TSTP Solution File: COL006-7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL006-7 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Fri Jul 15 00:39:43 EDT 2022
% Result : Unsatisfiable 215.77s 216.09s
% Output : Refutation 215.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL006-7 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.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 May 31 13:49:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 215.77/216.09 ============================== Prover9 ===============================
% 215.77/216.09 Prover9 (32) version 2009-11A, November 2009.
% 215.77/216.09 Process 2789 was started by sandbox on n023.cluster.edu,
% 215.77/216.09 Tue May 31 13:49:27 2022
% 215.77/216.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2636_n023.cluster.edu".
% 215.77/216.09 ============================== end of head ===========================
% 215.77/216.09
% 215.77/216.09 ============================== INPUT =================================
% 215.77/216.09
% 215.77/216.09 % Reading from file /tmp/Prover9_2636_n023.cluster.edu
% 215.77/216.09
% 215.77/216.09 set(prolog_style_variables).
% 215.77/216.09 set(auto2).
% 215.77/216.09 % set(auto2) -> set(auto).
% 215.77/216.09 % set(auto) -> set(auto_inference).
% 215.77/216.09 % set(auto) -> set(auto_setup).
% 215.77/216.09 % set(auto_setup) -> set(predicate_elim).
% 215.77/216.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 215.77/216.09 % set(auto) -> set(auto_limits).
% 215.77/216.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 215.77/216.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 215.77/216.09 % set(auto) -> set(auto_denials).
% 215.77/216.09 % set(auto) -> set(auto_process).
% 215.77/216.09 % set(auto2) -> assign(new_constants, 1).
% 215.77/216.09 % set(auto2) -> assign(fold_denial_max, 3).
% 215.77/216.09 % set(auto2) -> assign(max_weight, "200.000").
% 215.77/216.09 % set(auto2) -> assign(max_hours, 1).
% 215.77/216.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 215.77/216.09 % set(auto2) -> assign(max_seconds, 0).
% 215.77/216.09 % set(auto2) -> assign(max_minutes, 5).
% 215.77/216.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 215.77/216.09 % set(auto2) -> set(sort_initial_sos).
% 215.77/216.09 % set(auto2) -> assign(sos_limit, -1).
% 215.77/216.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 215.77/216.09 % set(auto2) -> assign(max_megs, 400).
% 215.77/216.09 % set(auto2) -> assign(stats, some).
% 215.77/216.09 % set(auto2) -> clear(echo_input).
% 215.77/216.09 % set(auto2) -> set(quiet).
% 215.77/216.09 % set(auto2) -> clear(print_initial_clauses).
% 215.77/216.09 % set(auto2) -> clear(print_given).
% 215.77/216.09 assign(lrs_ticks,-1).
% 215.77/216.09 assign(sos_limit,10000).
% 215.77/216.09 assign(order,kbo).
% 215.77/216.09 set(lex_order_vars).
% 215.77/216.09 clear(print_given).
% 215.77/216.09
% 215.77/216.09 % formulas(sos). % not echoed (4 formulas)
% 215.77/216.09
% 215.77/216.09 ============================== end of input ==========================
% 215.77/216.09
% 215.77/216.09 % From the command line: assign(max_seconds, 300).
% 215.77/216.09
% 215.77/216.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 215.77/216.09
% 215.77/216.09 % Formulas that are not ordinary clauses:
% 215.77/216.09
% 215.77/216.09 ============================== end of process non-clausal formulas ===
% 215.77/216.09
% 215.77/216.09 ============================== PROCESS INITIAL CLAUSES ===============
% 215.77/216.09
% 215.77/216.09 ============================== PREDICATE ELIMINATION =================
% 215.77/216.09
% 215.77/216.09 ============================== end predicate elimination =============
% 215.77/216.09
% 215.77/216.09 Auto_denials:
% 215.77/216.09 % copying label prove_strong_fixed_point to answer in negative clause
% 215.77/216.09
% 215.77/216.09 Term ordering decisions:
% 215.77/216.09 Function symbol KB weights: s=1. k=1. strong_fixed_point=1. fixed_pt=1. apply=1.
% 215.77/216.09
% 215.77/216.09 ============================== end of process initial clauses ========
% 215.77/216.09
% 215.77/216.09 ============================== CLAUSES FOR SEARCH ====================
% 215.77/216.09
% 215.77/216.09 ============================== end of clauses for search =============
% 215.77/216.09
% 215.77/216.09 ============================== SEARCH ================================
% 215.77/216.09
% 215.77/216.09 % Starting search at 0.01 seconds.
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=43.000, iters=3366
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=41.000, iters=3483
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=39.000, iters=3375
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=37.000, iters=3385
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=35.000, iters=3344
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=33.000, iters=3352
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=31.000, iters=3351
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=29.000, iters=3350
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=27.000, iters=3352
% 215.77/216.09
% 215.77/216.09 Low Water (displace): id=2896, wt=57.000
% 215.77/216.09
% 215.77/216.09 Low Water (keep): wt=25.000, iters=3335
% 215.77/216.09
% 215.77/216.09 ============================== PROOF =================================
% 215.77/216.09 % SZS status Unsatisfiable
% 215.77/216.09 % SZS output start Refutation
% 215.77/216.09
% 215.77/216.09 % Proof 1 at 214.00 (+ 1.09) seconds: prove_strong_fixed_point.
% 215.77/216.09 % Length of proof is 34.
% 215.77/216.09 % Level of proof is 10.
% 215.77/216.09 % Maximum clause weight is 65.000.
% 215.77/216.09 % Given clauses 1889.
% 215.77/216.09
% 215.77/216.09 1 apply(apply(k,A),B) = A # label(k_definition) # label(axiom). [assumption].
% 215.77/216.09 2 apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)) # label(s_definition) # label(axiom). [assumption].
% 215.77/216.09 3 strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)) # label(strong_fixed_point) # label(axiom). [assumption].
% 215.77/216.09 4 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point). [assumption].
% 215.77/216.09 5 apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt)) != apply(apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),fixed_pt) # answer(prove_strong_fixed_point). [copy(4),rewrite([3(1),3(33)]),flip(a)].
% 215.77/216.09 6 apply(apply(apply(s,k),A),B) = B. [para(2(a,2),1(a,1))].
% 215.77/216.09 7 apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)). [para(1(a,1),2(a,2,1))].
% 215.77/216.09 8 apply(apply(apply(s,A),apply(k,B)),C) = apply(apply(A,C),B). [para(1(a,1),2(a,2,2))].
% 215.77/216.09 9 apply(apply(apply(s,apply(apply(s,A),B)),C),D) = apply(apply(apply(A,D),apply(B,D)),apply(C,D)). [para(2(a,1),2(a,2,1))].
% 215.77/216.09 14 apply(apply(A,apply(B,C)),apply(apply(apply(s,D),B),C)) = apply(apply(apply(s,A),apply(D,C)),apply(B,C)). [para(2(a,2),2(a,2,2)),flip(a)].
% 215.77/216.09 15 apply(fixed_pt,apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [back_rewrite(5),rewrite([7(32),7(27),7(56),7(51)])].
% 215.77/216.09 19 apply(apply(apply(s,A),apply(apply(s,k),B)),C) = apply(apply(A,C),C). [para(6(a,1),2(a,2,2))].
% 215.77/216.09 20 apply(apply(apply(s,apply(s,k)),A),B) = apply(A,B). [para(6(a,1),2(a,2))].
% 215.77/216.09 22 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(2(a,1),15(a,1,2,1)),rewrite([6(23)])].
% 215.77/216.09 25 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(2(a,1),22(a,2,1)),rewrite([6(47)])].
% 215.77/216.09 35 apply(apply(apply(s,apply(s,apply(s,k))),A),B) = apply(B,apply(A,B)). [para(20(a,1),2(a,2))].
% 215.77/216.09 43 apply(apply(apply(s,apply(s,apply(k,A))),B),C) = apply(A,apply(C,apply(B,C))). [para(7(a,1),2(a,2))].
% 215.77/216.09 45 apply(apply(A,apply(B,C)),apply(D,apply(B,C))) = apply(apply(apply(s,A),D),apply(B,C)). [para(2(a,1),7(a,2)),rewrite([7(9)]),flip(a)].
% 215.77/216.09 51 apply(apply(apply(apply(s,s),k),A),B) = apply(apply(A,B),A). [para(2(a,2),8(a,1,1))].
% 215.77/216.09 253 apply(apply(apply(apply(s,s),apply(s,k)),A),B) = apply(apply(A,B),B). [para(2(a,2),19(a,1,1))].
% 215.77/216.09 261 apply(fixed_pt,apply(apply(apply(apply(s,s),apply(apply(s,k),A)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(19(a,2),25(a,1,2,1))].
% 215.77/216.09 301 apply(apply(apply(apply(s,s),apply(apply(s,k),A)),apply(apply(s,B),C)),D) = apply(apply(apply(s,apply(B,D)),apply(B,D)),apply(C,D)). [para(19(a,2),9(a,1,1)),rewrite([14(21)])].
% 215.77/216.09 1184 apply(apply(apply(apply(s,apply(s,s)),A),apply(s,k)),B) = apply(apply(apply(A,apply(s,k)),B),B). [para(2(a,2),253(a,1,1))].
% 215.77/216.09 1189 apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),A) = apply(A,A). [para(253(a,2),20(a,1)),rewrite([45(13)])].
% 215.77/216.09 1206 apply(apply(A,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))) = apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),A). [para(253(a,1),51(a,2)),flip(a)].
% 215.77/216.09 1338 apply(fixed_pt,apply(apply(apply(apply(s,s),apply(apply(s,k),A)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [back_rewrite(261),rewrite([1206(41)])].
% 215.77/216.09 1397 apply(apply(A,apply(apply(apply(s,B),apply(s,k)),C)),apply(apply(apply(s,B),apply(s,k)),C)) = apply(apply(apply(s,apply(s,A)),apply(B,C)),apply(apply(s,k),C)). [para(14(a,1),19(a,1)),flip(a)].
% 215.77/216.09 1406 apply(apply(apply(apply(s,A),B),C),apply(apply(B,C),apply(apply(apply(s,A),B),C))) = apply(apply(apply(s,apply(s,apply(s,apply(s,k)))),apply(A,C)),apply(B,C)). [para(14(a,1),35(a,1)),flip(a)].
% 215.77/216.09 2201 apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),apply(A,B)) = apply(apply(apply(s,A),A),B). [para(1189(a,2),2(a,2)),flip(a)].
% 215.77/216.09 3222 apply(A,apply(apply(apply(s,apply(s,apply(s,apply(s,k)))),apply(B,C)),apply(D,C))) = apply(apply(apply(s,apply(s,apply(s,apply(k,A)))),apply(B,C)),apply(D,C)). [para(43(a,1),14(a,1)),rewrite([1406(11)])].
% 215.77/216.09 118296 apply(fixed_pt,apply(apply(apply(s,apply(s,apply(s,apply(k,fixed_pt)))),apply(s,apply(s,apply(k,fixed_pt)))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(301(a,1),1338(a,1,2))].
% 215.77/216.09 168766 apply(fixed_pt,apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(2201(a,2),118296(a,1,2)),rewrite([45(29)])].
% 215.77/216.09 169055 apply(apply(apply(s,apply(s,apply(s,apply(k,fixed_pt)))),apply(s,apply(s,apply(k,fixed_pt)))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(1184(a,1),168766(a,1,2)),rewrite([1397(34),3222(29)])].
% 215.77/216.09 169072 $F # answer(prove_strong_fixed_point). [para(2(a,1),169055(a,1)),rewrite([45(17),45(30),45(27),1206(17)]),xx(a)].
% 215.77/216.09
% 215.77/216.09 % SZS output end Refutation
% 215.77/216.09 ============================== end of proof ==========================
% 215.77/216.09
% 215.77/216.09 ============================== STATISTICS ============================
% 215.77/216.09
% 215.77/216.09 Given=1889. Generated=1619286. Kept=169070. proofs=1.
% 215.77/216.09 Usable=1798. Sos=9999. Demods=4906. Limbo=0, Disabled=157277. Hints=0.
% 215.77/216.09 Megabytes=316.59.
% 215.77/216.09 User_CPU=214.00, System_CPU=1.09, Wall_clock=215.
% 215.77/216.09
% 215.77/216.09 ============================== end of statistics =====================
% 215.77/216.09
% 215.77/216.09 ============================== end of search =========================
% 215.77/216.09
% 215.77/216.09 THEOREM PROVED
% 215.77/216.09 % SZS status Unsatisfiable
% 215.77/216.09
% 215.77/216.09 Exiting with 1 proof.
% 215.77/216.09
% 215.77/216.09 Process 2789 exit (max_proofs) Tue May 31 13:53:02 2022
% 215.77/216.09 Prover9 interrupted
%------------------------------------------------------------------------------