TSTP Solution File: COL006-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 00:39:42 EDT 2022
% Result : Unsatisfiable 3.70s 4.01s
% Output : Refutation 3.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.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 13:56:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.70/4.01 ============================== Prover9 ===============================
% 3.70/4.01 Prover9 (32) version 2009-11A, November 2009.
% 3.70/4.01 Process 19117 was started by sandbox on n020.cluster.edu,
% 3.70/4.01 Tue May 31 13:56:54 2022
% 3.70/4.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18963_n020.cluster.edu".
% 3.70/4.01 ============================== end of head ===========================
% 3.70/4.01
% 3.70/4.01 ============================== INPUT =================================
% 3.70/4.01
% 3.70/4.01 % Reading from file /tmp/Prover9_18963_n020.cluster.edu
% 3.70/4.01
% 3.70/4.01 set(prolog_style_variables).
% 3.70/4.01 set(auto2).
% 3.70/4.01 % set(auto2) -> set(auto).
% 3.70/4.01 % set(auto) -> set(auto_inference).
% 3.70/4.01 % set(auto) -> set(auto_setup).
% 3.70/4.01 % set(auto_setup) -> set(predicate_elim).
% 3.70/4.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.70/4.01 % set(auto) -> set(auto_limits).
% 3.70/4.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.70/4.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.70/4.01 % set(auto) -> set(auto_denials).
% 3.70/4.01 % set(auto) -> set(auto_process).
% 3.70/4.01 % set(auto2) -> assign(new_constants, 1).
% 3.70/4.01 % set(auto2) -> assign(fold_denial_max, 3).
% 3.70/4.01 % set(auto2) -> assign(max_weight, "200.000").
% 3.70/4.01 % set(auto2) -> assign(max_hours, 1).
% 3.70/4.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.70/4.01 % set(auto2) -> assign(max_seconds, 0).
% 3.70/4.01 % set(auto2) -> assign(max_minutes, 5).
% 3.70/4.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.70/4.01 % set(auto2) -> set(sort_initial_sos).
% 3.70/4.01 % set(auto2) -> assign(sos_limit, -1).
% 3.70/4.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.70/4.01 % set(auto2) -> assign(max_megs, 400).
% 3.70/4.01 % set(auto2) -> assign(stats, some).
% 3.70/4.01 % set(auto2) -> clear(echo_input).
% 3.70/4.01 % set(auto2) -> set(quiet).
% 3.70/4.01 % set(auto2) -> clear(print_initial_clauses).
% 3.70/4.01 % set(auto2) -> clear(print_given).
% 3.70/4.01 assign(lrs_ticks,-1).
% 3.70/4.01 assign(sos_limit,10000).
% 3.70/4.01 assign(order,kbo).
% 3.70/4.01 set(lex_order_vars).
% 3.70/4.01 clear(print_given).
% 3.70/4.01
% 3.70/4.01 % formulas(sos). % not echoed (4 formulas)
% 3.70/4.01
% 3.70/4.01 ============================== end of input ==========================
% 3.70/4.01
% 3.70/4.01 % From the command line: assign(max_seconds, 300).
% 3.70/4.01
% 3.70/4.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.70/4.01
% 3.70/4.01 % Formulas that are not ordinary clauses:
% 3.70/4.01
% 3.70/4.01 ============================== end of process non-clausal formulas ===
% 3.70/4.01
% 3.70/4.01 ============================== PROCESS INITIAL CLAUSES ===============
% 3.70/4.01
% 3.70/4.01 ============================== PREDICATE ELIMINATION =================
% 3.70/4.01
% 3.70/4.01 ============================== end predicate elimination =============
% 3.70/4.01
% 3.70/4.01 Auto_denials:
% 3.70/4.01 % copying label prove_strong_fixed_point to answer in negative clause
% 3.70/4.01
% 3.70/4.01 Term ordering decisions:
% 3.70/4.01 Function symbol KB weights: fixed_pt=1. k=1. s=1. apply=1.
% 3.70/4.01
% 3.70/4.01 ============================== end of process initial clauses ========
% 3.70/4.01
% 3.70/4.01 ============================== CLAUSES FOR SEARCH ====================
% 3.70/4.01
% 3.70/4.01 ============================== end of clauses for search =============
% 3.70/4.01
% 3.70/4.01 ============================== SEARCH ================================
% 3.70/4.01
% 3.70/4.01 % Starting search at 0.01 seconds.
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=47.000, iters=3394
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=45.000, iters=3407
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=43.000, iters=3525
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=41.000, iters=3435
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=39.000, iters=3480
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=37.000, iters=3345
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=35.000, iters=3462
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=33.000, iters=3380
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=31.000, iters=3349
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=29.000, iters=3345
% 3.70/4.01
% 3.70/4.01 Low Water (keep): wt=27.000, iters=3348
% 3.70/4.01
% 3.70/4.01 ============================== PROOF =================================
% 3.70/4.01 % SZS status Unsatisfiable
% 3.70/4.01 % SZS output start Refutation
% 3.70/4.01
% 3.70/4.01 % Proof 1 at 3.01 (+ 0.05) seconds: prove_strong_fixed_point.
% 3.70/4.01 % Length of proof is 25.
% 3.70/4.01 % Level of proof is 7.
% 3.70/4.01 % Maximum clause weight is 57.000.
% 3.70/4.01 % Given clauses 391.
% 3.70/4.01
% 3.70/4.01 1 apply(apply(k,A),B) = A # label(k_definition) # label(axiom). [assumption].
% 3.70/4.01 2 apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)) # label(s_definition) # label(axiom). [assumption].
% 3.70/4.01 3 -fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point). [assumption].
% 3.70/4.01 4 apply(A,fixed_pt) != apply(fixed_pt,apply(A,fixed_pt)) | fixed_point(A) # label(strong_fixed_point) # label(axiom). [assumption].
% 3.70/4.01 5 apply(fixed_pt,apply(A,fixed_pt)) != apply(A,fixed_pt) | fixed_point(A). [copy(4),flip(a)].
% 3.70/4.01 6 apply(apply(apply(s,k),A),B) = B. [para(2(a,2),1(a,1))].
% 3.70/4.01 7 apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)). [para(1(a,1),2(a,2,1))].
% 3.70/4.01 8 apply(apply(apply(s,A),apply(k,B)),C) = apply(apply(A,C),B). [para(1(a,1),2(a,2,2))].
% 3.70/4.01 15 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) # answer(prove_strong_fixed_point). [ur(5,b,3,a),rewrite([7(40),7(35),7(30),7(68),7(63),7(58)])].
% 3.70/4.01 19 apply(apply(apply(s,apply(apply(s,k),A)),B),C) = apply(C,apply(B,C)). [para(6(a,1),2(a,2,1))].
% 3.70/4.01 20 apply(apply(apply(s,A),apply(apply(s,k),B)),C) = apply(apply(A,C),C). [para(6(a,1),2(a,2,2))].
% 3.70/4.01 22 apply(apply(apply(apply(s,s),A),k),B) = B. [para(2(a,2),6(a,1,1))].
% 3.70/4.01 27 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) # answer(prove_strong_fixed_point). [para(2(a,1),15(a,2)),rewrite([6(48),6(61)])].
% 3.70/4.01 37 apply(apply(apply(s,A),apply(apply(apply(s,s),B),k)),C) = apply(apply(A,C),C). [para(22(a,1),2(a,2,2))].
% 3.70/4.01 48 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))].
% 3.70/4.01 50 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)].
% 3.70/4.01 53 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(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). [back_rewrite(27),rewrite([50(56)])].
% 3.70/4.01 64 apply(apply(apply(apply(s,s),k),A),B) = apply(apply(A,B),A). [para(2(a,2),8(a,1,1))].
% 3.70/4.01 379 apply(apply(apply(apply(s,s),apply(s,k)),A),B) = apply(apply(A,B),B). [para(2(a,2),20(a,1,1))].
% 3.70/4.01 1765 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(379(a,1),64(a,2)),flip(a)].
% 3.70/4.01 1921 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),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). [back_rewrite(53),rewrite([1765(46)])].
% 3.70/4.01 2463 apply(apply(apply(s,A),apply(apply(apply(s,s),B),k)),C) = apply(apply(apply(apply(s,s),apply(s,k)),A),C). [para(37(a,2),379(a,2)),flip(a)].
% 3.70/4.01 4570 apply(A,apply(apply(apply(s,apply(apply(s,k),B)),C),D)) = apply(apply(apply(s,apply(s,apply(k,A))),C),D). [para(19(a,2),48(a,2,2)),flip(a)].
% 3.70/4.01 4918 apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),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). [back_rewrite(1921),rewrite([4570(29)])].
% 3.70/4.01 11674 $F # answer(prove_strong_fixed_point). [para(20(a,2),4918(a,1,1,2)),rewrite([2463(32),50(27),1765(17)]),xx(a)].
% 3.70/4.01
% 3.70/4.01 % SZS output end Refutation
% 3.70/4.01 ============================== end of proof ==========================
% 3.70/4.01
% 3.70/4.01 ============================== STATISTICS ============================
% 3.70/4.01
% 3.70/4.01 Given=391. Generated=61689. Kept=11672. proofs=1.
% 3.70/4.01 Usable=345. Sos=9117. Demods=2691. Limbo=2, Disabled=2212. Hints=0.
% 3.70/4.01 Megabytes=21.47.
% 3.70/4.01 User_CPU=3.01, System_CPU=0.05, Wall_clock=3.
% 3.70/4.01
% 3.70/4.01 ============================== end of statistics =====================
% 3.70/4.01
% 3.70/4.01 ============================== end of search =========================
% 3.70/4.01
% 3.70/4.01 THEOREM PROVED
% 3.70/4.01 % SZS status Unsatisfiable
% 3.70/4.01
% 3.70/4.01 Exiting with 1 proof.
% 3.70/4.01
% 3.70/4.01 Process 19117 exit (max_proofs) Tue May 31 13:56:57 2022
% 3.70/4.01 Prover9 interrupted
%------------------------------------------------------------------------------