1,A,B) | -strictly_less_than(B,C) | pair_in_list(update_slb(c1,C),A,C) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 Derived: -pair_in_list(c1,A,c3) | pair_in_list(update_slb(c1,c4),A,c4). [resolve(23,b,20,a)].
% 3.62/3.93 Derived: -pair_in_list(c1,A,B) | pair_in_list(update_slb(c1,C),A,C) | -less_than(B,C) | less_than(C,B). [resolve(23,b,22,a)].
% 3.62/3.93 24 -strictly_less_than(A,B) | update_slb(insert_slb(C,pair(D,A)),B) = insert_slb(update_slb(C,B),pair(D,B)) # label(ax29) # label(axiom). [clausify(16)].
% 3.62/3.93 Derived: update_slb(insert_slb(A,pair(B,c3)),c4) = insert_slb(update_slb(A,c4),pair(B,c4)). [resolve(24,a,20,a)].
% 3.62/3.93 Derived: update_slb(insert_slb(A,pair(B,C)),D) = insert_slb(update_slb(A,D),pair(B,D)) | -less_than(C,D) | less_than(D,C). [resolve(24,a,22,a)].
% 3.62/3.93
% 3.62/3.93 ============================== end predicate elimination =============
% 3.62/3.93
% 3.62/3.93 Auto_denials: (non-Horn, no changes).
% 3.62/3.93
% 3.62/3.93 Term ordering decisions:
% 3.62/3.93 Function symbol KB weights: create_slb=1. bottom=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. insert_slb=1. pair=1. update_slb=1. lookup_slb=1. remove_slb=1.
% 3.62/3.93
% 3.62/3.93 ============================== end of process initial clauses ========
% 3.62/3.93
% 3.62/3.93 ============================== CLAUSES FOR SEARCH ====================
% 3.62/3.93
% 3.62/3.93 ============================== end of clauses for search =============
% 3.62/3.93
% 3.62/3.93 ============================== SEARCH ================================
% 3.62/3.93
% 3.62/3.93 % Starting search at 0.01 seconds.
% 3.62/3.93
% 3.62/3.93 ============================== PROOF =================================
% 3.62/3.93 % SZS status Theorem
% 3.62/3.93 % SZS output start Refutation
% 3.62/3.93
% 3.62/3.93 % Proof 1 at 3.10 (+ 0.02) seconds.
% 3.62/3.93 % Length of proof is 43.
% 3.62/3.93 % Level of proof is 11.
% 3.62/3.93 % Maximum clause weight is 30.000.
% 3.62/3.93 % Given clauses 338.
% 3.62/3.93
% 3.62/3.93 2 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause). [assumption].
% 3.62/3.93 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].
% 3.62/3.93 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].
% 3.62/3.93 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].
% 3.62/3.93 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].
% 3.62/3.93 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].
% 3.62/3.93 18 -(all U ((all V all W all X (pair_in_list(U,V,W) & strictly_less_than(W,X) -> pair_in_list(update_slb(U,X),V,X))) -> (all Y all Z all X1 all X2 all X3 (pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z) & strictly_less_than(Z,X1) -> pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1))))) # label(l39_co) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.62/3.93 19 -strictly_less_than(A,B) | -less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 3.62/3.93 20 strictly_less_than(c3,c4) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 22 strictly_less_than(A,B) | -less_than(A,B) | less_than(B,A) # label(stricly_smaller_definition) # label(axiom). [clausify(4)].
% 3.62/3.93 23 -pair_in_list(c1,A,B) | -strictly_less_than(B,C) | pair_in_list(update_slb(c1,C),A,C) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 24 -strictly_less_than(A,B) | update_slb(insert_slb(C,pair(D,A)),B) = insert_slb(update_slb(C,B),pair(D,B)) # label(ax29) # label(axiom). [clausify(16)].
% 3.62/3.93 28 less_than(A,B) | less_than(B,A) # label(totality) # label(axiom). [clausify(2)].
% 3.62/3.93 30 pair_in_list(insert_slb(c1,pair(c5,c6)),c2,c3) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 32 lookup_slb(insert_slb(A,pair(B,C)),B) = C # label(ax26) # label(axiom). [clausify(13)].
% 3.62/3.93 36 -pair_in_list(update_slb(insert_slb(c1,pair(c5,c6)),c4),c2,c4) # label(l39_co) # label(negated_conjecture). [clausify(18)].
% 3.62/3.93 40 pair_in_list(insert_slb(A,pair(B,C)),D,E) | -pair_in_list(A,D,E) # label(ax23) # label(axiom). [clausify(10)].
% 3.62/3.93 42 pair_in_list(insert_slb(A,pair(B,C)),D,E) | D != B | E != C # label(ax23) # label(axiom). [clausify(10)].
% 3.62/3.93 43 -pair_in_list(insert_slb(A,pair(B,C)),D,E) | pair_in_list(A,D,E) | D = B # label(ax23) # label(axiom). [clausify(10)].
% 3.62/3.93 44 -pair_in_list(insert_slb(A,pair(B,C)),D,E) | pair_in_list(A,D,E) | E = C # label(ax23) # label(axiom). [clausify(10)].
% 3.62/3.93 46 -less_than(A,B) | update_slb(insert_slb(C,pair(D,B)),A) = insert_slb(update_slb(C,A),pair(D,B)) # label(ax30) # label(axiom). [clausify(17)].
% 3.62/3.93 48 -less_than(c4,c3). [resolve(19,a,20,a)].
% 3.62/3.93 51 -pair_in_list(c1,A,B) | pair_in_list(update_slb(c1,C),A,C) | -less_than(B,C) | less_than(C,B). [resolve(23,b,22,a)].
% 3.62/3.93 52 update_slb(insert_slb(A,pair(B,c3)),c4) = insert_slb(update_slb(A,c4),pair(B,c4)). [resolve(24,a,20,a)].
% 3.62/3.93 53 update_slb(insert_slb(A,pair(B,C)),D) = insert_slb(update_slb(A,D),pair(B,D)) | -less_than(C,D) | less_than(D,C). [resolve(24,a,22,a)].
% 3.62/3.93 60 pair_in_list(insert_slb(A,pair(B,C)),D,C) | D != B. [resolve(42,c,32,a),rewrite([32(5)])].
% 3.62/3.93 61 pair_in_list(c1,c2,c3) | c5 = c2. [resolve(43,a,30,a),flip(b)].
% 3.62/3.93 62 pair_in_list(c1,c2,c3) | c6 = c3. [resolve(44,a,30,a),flip(b)].
% 3.62/3.93 70 update_slb(insert_slb(A,pair(B,C)),D) = insert_slb(update_slb(A,D),pair(B,D)) | less_than(D,C). [resolve(53,b,28,b),merge(c)].
% 3.62/3.93 84 c5 = c2 | pair_in_list(update_slb(c1,A),c2,A) | -less_than(c3,A) | less_than(A,c3). [resolve(61,a,51,a)].
% 3.62/3.93 87 c6 = c3 | pair_in_list(update_slb(c1,A),c2,A) | -less_than(c3,A) | less_than(A,c3). [resolve(62,a,51,a)].
% 3.62/3.93 140 c5 = c2 | pair_in_list(update_slb(c1,A),c2,A) | less_than(A,c3). [resolve(84,c,28,b),merge(d)].
% 3.62/3.93 141 c5 = c2 | less_than(A,c3) | pair_in_list(insert_slb(update_slb(c1,A),pair(B,C)),c2,A). [resolve(140,b,40,b)].
% 3.62/3.93 148 c6 = c3 | pair_in_list(update_slb(c1,A),c2,A) | less_than(A,c3). [resolve(87,c,28,b),merge(d)].
% 3.62/3.93 162 update_slb(insert_slb(A,pair(B,C)),D) = insert_slb(update_slb(A,D),pair(B,D)) | update_slb(insert_slb(E,pair(F,C)),D) = insert_slb(update_slb(E,D),pair(F,C)). [resolve(70,b,46,a)].
% 3.62/3.93 165 c6 = c3 | less_than(A,c3) | pair_in_list(insert_slb(update_slb(c1,A),pair(B,C)),c2,A). [resolve(148,b,40,b)].
% 3.62/3.93 629 update_slb(insert_slb(A,pair(B,c6)),c4) = insert_slb(update_slb(A,c4),pair(B,c6)) | -pair_in_list(insert_slb(update_slb(c1,c4),pair(c5,c4)),c2,c4). [para(162(a,1),36(a,1))].
% 3.62/3.93 3325 update_slb(insert_slb(A,pair(B,c6)),c4) = insert_slb(update_slb(A,c4),pair(B,c6)) | c6 = c3. [resolve(629,b,165,c),unit_del(c,48)].
% 3.62/3.93 3373 c6 = c3 | -pair_in_list(insert_slb(update_slb(c1,c4),pair(c5,c6)),c2,c4). [para(3325(a,1),36(a,1))].
% 3.62/3.93 3403 c6 = c3. [resolve(3373,b,165,c),merge(b),unit_del(b,48)].
% 3.62/3.93 3447 -pair_in_list(insert_slb(update_slb(c1,c4),pair(c5,c4)),c2,c4). [back_rewrite(36),rewrite([3403(3),52(7)])].
% 3.62/3.93 3451 c5 = c2. [resolve(3447,a,141,c),unit_del(b,48)].
% 3.62/3.93 3452 $F. [ur(60,a,3447,a),rewrite([3451(2)]),xx(a)].
% 3.62/3.93
% 3.62/3.93 % SZS output end Refutation
% 3.62/3.93 ============================== end of proof ==========================
% 3.62/3.93
% 3.62/3.93 ============================== STATISTICS ============================
% 3.62/3.93
% 3.62/3.93 Given=338. Generated=35133. Kept=3427. proofs=1.
% 3.62/3.93 Usable=248. Sos=1655. Demods=10. Limbo=1, Disabled=1558. Hints=0.
% 3.62/3.93 Megabytes=5.32.
% 3.62/3.93 User_CPU=3.10, System_CPU=0.02, Wall_clock=3.
% 3.62/3.93
% 3.62/3.93 ============================== end of statistics =====================
% 3.62/3.93
% 3.62/3.93 ============================== end of search =========================
% 3.62/3.93
% 3.62/3.93 THEOREM PROVED
% 3.62/3.93 % SZS status Theorem
% 3.62/3.93
% 3.62/3.93 Exiting with 1 proof.
% 3.62/3.93
% 3.62/3.93 Process 21800 exit (max_proofs) Tue Jun 14 20:42:16 2022
% 3.62/3.93 Prover9 interrupted
%------------------------------------------------------------------------------