TSTP Solution File: COL006-5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL006-5 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 1.30s 1.60s
% Output : Refutation 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL006-5 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 08:56:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.30/1.60 ============================== Prover9 ===============================
% 1.30/1.60 Prover9 (32) version 2009-11A, November 2009.
% 1.30/1.60 Process 3655 was started by sandbox on n018.cluster.edu,
% 1.30/1.60 Tue May 31 08:56:13 2022
% 1.30/1.60 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3502_n018.cluster.edu".
% 1.30/1.60 ============================== end of head ===========================
% 1.30/1.60
% 1.30/1.60 ============================== INPUT =================================
% 1.30/1.60
% 1.30/1.60 % Reading from file /tmp/Prover9_3502_n018.cluster.edu
% 1.30/1.60
% 1.30/1.60 set(prolog_style_variables).
% 1.30/1.60 set(auto2).
% 1.30/1.60 % set(auto2) -> set(auto).
% 1.30/1.60 % set(auto) -> set(auto_inference).
% 1.30/1.60 % set(auto) -> set(auto_setup).
% 1.30/1.60 % set(auto_setup) -> set(predicate_elim).
% 1.30/1.60 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.30/1.60 % set(auto) -> set(auto_limits).
% 1.30/1.60 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.30/1.60 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.30/1.60 % set(auto) -> set(auto_denials).
% 1.30/1.60 % set(auto) -> set(auto_process).
% 1.30/1.60 % set(auto2) -> assign(new_constants, 1).
% 1.30/1.60 % set(auto2) -> assign(fold_denial_max, 3).
% 1.30/1.60 % set(auto2) -> assign(max_weight, "200.000").
% 1.30/1.60 % set(auto2) -> assign(max_hours, 1).
% 1.30/1.60 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.30/1.60 % set(auto2) -> assign(max_seconds, 0).
% 1.30/1.60 % set(auto2) -> assign(max_minutes, 5).
% 1.30/1.60 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.30/1.60 % set(auto2) -> set(sort_initial_sos).
% 1.30/1.60 % set(auto2) -> assign(sos_limit, -1).
% 1.30/1.60 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.30/1.60 % set(auto2) -> assign(max_megs, 400).
% 1.30/1.60 % set(auto2) -> assign(stats, some).
% 1.30/1.60 % set(auto2) -> clear(echo_input).
% 1.30/1.60 % set(auto2) -> set(quiet).
% 1.30/1.60 % set(auto2) -> clear(print_initial_clauses).
% 1.30/1.60 % set(auto2) -> clear(print_given).
% 1.30/1.60 assign(lrs_ticks,-1).
% 1.30/1.60 assign(sos_limit,10000).
% 1.30/1.60 assign(order,kbo).
% 1.30/1.60 set(lex_order_vars).
% 1.30/1.60 clear(print_given).
% 1.30/1.60
% 1.30/1.60 % formulas(sos). % not echoed (4 formulas)
% 1.30/1.60
% 1.30/1.60 ============================== end of input ==========================
% 1.30/1.60
% 1.30/1.60 % From the command line: assign(max_seconds, 300).
% 1.30/1.60
% 1.30/1.60 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.30/1.60
% 1.30/1.60 % Formulas that are not ordinary clauses:
% 1.30/1.60
% 1.30/1.60 ============================== end of process non-clausal formulas ===
% 1.30/1.60
% 1.30/1.60 ============================== PROCESS INITIAL CLAUSES ===============
% 1.30/1.60
% 1.30/1.60 ============================== PREDICATE ELIMINATION =================
% 1.30/1.60
% 1.30/1.60 ============================== end predicate elimination =============
% 1.30/1.60
% 1.30/1.60 Auto_denials:
% 1.30/1.60 % copying label prove_strong_fixed_point to answer in negative clause
% 1.30/1.60
% 1.30/1.60 Term ordering decisions:
% 1.30/1.60 Function symbol KB weights: s=1. k=1. strong_fixed_point=1. fixed_pt=1. apply=1.
% 1.30/1.60
% 1.30/1.60 ============================== end of process initial clauses ========
% 1.30/1.60
% 1.30/1.60 ============================== CLAUSES FOR SEARCH ====================
% 1.30/1.60
% 1.30/1.60 ============================== end of clauses for search =============
% 1.30/1.60
% 1.30/1.60 ============================== SEARCH ================================
% 1.30/1.60
% 1.30/1.60 % Starting search at 0.01 seconds.
% 1.30/1.60
% 1.30/1.60 ============================== PROOF =================================
% 1.30/1.60 % SZS status Unsatisfiable
% 1.30/1.60 % SZS output start Refutation
% 1.30/1.60
% 1.30/1.60 % Proof 1 at 0.62 (+ 0.01) seconds: prove_strong_fixed_point.
% 1.30/1.60 % Length of proof is 38.
% 1.30/1.60 % Level of proof is 11.
% 1.30/1.60 % Maximum clause weight is 81.000.
% 1.30/1.60 % Given clauses 114.
% 1.30/1.60
% 1.30/1.60 1 apply(apply(k,A),B) = A # label(k_definition) # label(axiom). [assumption].
% 1.30/1.60 2 apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)) # label(s_definition) # label(axiom). [assumption].
% 1.30/1.60 3 strong_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(strong_fixed_point) # label(axiom). [assumption].
% 1.30/1.60 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].
% 1.30/1.60 5 apply(fixed_pt,apply(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))),fixed_pt)) != apply(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))),fixed_pt) # answer(prove_strong_fixed_point). [copy(4),rewrite([3(1),3(41)]),flip(a)].
% 1.30/1.60 6 apply(apply(apply(s,k),A),B) = B. [para(2(a,2),1(a,1))].
% 1.30/1.60 7 apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)). [para(1(a,1),2(a,2,1))].
% 1.30/1.60 8 apply(apply(apply(s,A),apply(k,B)),C) = apply(apply(A,C),B). [para(1(a,1),2(a,2,2))].
% 1.30/1.60 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))].
% 1.30/1.60 12 apply(apply(apply(apply(s,s),A),B),C) = apply(apply(B,C),apply(apply(A,B),C)). [para(2(a,2),2(a,1,1))].
% 1.30/1.60 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)].
% 1.30/1.60 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). [back_rewrite(5),rewrite([7(40),7(35),7(30),7(68),7(63),7(58)])].
% 1.30/1.60 17 apply(apply(apply(s,A),apply(apply(s,k),B)),C) = apply(apply(A,C),C). [para(6(a,1),2(a,2,2))].
% 1.30/1.60 18 apply(apply(apply(s,apply(s,k)),A),B) = apply(A,B). [para(6(a,1),2(a,2))].
% 1.30/1.60 19 apply(apply(apply(apply(s,s),A),k),B) = B. [para(2(a,2),6(a,1,1))].
% 1.30/1.60 23 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)])].
% 1.30/1.60 32 apply(apply(apply(s,apply(apply(apply(s,s),A),k)),B),C) = apply(C,apply(B,C)). [para(19(a,1),2(a,2,1))].
% 1.30/1.60 38 apply(apply(apply(s,apply(s,apply(s,k))),A),B) = apply(B,apply(A,B)). [para(18(a,1),2(a,2))].
% 1.30/1.60 46 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))].
% 1.30/1.60 48 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)].
% 1.30/1.60 50 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(23),rewrite([48(56)])].
% 1.30/1.60 55 apply(apply(apply(apply(s,s),k),A),B) = apply(apply(A,B),A). [para(2(a,2),8(a,1,1))].
% 1.30/1.60 162 apply(apply(apply(A,B),apply(C,B)),apply(apply(D,apply(apply(s,A),C)),B)) = apply(apply(apply(apply(s,s),D),apply(apply(s,A),C)),B). [para(2(a,2),9(a,1,1)),flip(a)].
% 1.30/1.60 259 apply(apply(apply(apply(s,s),apply(s,k)),A),B) = apply(apply(A,B),B). [para(2(a,2),17(a,1,1))].
% 1.30/1.60 291 apply(fixed_pt,apply(apply(apply(s,apply(apply(apply(s,s),apply(apply(s,k),A)),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). [para(17(a,2),50(a,1,2,1,1,2))].
% 1.30/1.60 324 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(17(a,2),9(a,1,1)),rewrite([14(21)])].
% 1.30/1.60 676 apply(apply(apply(apply(apply(s,s),A),s),apply(apply(s,B),C)),D) = apply(apply(apply(apply(s,s),apply(A,s)),apply(apply(s,B),C)),D). [para(12(a,2),9(a,1,1)),rewrite([162(22)])].
% 1.30/1.60 1216 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(259(a,1),55(a,2)),flip(a)].
% 1.30/1.60 1339 apply(fixed_pt,apply(apply(apply(s,apply(apply(apply(s,s),apply(apply(s,k),A)),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(291),rewrite([1216(51)])].
% 1.30/1.60 1404 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),17(a,1)),flip(a)].
% 1.30/1.60 1413 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),38(a,1)),flip(a)].
% 1.30/1.60 1699 apply(apply(apply(s,apply(apply(apply(s,s),A),k)),B),C) = apply(apply(apply(s,apply(s,apply(s,k))),B),C). [para(32(a,2),38(a,2)),flip(a)].
% 1.30/1.60 1727 apply(fixed_pt,apply(apply(apply(s,apply(s,apply(s,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(1339),rewrite([1699(33)])].
% 1.30/1.60 2564 apply(fixed_pt,apply(apply(apply(s,apply(s,apply(s,apply(s,k)))),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(2(a,1),1727(a,1,2)),rewrite([6(39),1404(34)])].
% 1.30/1.60 2962 apply(fixed_pt,apply(apply(apply(s,apply(s,apply(s,apply(s,k)))),apply(s,apply(s,apply(k,fixed_pt)))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(apply(s,s),apply(apply(s,k),s)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [para(55(a,1),2564(a,2,1)),rewrite([676(52)])].
% 1.30/1.60 3209 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(46(a,1),14(a,1)),rewrite([1413(11)])].
% 1.30/1.60 3370 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(s,s),apply(apply(s,k),s)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) # answer(prove_strong_fixed_point). [back_rewrite(2962),rewrite([3209(29)])].
% 1.30/1.60 3371 $F # answer(prove_strong_fixed_point). [resolve(3370,a,324,a(flip))].
% 1.30/1.60
% 1.30/1.60 % SZS output end Refutation
% 1.30/1.60 ============================== end of proof ==========================
% 1.30/1.60
% 1.30/1.60 ============================== STATISTICS ============================
% 1.30/1.60
% 1.30/1.60 Given=114. Generated=8478. Kept=3369. proofs=1.
% 1.30/1.60 Usable=83. Sos=2280. Demods=994. Limbo=161, Disabled=848. Hints=0.
% 1.30/1.60 Megabytes=5.41.
% 1.30/1.60 User_CPU=0.62, System_CPU=0.01, Wall_clock=1.
% 1.30/1.60
% 1.30/1.60 ============================== end of statistics =====================
% 1.30/1.60
% 1.30/1.60 ============================== end of search =========================
% 1.30/1.60
% 1.30/1.60 THEOREM PROVED
% 1.30/1.60 % SZS status Unsatisfiable
% 1.30/1.60
% 1.30/1.60 Exiting with 1 proof.
% 1.30/1.60
% 1.30/1.60 Process 3655 exit (max_proofs) Tue May 31 08:56:14 2022
% 1.30/1.60 Prover9 interrupted
%------------------------------------------------------------------------------