TSTP Solution File: COL044-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL044-7 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 00:39:49 EDT 2022
% Result : Unsatisfiable 0.82s 1.12s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL044-7 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.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 07:10:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/1.12 ============================== Prover9 ===============================
% 0.82/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.12 Process 26731 was started by sandbox on n017.cluster.edu,
% 0.82/1.12 Tue May 31 07:10:26 2022
% 0.82/1.12 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26507_n017.cluster.edu".
% 0.82/1.12 ============================== end of head ===========================
% 0.82/1.12
% 0.82/1.12 ============================== INPUT =================================
% 0.82/1.12
% 0.82/1.12 % Reading from file /tmp/Prover9_26507_n017.cluster.edu
% 0.82/1.12
% 0.82/1.12 set(prolog_style_variables).
% 0.82/1.12 set(auto2).
% 0.82/1.12 % set(auto2) -> set(auto).
% 0.82/1.12 % set(auto) -> set(auto_inference).
% 0.82/1.12 % set(auto) -> set(auto_setup).
% 0.82/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.12 % set(auto) -> set(auto_limits).
% 0.82/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.12 % set(auto) -> set(auto_denials).
% 0.82/1.12 % set(auto) -> set(auto_process).
% 0.82/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.12 % set(auto2) -> assign(stats, some).
% 0.82/1.12 % set(auto2) -> clear(echo_input).
% 0.82/1.12 % set(auto2) -> set(quiet).
% 0.82/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.12 % set(auto2) -> clear(print_given).
% 0.82/1.12 assign(lrs_ticks,-1).
% 0.82/1.12 assign(sos_limit,10000).
% 0.82/1.12 assign(order,kbo).
% 0.82/1.12 set(lex_order_vars).
% 0.82/1.12 clear(print_given).
% 0.82/1.12
% 0.82/1.12 % formulas(sos). % not echoed (4 formulas)
% 0.82/1.12
% 0.82/1.12 ============================== end of input ==========================
% 0.82/1.12
% 0.82/1.12 % From the command line: assign(max_seconds, 300).
% 0.82/1.12
% 0.82/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.12
% 0.82/1.12 % Formulas that are not ordinary clauses:
% 0.82/1.12
% 0.82/1.12 ============================== end of process non-clausal formulas ===
% 0.82/1.12
% 0.82/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.12
% 0.82/1.12 ============================== PREDICATE ELIMINATION =================
% 0.82/1.12
% 0.82/1.12 ============================== end predicate elimination =============
% 0.82/1.12
% 0.82/1.12 Auto_denials:
% 0.82/1.12 % copying label prove_strong_fixed_point to answer in negative clause
% 0.82/1.12
% 0.82/1.12 Term ordering decisions:
% 0.82/1.12 Function symbol KB weights: b=1. n=1. strong_fixed_point=1. fixed_pt=1. apply=1.
% 0.82/1.12
% 0.82/1.12 ============================== end of process initial clauses ========
% 0.82/1.12
% 0.82/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.12
% 0.82/1.12 ============================== end of clauses for search =============
% 0.82/1.12
% 0.82/1.12 ============================== SEARCH ================================
% 0.82/1.12
% 0.82/1.12 % Starting search at 0.01 seconds.
% 0.82/1.12
% 0.82/1.12 ============================== PROOF =================================
% 0.82/1.12 % SZS status Unsatisfiable
% 0.82/1.12 % SZS output start Refutation
% 0.82/1.12
% 0.82/1.12 % Proof 1 at 0.14 (+ 0.00) seconds: prove_strong_fixed_point.
% 0.82/1.12 % Length of proof is 13.
% 0.82/1.12 % Level of proof is 6.
% 0.82/1.12 % Maximum clause weight is 49.000.
% 0.82/1.12 % Given clauses 34.
% 0.82/1.12
% 0.82/1.12 1 apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)) # label(b_definition) # label(axiom). [assumption].
% 0.82/1.12 2 apply(apply(apply(n,A),B),C) = apply(apply(apply(A,C),B),C) # label(n_definition) # label(axiom). [assumption].
% 0.82/1.12 3 strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b) # label(strong_fixed_point) # label(axiom). [assumption].
% 0.82/1.12 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].
% 0.82/1.12 5 apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt))) # answer(prove_strong_fixed_point). [copy(4),rewrite([3(1),1(27),1(25),3(25),1(51),1(49)]),flip(a)].
% 0.82/1.12 10 apply(apply(apply(n,apply(b,A)),B),C) = apply(apply(A,apply(C,B)),C). [para(1(a,1),2(a,2,1))].
% 0.82/1.12 12 apply(apply(apply(apply(A,B),C),B),C) = apply(apply(apply(n,apply(n,A)),B),C). [para(2(a,1),2(a,2,1)),flip(a)].
% 0.82/1.12 16 apply(fixed_pt,apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt))) # answer(prove_strong_fixed_point). [para(2(a,1),5(a,1,2)),rewrite([1(20),1(26)])].
% 0.82/1.12 38 apply(fixed_pt,apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point). [para(2(a,1),16(a,2)),rewrite([1(44),1(50)])].
% 0.82/1.12 96 apply(apply(apply(n,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(C,B),C)). [para(10(a,2),1(a,1))].
% 0.82/1.12 432 apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point). [para(12(a,2),38(a,1,2,1)),rewrite([1(12),1(18)])].
% 0.82/1.12 770 apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point). [para(12(a,2),432(a,2,1)),rewrite([1(36),1(42)])].
% 0.82/1.12 771 $F # answer(prove_strong_fixed_point). [resolve(770,a,96,a(flip))].
% 0.82/1.12
% 0.82/1.12 % SZS output end Refutation
% 0.82/1.12 ============================== end of proof ==========================
% 0.82/1.12
% 0.82/1.12 ============================== STATISTICS ============================
% 0.82/1.12
% 0.82/1.12 Given=34. Generated=2121. Kept=769. proofs=1.
% 0.82/1.12 Usable=33. Sos=686. Demods=163. Limbo=1, Disabled=52. Hints=0.
% 0.82/1.12 Megabytes=1.25.
% 0.82/1.12 User_CPU=0.14, System_CPU=0.00, Wall_clock=0.
% 0.82/1.12
% 0.82/1.12 ============================== end of statistics =====================
% 0.82/1.12
% 0.82/1.12 ============================== end of search =========================
% 0.82/1.12
% 0.82/1.12 THEOREM PROVED
% 0.82/1.12 % SZS status Unsatisfiable
% 0.82/1.12
% 0.82/1.12 Exiting with 1 proof.
% 0.82/1.12
% 0.82/1.12 Process 26731 exit (max_proofs) Tue May 31 07:10:26 2022
% 0.82/1.12 Prover9 interrupted
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