TSTP Solution File: COL002-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL002-10 : TPTP v8.1.0. Released v7.5.0.
% 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 00:39:39 EDT 2022
% Result : Unsatisfiable 46.97s 47.23s
% Output : Refutation 46.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL002-10 : TPTP v8.1.0. Released v7.5.0.
% 0.06/0.12 % 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 08:29:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 46.97/47.23 ============================== Prover9 ===============================
% 46.97/47.23 Prover9 (32) version 2009-11A, November 2009.
% 46.97/47.23 Process 29161 was started by sandbox on n023.cluster.edu,
% 46.97/47.23 Tue May 31 08:29:27 2022
% 46.97/47.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29007_n023.cluster.edu".
% 46.97/47.23 ============================== end of head ===========================
% 46.97/47.23
% 46.97/47.23 ============================== INPUT =================================
% 46.97/47.23
% 46.97/47.23 % Reading from file /tmp/Prover9_29007_n023.cluster.edu
% 46.97/47.23
% 46.97/47.23 set(prolog_style_variables).
% 46.97/47.23 set(auto2).
% 46.97/47.23 % set(auto2) -> set(auto).
% 46.97/47.23 % set(auto) -> set(auto_inference).
% 46.97/47.23 % set(auto) -> set(auto_setup).
% 46.97/47.23 % set(auto_setup) -> set(predicate_elim).
% 46.97/47.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 46.97/47.23 % set(auto) -> set(auto_limits).
% 46.97/47.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 46.97/47.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 46.97/47.23 % set(auto) -> set(auto_denials).
% 46.97/47.23 % set(auto) -> set(auto_process).
% 46.97/47.23 % set(auto2) -> assign(new_constants, 1).
% 46.97/47.23 % set(auto2) -> assign(fold_denial_max, 3).
% 46.97/47.23 % set(auto2) -> assign(max_weight, "200.000").
% 46.97/47.23 % set(auto2) -> assign(max_hours, 1).
% 46.97/47.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 46.97/47.23 % set(auto2) -> assign(max_seconds, 0).
% 46.97/47.23 % set(auto2) -> assign(max_minutes, 5).
% 46.97/47.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 46.97/47.23 % set(auto2) -> set(sort_initial_sos).
% 46.97/47.23 % set(auto2) -> assign(sos_limit, -1).
% 46.97/47.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 46.97/47.23 % set(auto2) -> assign(max_megs, 400).
% 46.97/47.23 % set(auto2) -> assign(stats, some).
% 46.97/47.23 % set(auto2) -> clear(echo_input).
% 46.97/47.23 % set(auto2) -> set(quiet).
% 46.97/47.23 % set(auto2) -> clear(print_initial_clauses).
% 46.97/47.23 % set(auto2) -> clear(print_given).
% 46.97/47.23 assign(lrs_ticks,-1).
% 46.97/47.23 assign(sos_limit,10000).
% 46.97/47.23 assign(order,kbo).
% 46.97/47.23 set(lex_order_vars).
% 46.97/47.23 clear(print_given).
% 46.97/47.23
% 46.97/47.23 % formulas(sos). % not echoed (7 formulas)
% 46.97/47.23
% 46.97/47.23 ============================== end of input ==========================
% 46.97/47.23
% 46.97/47.23 % From the command line: assign(max_seconds, 300).
% 46.97/47.23
% 46.97/47.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 46.97/47.23
% 46.97/47.23 % Formulas that are not ordinary clauses:
% 46.97/47.23
% 46.97/47.23 ============================== end of process non-clausal formulas ===
% 46.97/47.23
% 46.97/47.23 ============================== PROCESS INITIAL CLAUSES ===============
% 46.97/47.23
% 46.97/47.23 ============================== PREDICATE ELIMINATION =================
% 46.97/47.23
% 46.97/47.23 ============================== end predicate elimination =============
% 46.97/47.23
% 46.97/47.23 Auto_denials:
% 46.97/47.23 % copying label prove_weak_fixed_point to answer in negative clause
% 46.97/47.23
% 46.97/47.23 Term ordering decisions:
% 46.97/47.23
% 46.97/47.23 % Assigning unary symbol fixed_point kb_weight 0 and highest precedence (10).
% 46.97/47.23 Function symbol KB weights: true=1. b=1. c=1. fixed_pt=1. i=1. s=1. apply=1. ifeq=1. fixed_point=0.
% 46.97/47.23
% 46.97/47.23 ============================== end of process initial clauses ========
% 46.97/47.23
% 46.97/47.23 ============================== CLAUSES FOR SEARCH ====================
% 46.97/47.23
% 46.97/47.23 ============================== end of clauses for search =============
% 46.97/47.23
% 46.97/47.23 ============================== SEARCH ================================
% 46.97/47.23
% 46.97/47.23 % Starting search at 0.01 seconds.
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=39.000, iters=3343
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=37.000, iters=3456
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=35.000, iters=3429
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=33.000, iters=3344
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=31.000, iters=3390
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=29.000, iters=3375
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=27.000, iters=3342
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=25.000, iters=3336
% 46.97/47.23
% 46.97/47.23 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 2.83 sec).
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=2823, wt=51.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=3800, wt=45.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=4014, wt=43.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=12706, wt=34.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=13322, wt=32.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=13334, wt=23.000
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=14231, wt=21.000
% 46.97/47.23
% 46.97/47.23 Low Water (keep): wt=23.000, iters=3333
% 46.97/47.23
% 46.97/47.23 Low Water (displace): id=61622, wt=19.000
% 46.97/47.23
% 46.97/47.23 ============================== PROOF =================================
% 46.97/47.23 % SZS status Unsatisfiable
% 46.97/47.23 % SZS output start Refutation
% 46.97/47.23
% 46.97/47.23 % Proof 1 at 45.27 (+ 0.93) seconds: prove_weak_fixed_point.
% 46.97/47.23 % Length of proof is 19.
% 46.97/47.23 % Level of proof is 6.
% 46.97/47.23 % Maximum clause weight is 29.000.
% 46.97/47.23 % Given clauses 2078.
% 46.97/47.23
% 46.97/47.23 1 apply(i,A) = A # label(i_definition) # label(axiom). [assumption].
% 46.97/47.23 2 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 46.97/47.23 3 ifeq(A,apply(fixed_pt,A),fixed_point(A),true) = true # label(weak_fixed_point) # label(axiom). [assumption].
% 46.97/47.23 4 apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)) # label(b_definition) # label(axiom). [assumption].
% 46.97/47.23 6 apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)) # label(s_definition) # label(axiom). [assumption].
% 46.97/47.23 7 fixed_point(apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i))) != true # label(prove_weak_fixed_point) # label(negated_conjecture) # answer(prove_weak_fixed_point). [assumption].
% 46.97/47.23 8 apply(apply(apply(s,i),A),B) = apply(B,apply(A,B)). [para(1(a,1),6(a,2,1))].
% 46.97/47.23 9 apply(apply(apply(s,A),i),B) = apply(apply(A,B),B). [para(1(a,1),6(a,2,2))].
% 46.97/47.23 11 apply(apply(A,apply(B,C)),apply(D,apply(B,C))) = apply(apply(apply(s,A),D),apply(B,C)). [para(6(a,1),4(a,2)),rewrite([4(7)]),flip(a)].
% 46.97/47.23 13 apply(apply(apply(s,apply(b,A)),B),C) = apply(A,apply(C,apply(B,C))). [para(6(a,2),4(a,1))].
% 46.97/47.23 29 apply(apply(apply(s,i),i),A) = apply(A,A). [para(1(a,1),8(a,2,2))].
% 46.97/47.23 78 apply(A,apply(apply(apply(s,i),i),B)) = apply(A,apply(B,B)). [para(29(a,1),4(a,2,2)),rewrite([4(9)])].
% 46.97/47.23 94 fixed_point(apply(apply(apply(s,i),i),apply(apply(s,apply(b,A)),i))) != true # answer(prove_weak_fixed_point). [para(29(a,2),7(a,1,1))].
% 46.97/47.23 107 apply(apply(apply(s,apply(b,A)),i),B) = apply(A,apply(B,B)). [para(9(a,2),4(a,1))].
% 46.97/47.23 283 ifeq(apply(A,A),apply(fixed_pt,apply(apply(apply(s,i),i),A)),fixed_point(apply(A,A)),true) = true. [para(78(a,2),3(a,1,2))].
% 46.97/47.23 519 apply(A,apply(apply(apply(s,B),B),apply(apply(s,apply(b,A)),i))) = apply(apply(apply(s,i),B),apply(apply(s,apply(b,A)),i)). [para(107(a,1),8(a,2)),rewrite([11(26)]),flip(a)].
% 46.97/47.23 887 apply(apply(apply(s,apply(b,A)),B),C) = apply(A,apply(apply(apply(s,i),B),C)). [para(8(a,2),13(a,2,2))].
% 46.97/47.23 111922 fixed_point(apply(apply(apply(s,i),i),apply(apply(s,apply(b,fixed_pt)),i))) = true. [para(519(a,1),283(a,1,2)),rewrite([887(15),519(15),887(41),519(41),2(42)])].
% 46.97/47.23 111923 $F # answer(prove_weak_fixed_point). [resolve(111922,a,94,a)].
% 46.97/47.23
% 46.97/47.23 % SZS output end Refutation
% 46.97/47.23 ============================== end of proof ==========================
% 46.97/47.23
% 46.97/47.23 ============================== STATISTICS ============================
% 46.97/47.23
% 46.97/47.23 Given=2078. Generated=1581676. Kept=111922. proofs=1.
% 46.97/47.23 Usable=1896. Sos=9999. Demods=4278. Limbo=136, Disabled=99897. Hints=0.
% 46.97/47.23 Megabytes=139.59.
% 46.97/47.23 User_CPU=45.27, System_CPU=0.93, Wall_clock=46.
% 46.97/47.23
% 46.97/47.23 ============================== end of statistics =====================
% 46.97/47.23
% 46.97/47.23 ============================== end of search =========================
% 46.97/47.23
% 46.97/47.23 THEOREM PROVED
% 46.97/47.23 % SZS status Unsatisfiable
% 46.97/47.23
% 46.97/47.23 Exiting with 1 proof.
% 46.97/47.23
% 46.97/47.23 Process 29161 exit (max_proofs) Tue May 31 08:30:13 2022
% 46.97/47.23 Prover9 interrupted
%------------------------------------------------------------------------------