TSTP Solution File: COL042-5 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL042-5 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 00:39:47 EDT 2022
% Result : Unsatisfiable 1.35s 1.65s
% Output : Refutation 1.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL042-5 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 08:26:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.35/1.65 ============================== Prover9 ===============================
% 1.35/1.65 Prover9 (32) version 2009-11A, November 2009.
% 1.35/1.65 Process 2740 was started by sandbox2 on n025.cluster.edu,
% 1.35/1.65 Tue May 31 08:26:58 2022
% 1.35/1.65 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2587_n025.cluster.edu".
% 1.35/1.65 ============================== end of head ===========================
% 1.35/1.65
% 1.35/1.65 ============================== INPUT =================================
% 1.35/1.65
% 1.35/1.65 % Reading from file /tmp/Prover9_2587_n025.cluster.edu
% 1.35/1.65
% 1.35/1.65 set(prolog_style_variables).
% 1.35/1.65 set(auto2).
% 1.35/1.65 % set(auto2) -> set(auto).
% 1.35/1.65 % set(auto) -> set(auto_inference).
% 1.35/1.65 % set(auto) -> set(auto_setup).
% 1.35/1.65 % set(auto_setup) -> set(predicate_elim).
% 1.35/1.65 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.35/1.65 % set(auto) -> set(auto_limits).
% 1.35/1.65 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.35/1.65 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.35/1.65 % set(auto) -> set(auto_denials).
% 1.35/1.65 % set(auto) -> set(auto_process).
% 1.35/1.65 % set(auto2) -> assign(new_constants, 1).
% 1.35/1.65 % set(auto2) -> assign(fold_denial_max, 3).
% 1.35/1.65 % set(auto2) -> assign(max_weight, "200.000").
% 1.35/1.65 % set(auto2) -> assign(max_hours, 1).
% 1.35/1.65 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.35/1.65 % set(auto2) -> assign(max_seconds, 0).
% 1.35/1.65 % set(auto2) -> assign(max_minutes, 5).
% 1.35/1.65 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.35/1.65 % set(auto2) -> set(sort_initial_sos).
% 1.35/1.65 % set(auto2) -> assign(sos_limit, -1).
% 1.35/1.65 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.35/1.65 % set(auto2) -> assign(max_megs, 400).
% 1.35/1.65 % set(auto2) -> assign(stats, some).
% 1.35/1.65 % set(auto2) -> clear(echo_input).
% 1.35/1.65 % set(auto2) -> set(quiet).
% 1.35/1.65 % set(auto2) -> clear(print_initial_clauses).
% 1.35/1.65 % set(auto2) -> clear(print_given).
% 1.35/1.65 assign(lrs_ticks,-1).
% 1.35/1.65 assign(sos_limit,10000).
% 1.35/1.65 assign(order,kbo).
% 1.35/1.65 set(lex_order_vars).
% 1.35/1.65 clear(print_given).
% 1.35/1.65
% 1.35/1.65 % formulas(sos). % not echoed (4 formulas)
% 1.35/1.65
% 1.35/1.65 ============================== end of input ==========================
% 1.35/1.65
% 1.35/1.65 % From the command line: assign(max_seconds, 300).
% 1.35/1.65
% 1.35/1.65 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.35/1.65
% 1.35/1.65 % Formulas that are not ordinary clauses:
% 1.35/1.65
% 1.35/1.65 ============================== end of process non-clausal formulas ===
% 1.35/1.65
% 1.35/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 1.35/1.65
% 1.35/1.65 ============================== PREDICATE ELIMINATION =================
% 1.35/1.65
% 1.35/1.65 ============================== end predicate elimination =============
% 1.35/1.65
% 1.35/1.65 Auto_denials:
% 1.35/1.65 % copying label prove_strong_fixed_point to answer in negative clause
% 1.35/1.65
% 1.35/1.65 Term ordering decisions:
% 1.35/1.65 Function symbol KB weights: fixed_pt=1. b=1. w1=1. apply=1.
% 1.35/1.65
% 1.35/1.65 ============================== end of process initial clauses ========
% 1.35/1.65
% 1.35/1.65 ============================== CLAUSES FOR SEARCH ====================
% 1.35/1.65
% 1.35/1.65 ============================== end of clauses for search =============
% 1.35/1.65
% 1.35/1.65 ============================== SEARCH ================================
% 1.35/1.65
% 1.35/1.65 % Starting search at 0.01 seconds.
% 1.35/1.65
% 1.35/1.65 ============================== PROOF =================================
% 1.35/1.65 % SZS status Unsatisfiable
% 1.35/1.65 % SZS output start Refutation
% 1.35/1.65
% 1.35/1.65 % Proof 1 at 0.62 (+ 0.01) seconds: prove_strong_fixed_point.
% 1.35/1.65 % Length of proof is 12.
% 1.35/1.65 % Level of proof is 5.
% 1.35/1.65 % Maximum clause weight is 29.000.
% 1.35/1.65 % Given clauses 122.
% 1.35/1.65
% 1.35/1.65 1 apply(apply(w1,A),B) = apply(apply(B,A),A) # label(w1_definition) # label(axiom). [assumption].
% 1.35/1.65 2 apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)) # label(b_definition) # label(axiom). [assumption].
% 1.35/1.65 3 -fixed_point(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b)))) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point). [assumption].
% 1.35/1.65 4 apply(A,fixed_pt) != apply(fixed_pt,apply(A,fixed_pt)) | fixed_point(A) # label(strong_fixed_point) # label(axiom). [assumption].
% 1.35/1.65 5 apply(fixed_pt,apply(A,fixed_pt)) != apply(A,fixed_pt) | fixed_point(A). [copy(4),flip(a)].
% 1.35/1.65 7 apply(apply(w1,A),w1) = apply(apply(A,A),A). [para(1(a,1),1(a,2))].
% 1.35/1.65 14 apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point). [ur(5,b,3,a),rewrite([2(20),2(17),2(14),2(34),2(31),2(28)])].
% 1.35/1.65 33 apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) # answer(prove_strong_fixed_point). [para(1(a,1),14(a,1,2)),rewrite([2(12)]),flip(a)].
% 1.35/1.65 35 apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1) # answer(prove_strong_fixed_point). [para(1(a,1),33(a,1)),rewrite([2(11)]),flip(a)].
% 1.35/1.65 38 apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)) = apply(apply(w1,apply(apply(b,A),B)),w1). [para(2(a,1),7(a,2,1)),flip(a)].
% 1.35/1.65 3634 apply(A,apply(apply(w1,apply(apply(b,apply(b,A)),B)),B)) = apply(apply(w1,apply(apply(b,apply(b,A)),B)),w1). [para(38(a,1),2(a,1)),rewrite([1(21,R)]),flip(a)].
% 1.35/1.65 3635 $F # answer(prove_strong_fixed_point). [resolve(3634,a,35,a)].
% 1.35/1.65
% 1.35/1.65 % SZS output end Refutation
% 1.35/1.65 ============================== end of proof ==========================
% 1.35/1.65
% 1.35/1.65 ============================== STATISTICS ============================
% 1.35/1.65
% 1.35/1.65 Given=122. Generated=12401. Kept=3633. proofs=1.
% 1.35/1.65 Usable=102. Sos=3144. Demods=1169. Limbo=3, Disabled=387. Hints=0.
% 1.35/1.65 Megabytes=5.60.
% 1.35/1.65 User_CPU=0.62, System_CPU=0.01, Wall_clock=1.
% 1.35/1.65
% 1.35/1.65 ============================== end of statistics =====================
% 1.35/1.65
% 1.35/1.65 ============================== end of search =========================
% 1.35/1.65
% 1.35/1.65 THEOREM PROVED
% 1.35/1.65 % SZS status Unsatisfiable
% 1.35/1.65
% 1.35/1.65 Exiting with 1 proof.
% 1.35/1.65
% 1.35/1.65 Process 2740 exit (max_proofs) Tue May 31 08:26:59 2022
% 1.35/1.65 Prover9 interrupted
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