TSTP Solution File: COL006-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 0.45s 1.00s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.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 15:23:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.00 ============================== Prover9 ===============================
% 0.45/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.00 Process 22062 was started by sandbox2 on n022.cluster.edu,
% 0.45/1.00 Tue May 31 15:23:23 2022
% 0.45/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21907_n022.cluster.edu".
% 0.45/1.00 ============================== end of head ===========================
% 0.45/1.00
% 0.45/1.00 ============================== INPUT =================================
% 0.45/1.00
% 0.45/1.00 % Reading from file /tmp/Prover9_21907_n022.cluster.edu
% 0.45/1.00
% 0.45/1.00 set(prolog_style_variables).
% 0.45/1.00 set(auto2).
% 0.45/1.00 % set(auto2) -> set(auto).
% 0.45/1.00 % set(auto) -> set(auto_inference).
% 0.45/1.00 % set(auto) -> set(auto_setup).
% 0.45/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.00 % set(auto) -> set(auto_limits).
% 0.45/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.00 % set(auto) -> set(auto_denials).
% 0.45/1.00 % set(auto) -> set(auto_process).
% 0.45/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.00 % set(auto2) -> assign(stats, some).
% 0.45/1.00 % set(auto2) -> clear(echo_input).
% 0.45/1.00 % set(auto2) -> set(quiet).
% 0.45/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.00 % set(auto2) -> clear(print_given).
% 0.45/1.00 assign(lrs_ticks,-1).
% 0.45/1.00 assign(sos_limit,10000).
% 0.45/1.00 assign(order,kbo).
% 0.45/1.00 set(lex_order_vars).
% 0.45/1.00 clear(print_given).
% 0.45/1.00
% 0.45/1.00 % formulas(sos). % not echoed (4 formulas)
% 0.45/1.00
% 0.45/1.00 ============================== end of input ==========================
% 0.45/1.00
% 0.45/1.00 % From the command line: assign(max_seconds, 300).
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.00
% 0.45/1.00 % Formulas that are not ordinary clauses:
% 0.45/1.00
% 0.45/1.00 ============================== end of process non-clausal formulas ===
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.00
% 0.45/1.00 ============================== PREDICATE ELIMINATION =================
% 0.45/1.00
% 0.45/1.00 ============================== end predicate elimination =============
% 0.45/1.00
% 0.45/1.00 Auto_denials:
% 0.45/1.00 % copying label prove_strong_fixed_point to answer in negative clause
% 0.45/1.00
% 0.45/1.00 Term ordering decisions:
% 0.45/1.00 Function symbol KB weights: fixed_pt=1. k=1. s=1. apply=1.
% 0.45/1.00
% 0.45/1.00 ============================== end of process initial clauses ========
% 0.45/1.00
% 0.45/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.00
% 0.45/1.00 ============================== end of clauses for search =============
% 0.45/1.00
% 0.45/1.00 ============================== SEARCH ================================
% 0.45/1.00
% 0.45/1.00 % Starting search at 0.01 seconds.
% 0.45/1.00
% 0.45/1.00 ============================== PROOF =================================
% 0.45/1.00 % SZS status Unsatisfiable
% 0.45/1.00 % SZS output start Refutation
% 0.45/1.00
% 0.45/1.00 % Proof 1 at 0.01 (+ 0.00) seconds: prove_strong_fixed_point.
% 0.45/1.00 % Length of proof is 13.
% 0.45/1.00 % Level of proof is 4.
% 0.45/1.00 % Maximum clause weight is 69.000.
% 0.45/1.00 % Given clauses 15.
% 0.45/1.00
% 0.45/1.00 1 apply(apply(k,A),B) = A # label(k_definition) # label(axiom). [assumption].
% 0.45/1.00 2 apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)) # label(s_definition) # label(axiom). [assumption].
% 0.45/1.00 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(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point). [assumption].
% 0.45/1.00 4 apply(A,fixed_pt) != apply(fixed_pt,apply(A,fixed_pt)) | fixed_point(A) # label(strong_fixed_point) # label(axiom). [assumption].
% 0.45/1.00 5 apply(fixed_pt,apply(A,fixed_pt)) != apply(A,fixed_pt) | fixed_point(A). [copy(4),flip(a)].
% 0.45/1.00 6 apply(apply(apply(s,k),A),B) = B. [para(2(a,2),1(a,1))].
% 0.45/1.00 7 apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)). [para(1(a,1),2(a,2,1))].
% 0.45/1.00 8 apply(apply(apply(s,A),apply(k,B)),C) = apply(apply(A,C),B). [para(1(a,1),2(a,2,2))].
% 0.45/1.00 16 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) # answer(prove_strong_fixed_point). [ur(5,b,3,a),rewrite([7(46),8(41),7(23),7(80),8(75),7(57)])].
% 0.45/1.00 42 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))].
% 0.45/1.00 44 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)].
% 0.45/1.00 48 apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))) # answer(prove_strong_fixed_point). [para(2(a,1),16(a,2)),rewrite([6(60),6(79),44(74)])].
% 0.45/1.00 49 $F # answer(prove_strong_fixed_point). [resolve(48,a,42,a(flip))].
% 0.45/1.00
% 0.45/1.00 % SZS output end Refutation
% 0.45/1.00 ============================== end of proof ==========================
% 0.45/1.00
% 0.45/1.00 ============================== STATISTICS ============================
% 0.45/1.00
% 0.45/1.00 Given=15. Generated=96. Kept=47. proofs=1.
% 0.45/1.00 Usable=14. Sos=29. Demods=12. Limbo=1, Disabled=6. Hints=0.
% 0.45/1.00 Megabytes=0.15.
% 0.45/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.45/1.00
% 0.45/1.00 ============================== end of statistics =====================
% 0.45/1.00
% 0.45/1.00 ============================== end of search =========================
% 0.45/1.00
% 0.45/1.00 THEOREM PROVED
% 0.45/1.00 % SZS status Unsatisfiable
% 0.45/1.00
% 0.45/1.00 Exiting with 1 proof.
% 0.45/1.00
% 0.45/1.00 Process 22062 exit (max_proofs) Tue May 31 15:23:23 2022
% 0.45/1.00 Prover9 interrupted
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